State Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington Washington D.C. West Virginia Wisconsin Wyoming Puerto Rico US Virgin Islands Armed Forces Americas Armed Forces Pacific Armed Forces Europe Northern Mariana Islands Marshall Islands American Samoa Federated States of Micronesia Guam Palau Alberta, Canada British Columbia, Canada Manitoba, Canada New Brunswick, Canada Newfoundland, Canada Nova Scotia, Canada Northwest Territories, Canada Nunavut, Canada Ontario, Canada Prince Edward Island, Canada Quebec, Canada Saskatchewan, Canada Yukon Territory, Canada
Zip Code
Country United States of America US Virgin Islands United States Minor Outlying Islands Canada Mexico, United Mexican States Bahamas, Commonwealth of the Cuba, Republic of Dominican Republic Haiti, Republic of Jamaica Afghanistan Albania, People's Socialist Republic of Algeria, People's Democratic Republic of American Samoa Andorra, Principality of Angola, Republic of Anguilla Antarctica (the territory South of 60 deg S) Antigua and Barbuda Argentina, Argentine Republic Armenia Aruba Australia, Commonwealth of Austria, Republic of Azerbaijan, Republic of Bahrain, Kingdom of Bangladesh, People's Republic of Barbados Belarus Belgium, Kingdom of Belize Benin, People's Republic of Bermuda Bhutan, Kingdom of Bolivia, Republic of Bosnia and Herzegovina Botswana, Republic of Bouvet Island (Bouvetoya) Brazil, Federative Republic of British Indian Ocean Territory (Chagos Archipelago) British Virgin Islands Brunei Darussalam Bulgaria, People's Republic of Burkina Faso Burundi, Republic of Cambodia, Kingdom of Cameroon, United Republic of Cape Verde, Republic of Cayman Islands Central African Republic Chad, Republic of Chile, Republic of China, People's Republic of Christmas Island Cocos (Keeling) Islands Colombia, Republic of Comoros, Union of the Congo, Democratic Republic of Congo, People's Republic of Cook Islands Costa Rica, Republic of Cote D'Ivoire, Ivory Coast, Republic of the Cyprus, Republic of Czech Republic Denmark, Kingdom of Djibouti, Republic of Dominica, Commonwealth of Ecuador, Republic of Egypt, Arab Republic of El Salvador, Republic of Equatorial Guinea, Republic of Eritrea Estonia Ethiopia Faeroe Islands Falkland Islands (Malvinas) Fiji, Republic of the Fiji Islands Finland, Republic of France, French Republic French Guiana French Polynesia French Southern Territories Gabon, Gabonese Republic Gambia, Republic of the Georgia Germany Ghana, Republic of Gibraltar Greece, Hellenic Republic Greenland Grenada Guadaloupe Guam Guatemala, Republic of Guinea, Revolutionary People's Rep'c of Guinea-Bissau, Republic of Guyana, Republic of Heard and McDonald Islands Holy See (Vatican City State) Honduras, Republic of Hong Kong, Special Administrative Region of China Hrvatska (Croatia) Hungary, Hungarian People's Republic Iceland, Republic of India, Republic of Indonesia, Republic of Iran, Islamic Republic of Iraq, Republic of Ireland Israel, State of Italy, Italian Republic Japan Jordan, Hashemite Kingdom of Kazakhstan, Republic of Kenya, Republic of Kiribati, Republic of Korea, Democratic People's Republic of Korea, Republic of Kuwait, State of Kyrgyz Republic Lao People's Democratic Republic Latvia Lebanon, Lebanese Republic Lesotho, Kingdom of Liberia, Republic of Libyan Arab Jamahiriya Liechtenstein, Principality of Lithuania Luxembourg, Grand Duchy of Macao, Special Administrative Region of China Macedonia, the former Yugoslav Republic of Madagascar, Republic of Malawi, Republic of Malaysia Maldives, Republic of Mali, Republic of Malta, Republic of Marshall Islands Martinique Mauritania, Islamic Republic of Mauritius Mayotte Micronesia, Federated States of Moldova, Republic of Monaco, Principality of Mongolia, Mongolian People's Republic Montserrat Morocco, Kingdom of Mozambique, People's Republic of Myanmar Namibia Nauru, Republic of Nepal, Kingdom of Netherlands Antilles Netherlands, Kingdom of the New Caledonia New Zealand Nicaragua, Republic of Niger, Republic of the Nigeria, Federal Republic of Niue, Republic of Norfolk Island Northern Mariana Islands Norway, Kingdom of Oman, Sultanate of Pakistan, Islamic Republic of Palau Palestinian Territory, Occupied Panama, Republic of Papua New Guinea Paraguay, Republic of Peru, Republic of Philippines, Republic of the Pitcairn Island Poland, Polish People's Republic Portugal, Portuguese Republic Puerto Rico Qatar, State of Reunion Romania, Socialist Republic of Russian Federation Rwanda, Rwandese Republic Samoa, Independent State of San Marino, Republic of Sao Tome and Principe, Democratic Republic of Saudi Arabia, Kingdom of Senegal, Republic of Serbia and Montenegro Seychelles, Republic of Sierra Leone, Republic of Singapore, Republic of Slovakia (Slovak Republic) Slovenia Solomon Islands Somalia, Somali Republic South Africa, Republic of South Georgia and the South Sandwich Islands Spain, Spanish State Sri Lanka, Democratic Socialist Republic of St. Helena St. Kitts and Nevis St. Lucia St. Pierre and Miquelon St. Vincent and the Grenadines Sudan, Democratic Republic of the Suriname, Republic of Svalbard & Jan Mayen Islands Swaziland, Kingdom of Sweden, Kingdom of Switzerland, Swiss Confederation Syrian Arab Republic Taiwan, Province of China Tajikistan Tanzania, United Republic of Thailand, Kingdom of Timor-Leste, Democratic Republic of Togo, Togolese Republic Tokelau (Tokelau Islands) Tonga, Kingdom of Trinidad and Tobago, Republic of Tunisia, Republic of Turkey, Republic of Turkmenistan Turks and Caicos Islands Tuvalu Uganda, Republic of Ukraine United Arab Emirates United Kingdom of Great Britain & N. Ireland Uruguay, Eastern Republic of Uzbekistan Vanuatu Venezuela, Bolivarian Republic of Viet Nam, Socialist Republic of Wallis and Futuna Islands Western Sahara Yemen Zambia, Republic of Zimbabwe
CLAIM
A video showed people preparing body bags for the evening news clip during the pandemic
DETAILS
Misrepresents source: The post interpreted a video showing body bags as fake COVID-19 victims being staged for the news. However, the video is, in fact, an excerpt from a Russian music video.
KEY TAKE AWAY
Excess mortality is a useful way to measure the overall impact of emerging threatslike war and diseaseon a populations health. Claims that the COVID-19 pandemic was a hoax or was simply never that bad belie the fact that it caused an estimated 14 million excess deaths from 2020 to 2021 worldwide, according to the World Health Organization.
These words and the footage combined strongly implied that COVID-19 deaths during the pandemic were fake, and that COVID-19 mortality was exaggerated by the media.
Claims of this ilk arent new. The narrative that the COVID-19 pandemic was a hoax and that it was staged is popular in conspiratorial circles. Science Feedback and other fact-checking organizations debunked various claims that bolstered this narrative (see here, here, and here). In fact, the same video was used to imply the same thing as early as 2021. At the time, several fact-checking organizations demonstrated that the claim was inaccurate and misrepresented the true nature of the video.
The AFP explained that the video is behind-the-scenes footage filmed by Russian artist Husky. Vasya Ivanov, credited as the production designer in the clips credits, posted the clip on the video-sharing platform Vimeo in November 2020. Ivanov then posted the footage showing the black bags and the smoking man on TikTok in March 2021.
Comparing the video footage posted on TikTok and the Facebook reel confirmed that this is indeed the same video. The main visual difference is that the version in the reel is a mirror image of the TikTok video (Figure 1).
Figure 1 Comparison of the video in the Facebook reel (left) and the original TikTok video clip (right). Note that the Facebook reel is a mirror image of the TikTok video.
Thus, the video is from an artistic production. It doesnt depict an attempt to exaggerate COVID-19 mortality by staging a pile of COVID-19 victims, as implied in the reel.
Contrary to the videos implication, the COVID-19 pandemic was real and its death toll is elevated. Most countries registered excess all-cause mortality during the pandemic. All-cause mortality is better at capturing the real toll of the pandemic than only looking at COVID-19 deaths because it also includes COVID-19 deaths that were not correctly diagnosed and reported. The World Health Organization estimated that the COVID-19 pandemic is associated with more than 14 million excess deaths between 2020 and 2021[1].
State Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington Washington D.C. West Virginia Wisconsin Wyoming Puerto Rico US Virgin Islands Armed Forces Americas Armed Forces Pacific Armed Forces Europe Northern Mariana Islands Marshall Islands American Samoa Federated States of Micronesia Guam Palau Alberta, Canada British Columbia, Canada Manitoba, Canada New Brunswick, Canada Newfoundland, Canada Nova Scotia, Canada Northwest Territories, Canada Nunavut, Canada Ontario, Canada Prince Edward Island, Canada Quebec, Canada Saskatchewan, Canada Yukon Territory, Canada
Zip Code
Country United States of America US Virgin Islands United States Minor Outlying Islands Canada Mexico, United Mexican States Bahamas, Commonwealth of the Cuba, Republic of Dominican Republic Haiti, Republic of Jamaica Afghanistan Albania, People's Socialist Republic of Algeria, People's Democratic Republic of American Samoa Andorra, Principality of Angola, Republic of Anguilla Antarctica (the territory South of 60 deg S) Antigua and Barbuda Argentina, Argentine Republic Armenia Aruba Australia, Commonwealth of Austria, Republic of Azerbaijan, Republic of Bahrain, Kingdom of Bangladesh, People's Republic of Barbados Belarus Belgium, Kingdom of Belize Benin, People's Republic of Bermuda Bhutan, Kingdom of Bolivia, Republic of Bosnia and Herzegovina Botswana, Republic of Bouvet Island (Bouvetoya) Brazil, Federative Republic of British Indian Ocean Territory (Chagos Archipelago) British Virgin Islands Brunei Darussalam Bulgaria, People's Republic of Burkina Faso Burundi, Republic of Cambodia, Kingdom of Cameroon, United Republic of Cape Verde, Republic of Cayman Islands Central African Republic Chad, Republic of Chile, Republic of China, People's Republic of Christmas Island Cocos (Keeling) Islands Colombia, Republic of Comoros, Union of the Congo, Democratic Republic of Congo, People's Republic of Cook Islands Costa Rica, Republic of Cote D'Ivoire, Ivory Coast, Republic of the Cyprus, Republic of Czech Republic Denmark, Kingdom of Djibouti, Republic of Dominica, Commonwealth of Ecuador, Republic of Egypt, Arab Republic of El Salvador, Republic of Equatorial Guinea, Republic of Eritrea Estonia Ethiopia Faeroe Islands Falkland Islands (Malvinas) Fiji, Republic of the Fiji Islands Finland, Republic of France, French Republic French Guiana French Polynesia French Southern Territories Gabon, Gabonese Republic Gambia, Republic of the Georgia Germany Ghana, Republic of Gibraltar Greece, Hellenic Republic Greenland Grenada Guadaloupe Guam Guatemala, Republic of Guinea, Revolutionary People's Rep'c of Guinea-Bissau, Republic of Guyana, Republic of Heard and McDonald Islands Holy See (Vatican City State) Honduras, Republic of Hong Kong, Special Administrative Region of China Hrvatska (Croatia) Hungary, Hungarian People's Republic Iceland, Republic of India, Republic of Indonesia, Republic of Iran, Islamic Republic of Iraq, Republic of Ireland Israel, State of Italy, Italian Republic Japan Jordan, Hashemite Kingdom of Kazakhstan, Republic of Kenya, Republic of Kiribati, Republic of Korea, Democratic People's Republic of Korea, Republic of Kuwait, State of Kyrgyz Republic Lao People's Democratic Republic Latvia Lebanon, Lebanese Republic Lesotho, Kingdom of Liberia, Republic of Libyan Arab Jamahiriya Liechtenstein, Principality of Lithuania Luxembourg, Grand Duchy of Macao, Special Administrative Region of China Macedonia, the former Yugoslav Republic of Madagascar, Republic of Malawi, Republic of Malaysia Maldives, Republic of Mali, Republic of Malta, Republic of Marshall Islands Martinique Mauritania, Islamic Republic of Mauritius Mayotte Micronesia, Federated States of Moldova, Republic of Monaco, Principality of Mongolia, Mongolian People's Republic Montserrat Morocco, Kingdom of Mozambique, People's Republic of Myanmar Namibia Nauru, Republic of Nepal, Kingdom of Netherlands Antilles Netherlands, Kingdom of the New Caledonia New Zealand Nicaragua, Republic of Niger, Republic of the Nigeria, Federal Republic of Niue, Republic of Norfolk Island Northern Mariana Islands Norway, Kingdom of Oman, Sultanate of Pakistan, Islamic Republic of Palau Palestinian Territory, Occupied Panama, Republic of Papua New Guinea Paraguay, Republic of Peru, Republic of Philippines, Republic of the Pitcairn Island Poland, Polish People's Republic Portugal, Portuguese Republic Puerto Rico Qatar, State of Reunion Romania, Socialist Republic of Russian Federation Rwanda, Rwandese Republic Samoa, Independent State of San Marino, Republic of Sao Tome and Principe, Democratic Republic of Saudi Arabia, Kingdom of Senegal, Republic of Serbia and Montenegro Seychelles, Republic of Sierra Leone, Republic of Singapore, Republic of Slovakia (Slovak Republic) Slovenia Solomon Islands Somalia, Somali Republic South Africa, Republic of South Georgia and the South Sandwich Islands Spain, Spanish State Sri Lanka, Democratic Socialist Republic of St. Helena St. Kitts and Nevis St. Lucia St. Pierre and Miquelon St. Vincent and the Grenadines Sudan, Democratic Republic of the Suriname, Republic of Svalbard & Jan Mayen Islands Swaziland, Kingdom of Sweden, Kingdom of Switzerland, Swiss Confederation Syrian Arab Republic Taiwan, Province of China Tajikistan Tanzania, United Republic of Thailand, Kingdom of Timor-Leste, Democratic Republic of Togo, Togolese Republic Tokelau (Tokelau Islands) Tonga, Kingdom of Trinidad and Tobago, Republic of Tunisia, Republic of Turkey, Republic of Turkmenistan Turks and Caicos Islands Tuvalu Uganda, Republic of Ukraine United Arab Emirates United Kingdom of Great Britain & N. Ireland Uruguay, Eastern Republic of Uzbekistan Vanuatu Venezuela, Bolivarian Republic of Viet Nam, Socialist Republic of Wallis and Futuna Islands Western Sahara Yemen Zambia, Republic of Zimbabwe
Patients who are African American appeared to have worse clinical stages of colon and rectal cancer during surgery in 2020.
The number of patients with colon and rectal cancer undergoing surgery has decreased since the COVID-19 pandemic, which has accompanied a higher proportion of patients presenting with advanced disease, according to findings published in the Journal of the American College of Surgeons.
Among 105,517 patients who were assessed for colon (n = 83,128) or rectal (n = 22,389) cancer between 2019 and 2020, investigators reported a reduction in surgical operations of 17.3% during the first year of the COVID-19 pandemic. Specifically, this decrease included a 21.1% decline for rectal cancer surgery and a 16.3% reduction for colon cancer surgery.
For patients with colon cancer who were treated during the pandemic compared with those who received treatment before the pandemic, there was a significantly lower incidence of T1 tumors (35.5% vs 38.2%) and a higher incidence of T4 tumors (19.2% vs 15.7%).
In those with colon cancer, patients who received surgery in 2020 had a significantly higher likelihood of being diagnosed with high-stage tumors (odds ratio [OR], 1.07; 95% CI, 1.00-1.13; P = .039) per multivariate analysis. Additionally, African American race (OR, 1.20; 95% CI, 1.10-1.31; P <.001), Medicaid (OR, 1.27; 95% CI, 1.13-1.29; P <.001), and having no insurance compared with private insurance (OR, 1.32; 95% CI, 1.10-1.57; P = .002) conferred higher risks for having advanced disease. Being older (OR, 0.83; 95% CI, 0.80-0.86; P <.001) and having a Charlson Deyo score of at least 2 (OR, 0.83; 95% CI, 0.75-0.91; P <.001) were determined to be protective factors against advanced disease.
In the rectal cancer population, the rates of clinical T4 cancers significantly increased for patients treated during the pandemic (16.3%) compared with those who received treatment before the pandemic (13.6%; P = .009). A similar rise was reported for clinical N1 or N2 disease (50.3% vs 47.8%; P <.001), which investigators confirmed by pathology stage.
For patients with rectal cancer who underwent surgery during the pandemic, investigators highlighted a significantly increased risk of stage 3 and 4 tumors (OR, 1.08; 95% CI, 1.01-1.16; P = .024). Factors that correlated with worse disease-stage diagnoses included having Medicaid (OR, 1.22; 95% CI, 1.08-1.38; P = .001) and being uninsured (OR, 1.29; 95% CI, 1.06-1.58; P = .013). Additionally, older age (OR, 0.77; 95% CI, 0.74-0.80; P <.001) and a Charlson Deyo score of 2 or higher (OR, 0.72; 95% CI, 0.63-0.82; P <.001) appeared to be protective against an advanced stage diagnosis.
As the number of studies analyzing the effect of the pandemic on all aspects of medical care grows, the cumulative impact on clinical outcomes has not been fully understood. In cancer care, we are probably still seeing the tip of the iceberg, as the results of delayed screenings, diagnoses, and medical treatments could continue to present their bill in the future years, Davide Ferrari, MD, visiting research fellow the Mayo Clinic in Rochester, Minnesota, and the general surgery resident at the University of Milan, and coauthors wrote. Further retrospectives of public policy are needed to review, and report impacts on the healthcare system.
Investigators retrospectively analyzed data from the National Cancer Database (NCDB) related to adult patients who underwent surgery for colon and rectal cancer between January 2019 and December 2020. Patients were stratified based on whether they received treatment in 2019 before the pandemic or in 2020 during the pandemic. Investigators used a multivariate logistic regression model to assess the relationship between disease stage and socioeconomic variables.
The analysis included an evaluation of time from diagnosis to treatment for both colon and rectal cancer populations. Time to treatment appeared to be significantly shorter for those who underwent surgery before the beginning of the pandemic.
Among patients with colon cancer, there were no significant differences in length of hospital stay following surgery (P = .10) or readmission rates (P = .23) based on whether surgery was given before or during the pandemic. However, a higher proportion of patients during the pandemic underwent robotic surgery compared with those who were treated before the pandemic (23.2% vs 19.7%).
In the rectal cancer population, investigators reported a higher use of robotic surgery approaches in 2020 (41.5%) than before the pandemic (36.9%). In the pre-pandemic and pandemic groups, respectively, the rates of minimally invasive surgery were 34.3% vs 37.7%, and 24.1% vs 25.4% received open surgery.
Ferrari D, Violante T, Day CN, et al. Unveiling the hidden consequences: the initial impact of COVID-19 on colorectal cancer operation. J Am Coll Surg. Published online March 25, 2024. doi:10.1097/XCS.0000000000001042
In this weeks Shipping Number of the Week from BIMCO, Chief Shipping Analyst, Niels Rasmussen, examines the effect of the COVID pandemic on the container markets growth.
During the past four years, the container market has faced not only lower than expected growth in the global economy, but the ratio of market growth vs economic growth, the so-called GDP multiplier, was also substantially lower than normal.
Due to the COVID-19 pandemic, the global container market grew only 1.5% from 171.0 million TEU in 2019 to 173.5 million TEU in 2023. Without the pandemic, that figure would have been 24.6 million higher, landing at 198.1 million in 2023.
says Niels Rasmussen, Chief Shipping Analyst at BIMCO.
In October 2019, the International Monetary Fund (IMF) forecast that the global economy would grow at an average annual rate of 3.5% during 2020-2023, in line with the average annual rate of growth of 3.4% seen during the years leading up to the pandemic. Instead, the global economy ended with an average annual growth rate of only 2.6%.
At the same time, the container market grew at an average annual rate of 0.4% during the 2020-2023 period, equal to a GDP multiplier of just 0.14. Between 2013 and 2019 the GDP multiplier averaged 1.06. Had this been maintained during 2020-2023, the market would have grown at an average annual rate of 2.7% and the 2023 container market would have ended 16.8 million TEU higher.
..says Rasmussen.
The multiplier between regional GDP growth and regional container import volumes was lower than during the 2013-2019 period in all regions. However, in the East & Southeast Asia and Europe & Mediterranean regions, the multiplier was negative during 2020-2023 and import container volumes ended lower in 2023 than in 2019. In fact, 11.4 million of the 16.8 million TEU lost due to a lower GDP multiplier was lost in the two regions.
Average annual GDP growth in North America ended the 2020-2023 period 3.6% higher than the IMF predicted in October 2019. However, in other regions, GDP growth was lower than the 2019 projection and global average annual GDP growth ended 28% lower than the projection.
Had the global economy grown as originally predicted during 2020-2023, and had the GDP multiplier matched the 2013-2019 level, the global container market in 2023 would have been 24.6 million higher. Whether or not pent-up demand, and/or global economic growth above trend, can help recover part of the lost growth in coming years remains to be seen. However, current predictions for growth in the global economy do not indicate a resurgence in growth, says Rasmussen.
Boom will receive the 2024 Stephen L. Klineberg Award for outstanding leadership in health care at the 2024 Kinder Institute Luncheon on May 20. Ticket sales close May 8.
Boom, who has been a Houstonian since he was 14, is still a practicing physician while also leading a hospital system that has over 32,000 employees and had over 2 million outpatient visits in 2023. He has served in his role since 2012.
Houston Methodist is among the best hospitals in the country and tied for No. 1 in Texas according to U.S. News & World Reports Honor Roll released 2023. It was ranked in 10 specialties, more than any other hospital in Houston, with nine placing in the top 20 and two in the top five.
The Urban Edge interviewed Boom about Houston Methodists response to the COVID-19 pandemic, and the current and future state of health care in the Houston area. The interview has been edited for length and clarity.
What made you want to enter the medical profession and how did it bring you to Houston?
I always liked science in grade school. It kept my attention and sparked my curiosity. With a father who was an engineer, I initially thought I might become an engineer, but in high school, I began to pursue medical interests. At first, I thought Id combine my love of animals with my love of science, so I worked part time at a veterinary clinic. But later, I decided I would prefer to work with patients who could talk to me.
Ultimately, thats why I chose to be a primary care physician. The long-term relationships with patients helping them through good times and bad are what I find most meaningful. Now, having been in the profession for decades, I can say that working in medicine is a sacred calling. We are meant to help others, and thats what keeps me in this profession.
As for Houston, I consider it home. Both my parents are immigrants from Belgium and moved to the U.S. right after they were married. My dads job eventually brought us to Houston when I was 14, and its a remarkable city. I graduated from Baylor College of Medicine and did my residency on the East Coast, but I always knew that I wanted to come back.
What measures taken by Houston Methodist during the height of the COVID-19 pandemic are you most proud of?
Houston Methodist is an independent academic medical center, a very unique structure within the field. The advantages of this structure were on full display during the COVID-19 pandemic as we were extremely nimble and effective. For example, we developed a COVID-19 PCR test just a couple of weeks after the virus was discovered in China so that when the first cases hit Houston, we were able to get an answer in a couple of hours when most institutions were sending tests out to get answers in days to a couple of weeks.
We were the first in the world to use convalescent plasma in March 2020. We have sequenced the viral genome of every patient who tested positive, which has allowed us to have one of the largest databases of viral genomesin the world and has enabled our teams to gain valuable insights into the spread of the virus. We administered more monoclonal antibody infusions and more vaccines than any institution in the state of Texas. And, of course, we were the first medical institution to mandate the COVID-19 vaccine for our employees and physicians. It was courageous, and it was the right thing to do to protect our patients.
I am so proud of our Houston Methodist family for pulling together and rallying around this call to get vaccinated. There is no doubt in my mind it saved countless lives. To this day, when I meet hospital executives around the country, they are quick to thank Houston Methodist for leading the way.
Most of all, Im proud of how we were able to look out for our people. We are fortunate to have a strong balance sheet at Houston Methodist. So, we committed early to no layoffs, no furloughs, no benefit cuts and no pay cuts aspects that have reinforced our culture. We also invested heavily in support of our heroic employees and physicians who put their personal lives on hold to care for our community.
The pandemic made for a challenging time for the medical profession. What do you think are the best methods to confront burnout and the state of the workforce?
Theres no doubt the pandemic was very challenging for medical professionals. At Houston Methodist, weve worked hard to confront burnout. What is most important is connecting people to the passion and purpose we all derive from the sacred privilege of caring for others. When we think in terms of work-life integration rather than work-life balance, which implies that we choose one over the other, we can focus on how best to bring back the joy in medicine. Like everything that has to do with culture, it requires a very purposeful and deliberate approach.
At Houston Methodist, were seeing the results with employee engagement at the 96th percentile nationally, significantly reduced turnover and an embracing of many creative solutions, like a virtual nursing program that offers different career options for our nurses while easing some of the workload on those nurses who are at the bedside all while improving safety and quality. Combatting burnout is not a quick fix, and the best way to confront burnout is to care for the whole employee. We have an entire program to combat burnout and teach resiliency to our physicians. Houston Methodist also has an employee well-being clinic that brings mental health support directly to our employees. It makes a huge difference to know youre not alone.
Houston is renowned for its world-class Texas Medical Center. However, over 2 million people in the Houston metro area are medically uninsured, according to the U.S. Census Bureau. How would you describe the disconnect?
This is a big issue, one thats frankly at an existential level for our society. How can we be the wealthiest, most successful country on the planet yet still have so many people uninsured? Why is health care in the United States the envy of the rest of the world, but only if you have access to insurance? I wish we as a hospital system could solve it individually, but this will require a concerted effort that starts with an important societal discussion.
Unfortunately, these conversations are difficult to have in todays contentious and divided environment. This is why I speak so much about an and mentality, one in which diverse individuals with different points of view come together, hammer out compromise and do whats best for the American people. I firmly believe this is possible in health care.
In the meantime, at Houston Methodist, we focus on what we can impact. We provide hundreds of millions in direct charity care at cost. We provide well over $1 billion in community benefits. Through our Community Benefits Grant Program, Houston Methodist provides uninsured and underinsured patients improved access to health care services, mental health services and financial support. We have partnered with free clinics, federally qualified health centers and other nonprofit agencies in the Greater Houston area for more than 30 years as part of this program. Just this year, we awarded nearly $6.8 million in community grants to 30 local nonprofit organizations. The Community Benefits Grant Program allows us to continue to address crucial community issues, including reducing barriers to accessing primary and preventative care.
What high-level investments are needed for Houston to remain a leader in medicine in the future?
A continued investment in technology, infrastructure and people is a must for Houston to remain a leader in medicine. There is a tremendous opportunity to scale innovative treatments and technologies thanks to the large, diverse clinical base that we have in Houston. And if we continue to work together and work across industries, we will stay a leader in medicine.
A great example is the Ion District, an area in the middle of the city where Houston Methodist and Rice University both have a presence. The Ion gives us the chance to test the latest innovations in health care technology with the bonus of collaborating with experts from across industries, such as aerospace, energy, and oil and gas. That kind of collaboration works in everyones favor and positions us to bring treatments and innovations to our patients first.
How can the Houston area be prepared for another pandemic or large-scale public health emergency?
Several years before COVID-19, Houston-area hospitals prepared for an Ebola outbreak in Houston. Fortunately, we didnt see any patients, but that taught us the importance of preparing for a global infectious disease. We had set up an inpatient isolation unit for Ebola patients. When we started getting our first COVID-19 patients, we used that facility to control infection. Now, we arent waiting for the next pandemic; were preparing for it. Were using what we learned from COVID-19 to prepare for how well respond to the next public health emergency.
At Houston Methodist, we expanded and invested a lot of resources into our infectious diseases department. We also still collect data to inform us on how to anticipate and treat future infectious diseases. In the Houston area, its about investing in the resources and the people who have the expertise now so that we can mitigate the effects of the next public health emergency.
How does being a practicing physician help you stay connected to those who are seeking care at Houston Methodist?
When I was in business school, I knew I wanted to remain a practicing physician no matter where my career took me. When the administrative side of my work ramped up even further in 2004, I took my active primary care physician practice of more than 1,000 patients and decreased it significantly. Since then, I have had a very small practice with the same patients Ive been seeing for decades.
Being a practicing physician allows me to use the technologies that our employees and physicians use. For example, when we transitioned to a new health record management system, I had to learn it because I used it for my practice. I order tests, consult with radiologists and do all the things other primary care physicians do. It allows me to see how patients experience care at Houston Methodist in a tangible way. And at Houston Methodist, the patient is the center of everything we do. When Im caring for a patient, that brings me back to that sentiment.
Mortality among working age people in England and Wales remains higher than before the covid-19 pandemic, an analysis has found, despite an overall fall in mortality.
The analysis by the Institute and Faculty of Actuaries continuous mortality investigation (CMI) found that the decrease in all cause mortality was largely driven by a fall in older age mortality where most deaths occur.1
Cobus Daneel, chair of the CMI mortality projections committee, said, After periods of high and volatile mortality during the peak of the pandemic, we have now seen several months of lower mortality, more in line with typical seasonal variations.
The picture is less rosy for the working age population, however, who are still seeing mortality higher than pre-pandemic.
The analysis calculated standardised mortality rates (SMRs) based on provisional
Sumedha Bobba has been a picture-perfect student since beginning her collegiate career during the COVID-19 pandemic. How did adjusting to a new way of life impact her approach toward her views of community and success?
Sumedha Bobba, Photography: Ian LogueOn April 27, Sumedha Bobba will walk the commencement stage in Bartow Arena to accept her accelerated bachelors/masters degree inneurosciencefrom the University of Alabama at Birmingham College of Arts and Sciences and business administration from theCollat School of Business, respectively.
Bobba, a student leader and undergraduate researcher, is no stranger to resilience. Bobbas parents came to the United States in 2000, two years before she was born. This instilled in Bobba an appreciation for opportunities and education at an early age.
Bobba enrolled at UAB in the fall of 2020. And while the Madison, Alabama, native originally did not see herself as a Blazer, she soon realized that UAB was where she was meant to be.
Being a part of the inaugural COVID-19 Class, Bobba, along with students across the country, had to navigate the newfound terrain of missing important milestones while entering a new era of educational experience.
Coming into college after having the remainder of your senior year taken away was a tough adjustment, Bobba said. We missed prom, graduation and so much more. Consequently, I for one had high hopes for freshman year of college that I had to quickly reevaluate at the start of the semester. I knew we would be wearing masks, but the reality of having no in-person classes and confronting the isolation that COVID brought was a challenge in itself.
While the start of her freshman year may had been disheartening, Bobba did not let that stifle her opportunities and growth. Bobba joined Freshman Forum, an organization that allowed her to meet more of her peers. Bobba also became a member of Alpha Xi Delta sorority, for which she would go on to serve as continuous open bidding director and recruitment data director, organizing and executing sorority recruitment-related events.
Meeting more upperclassmen at UAB is when I realized how special the Blazer community is, Bobba said. These upperclassmen had no reason to show us kindness and mentorship, but they recognized what COVID did to the collegiate experience and took it upon themselves to make sure we still made the most of our freshman year.
Taking part in Blazing a path for new students The UAB Trailblazers are a competitive organization under the Office of Undergraduate Admissions who serve as the official student recruitment team for the university. Trailblazers offer campus tours to prospective students and their families while helping shape the first-touch perception of campus life at UAB.
In the fall of 2020, Bobba began doing undergraduate research in the lab of Laura Volpicelli-Daley, Ph.D. There she analyzed formation of -synuclein aggregates to prevent progression of Parkinsons disease.
Bobba went on to become a UAB Trailblazer in the spring semester.
Joining the Trailblazers allowed me to further develop a love for UAB through community, Bobba said. I was able to interact with other students and really developed a close bond with my fellow Trailblazers. This served as networking for me and immensely grew my sense of pride in my university.
Bobba says it is this networking that opened the door to other opportunities. Bobba participated in the White House COVID-19 College Vaccine Challenge, where she organized student testimonials and even served as a representative from UAB, receiving the opportunity to meet Anthony Fauci, Ph.D., chief medical adviser to the president of the United States, over virtual meeting space.
Bobba represented UAB via opportunities with local media as a student voice throughout her collegiate career.
These opportunities showed me that, if you put your best foot forward here at UAB, then there are so many more doors and opportunities that can come from it, Bobba said.
Announced on Oct. 23, 2021, at the Homecoming game, Bobba was selected to serve as the 2022 Ms. UAB.
I was so honored and grateful to have been chosen to serve as Ms. UAB, Bobba said. Having this opportunity was so much more than just a scholarship or award because it opened up an entirely different experience for me here at UAB.
As Ms. UAB, Bobba was required to serve as the president of the Student Alumni Society. The Ms. UAB position acts as the liaison between UAB alumni and current students. Bobba acknowledged the challenges of her generation of students and focused on creating opportunities for her peers.
One of my initiatives was to organize a way for students to network with each other and with alumni after the heavy restrictions of the COVID-19 pandemic, Bobba said. After five to six months of preparation, we hosted an alumni networking night geared toward connecting students with mentors who could help them develop throughout their collegiate careers.
Finding Traditions Presented by the UAB National Alumni Society, the Mr. and Ms. UAB Scholarship Competition has been a homecoming tradition at UAB since 1981. Applicants are expected to demonstrate a history of leadership and participation in extracurricular activities.
It is the successes of people she knows personally that remind Bobba of the importance of the work she did.
I have friends who recently thanked me for hosting that event because the connections they made are helping them with research opportunities and even with applying to schools after undergrad, Bobba said. It shows the significance of the Ms. UAB position and how important that role is in advocating for the student body.
Bobba experienced personal growth through her service as Ms. UAB, with her junior year antithetically paralleling her freshman and sophomore experience.
While I feel like I came into college more extroverted, my junior year taught me the importance of appreciating my own down time, Bobba said. While I desired more interaction coming into college, and I received that as restrictions lifted more so in my sophomore year, I learned that serving in important roles can keep you busy.
Bobba encourages all student leaders and even regular students to make sure they take time for themselves when needed.
I recommend to all future student leaders to make sure you take time to prioritize your own well-being, Bobba said. Its easy to get caught up in serving and always being busy, so its necessary that you take a step back sometimes and just recharge for your own mental and physical health.
Bobba is a member of the UAB Honors College on a personalized pathway. In 2022, Bobba worked as a strategy analyst intern at Southern Research. This role was one she says served as a moment of clarity for her medical field aspirations.
My internship with Southern Research was one of the most influential experiences in my college experience, Bobba said. That was a summer when I was excited to go to work and I gained a lot of confidence in my abilities.
In this role, Bobba worked closely with the Josh Carpenter, CEO and chief of Staff at Southern Research and UAB alumni, to lead the translational research organizations strategic planning process in various flagship projects.
Josh saw my potential and gave me the opportunity, Bobba said. This opportunity is a testament to the community and opportunities UAB offers. Josh invested in my collegiate career by attending my networking event for Ms. UAB after my internship to help provide new professional opportunities to fellow students.
This past summer, Bobba worked as a Sparkman Global Health Intern in Kingston, Jamaica. There she worked with the Caribbean Vulnerable Communities Coalition to organize advocacy workshops and empower marginalized populations affected by HIV and gender-based violence.
This opportunity reminded me why I needed to work hard and was really motivating for me because I was by myself in Jamaica for two months, but I missed my family so much, Bobba said. I couldnt imagine what it was like for my parents to move from India to the United States on their own to provide a better life for my brother and me. I could never take their sacrifice for granted, and it always serves as a reminder to keep making them proud.
To read more about the graduating class of 2024, click here.
She has served as a tutor at the Vulcan Materials Academic Success Center and at the STAIR of Birmingham. Bobba has volunteered with the UAB 1917 Clinic, Equal Access Birmingham and The Exceptional Foundation.
Bobba will be attending medical school in the fall with hopes that she will land at the UAB Heersink School of Medicine.
UAB comes with such an extensive community, and that is what makes this university so great, Bobba said. One piece of advice I would give to an incoming freshman is to just put yourself out there and take advantage of your opportunities because the UAB community is indeed a family.
The general population is divided into eight indistinguishable groups in this category, which are designated as susceptible people, (({textbf{S}})), latent TB patients who do not exhibit TB-associated indications and are not pathogenic ({{textbf{L}}}_{{textbf{T}}}), influential TB-infected people ({{textbf{I}}}_{{textbf{T}}}), COVID-19-infested humans who do not exhibit indications but are transmissible ({{textbf{E}}}_{{textbf{C}}}), COVID-19-diagnosed people who exhibit scientific backing indications and are pathogenic ({{textbf{I}}}_{{textbf{C}}}), both inactive TB and COVID-19-contaminated people ({{textbf{L}}}_{{textbf{T}}{textbf{C}}}), current TB and COVID-19-contaminated humans ({{textbf{I}}}_{{textbf{T}}{textbf{C}}}), and retrieved people ({{textbf{R}}}) consisting of both TB and COVID-19. The underlying computational framework for the codynamics of TB and COVID-19 is developed in this portion. Considering such, all people at moment (tau ), represented by ({textbf{N}}(tau )), are provided by
$$begin{aligned} {textbf{N}}(tau )={textbf{S}}(tau )+{{textbf{L}}}_{{textbf{T}}}(tau ) +{{textbf{I}}}_{{textbf{T}}}(tau )+{{textbf{E}}}_{{textbf{C}}}(tau )+{{textbf{I}}}_{{textbf{C}}}(tau ) +{{textbf{L}}}_{{textbf{T}}{textbf{C}}}(tau )+{{textbf{I}}}_{{textbf{T}}{textbf{C}}}(tau )+{{textbf{R}}}(tau ). end{aligned}$$
(1)
We hypothesized that acquisition increases the vulnerable community at an intensity of (nabla ). Every person in every compartment experiences an inevitable mortality rate of (beta ). Equivalent to formula (1), vulnerable individuals contract TB via interaction with current TB individuals via agent transmission (psi _{{textbf{T}}}). The acceptable interaction rate for TB transmission is indicated by (alpha _{1}) within this manifestation. It is believed that people with persistent TB are undiagnosed and cannot pass on the illness35. Likewise, those at risk contract COVID-19 at an intensity of transmission (psi _{{textbf{C}}}), which is determined as in formula (1), after effectively coming into proximity to COVID-19-infected people. The efficient interaction probability for COVID-19 infection is represented by (alpha _{2}) in this case. Furthermore, we hypothesized that people in the hidden TB segment ({{textbf{L}}}_{{textbf{T}}}) depart at an incidence of (mu ) to segment ({{textbf{I}}}_{{textbf{T}}}), at an incidence of transmission of (lambda psi _{{textbf{C}}}) to the persistent TB as well as COVID-19 contaminated group, whilst certain of them recuperate at an intervention incidence of (varpi ). Additionally, those in the TB-infected category ({{textbf{I}}}_{{textbf{T}}}) recuperate due to the illness at an incidence of (delta ), with the surviving percentage either transferring to the transmission category ({{textbf{I}}}_{{textbf{T}}{textbf{C}}}) at a pace of (varsigma _{3}) or dying at a speed of (zeta _{{textbf{T}}}) via TB-induced mortality.
The overall community in cohort ({{textbf{L}}}_{{textbf{T}}{textbf{C}}}) potentially dies at COVID-19-induced mortality pace (zeta _{{textbf{C}}}) or advances at an intensity of (rho ) to become contaminated category ({{textbf{I}}}_{{textbf{T}}{textbf{C}}}). As seen in Fig. 3, it is believed that the other people will be moved to the other cohort at a consistent multiplicity of (eta ). In other words, the general population classified as ({{textbf{L}}}_{{textbf{T}}{textbf{C}}}) migrates at an intensity of (varsigma _{2}eta ) to category ({{textbf{I}}}_{{textbf{T}}}), then at a pace of (varsigma _{1}eta ) to compartment ({{textbf{I}}}_{{textbf{C}}}) group, and finally recovers at a pace of ((1-(varsigma _{1}+varsigma _{2}))eta ). Additionally, we hypothesized that, although the codynamics-induced mortality prevalence is represented by (zeta _{{textbf{T}}{textbf{C}}}), people in compartment ({{textbf{I}}}_{{textbf{T}}{textbf{C}}}) depart for compartments ({{textbf{I}}}_{{textbf{T}}},~{{textbf{I}}}_{{textbf{C}}}) or ({textbf{R}}), correspondingly, at an intensity of (theta _{2}xi ,~theta _{1}xi ) or ((1-(theta _{1}+theta _{2}))xi .) Furthermore, at an intensity of (epsilon psi _{{textbf{T}}},phi ) or (varphi _{2},) the COVID-19 exposure people ({{textbf{E}}}_{{textbf{C}}}) can choose to depart to compartment ({{textbf{L}}}_{{textbf{T}}{textbf{C}}},~{{textbf{I}}}_{{textbf{C}}}) or ({textbf{R}}), respectively. Comparably, the number of individuals in compartment ({{textbf{I}}}_{{textbf{C}}}) is either moved to the codynamics cohort at an intensity of (nu ) or restored at a steady pace of (varphi _{3}). (zeta _{{textbf{C}}}) represents the disease-induced fatality rate within this category. Figure 3 displays the suggested systems process layout.
Flow diagram for depicting the codynamics process of TB-COVID-19 model (2).
It leads to frameworks for the subsequent nonlinear DEs determined by the procedure illustration:
$$begin{aligned} {left{ begin{array}{ll} dot{{textbf{S}}}=nabla -(psi _{{textbf{T}}}+psi _{{textbf{C}}}+beta ){textbf{S}},\ dot{{{textbf{L}}}_{{textbf{T}}}}=psi _{{textbf{T}}}{textbf{S}}-(beta +mu +lambda psi _{{textbf{C}}}+varpi ){{textbf{L}}}_{{textbf{T}}},\ dot{{{textbf{I}}}_{{textbf{T}}}}=mu {{textbf{L}}}_{{textbf{T}}}+varsigma _{2}eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{2}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta ){{textbf{I}}}_{{textbf{T}}},\ dot{{{textbf{E}}}_{{textbf{C}}}}=psi _{{textbf{C}}}{textbf{S}}-(beta +epsilon psi _{{textbf{T}}}+varphi _{1}+varphi _{2}){{textbf{E}}}_{{textbf{C}}},~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0le tau le intercal _{1},\ dot{{{textbf{I}}}_{{textbf{C}}}}=varphi _{1} {{textbf{E}}}_{{textbf{C}}}+rho eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{1}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +zeta _{{textbf{C}}}+nu +varphi _{3}){{textbf{I}}}_{{textbf{C}}},\ dot{{{textbf{L}}}_{{textbf{T}}{textbf{C}}}}=lambda psi _{{textbf{C}}}{{textbf{L}}}_{{textbf{T}}}+epsilon psi _{{textbf{T}}}{{textbf{E}}}_{{textbf{C}}}-(beta +zeta _{{textbf{C}}}+rho +eta ){{textbf{L}}}_{{textbf{T}}{textbf{C}}},\ dot{{{textbf{I}}}_{{textbf{T}}{textbf{C}}}}=rho {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+varsigma _{3}{{textbf{I}}}_{{textbf{T}}}+nu {{textbf{I}}}_{{textbf{C}}}-(beta +zeta _{{textbf{T}}{textbf{C}}}+xi ){{textbf{I}}}_{{textbf{T}}{textbf{C}}},\ dot{{{textbf{R}}}}=varpi {{textbf{L}}}_{{textbf{T}}}+varphi _{2}{{textbf{E}}}_{{textbf{C}}}+delta {{textbf{I}}}_{{textbf{T}}}+varphi _{3}{{textbf{I}}}_{{textbf{C}}}+(1-(varsigma _{1}+varsigma _{2}))eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+(1-(theta _{1}+theta _{2}))xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-beta {textbf{R}},end{array}right. } end{aligned}$$
(2)
where (psi _{{textbf{T}}}=frac{alpha _{1}}{{textbf{N}}(tau )}big ({{textbf{I}}}_{{textbf{T}}}(tau )+{{textbf{I}}}_{{textbf{T}}{textbf{C}}}(tau )big )) and (psi _{{textbf{C}}}=frac{alpha _{2}}{{textbf{N}}(tau )}big ({{textbf{E}}}_{{textbf{C}}}(tau )+{{textbf{I}}}_{{textbf{C}}}(tau )+{{textbf{L}}}_{{textbf{T}}{textbf{C}}}(tau )+{{textbf{I}}}_{{textbf{T}}{textbf{C}}}(tau )big ),) containing positive initial conditions (ICs) ({{textbf{S}}}(0)ge 0,~{{textbf{L}}}_{{textbf{T}}}ge 0,~{{textbf{I}}}_{{textbf{T}}}ge 0,~{{textbf{E}}}_{{textbf{C}}}ge 0,~{{textbf{I}}}_{{textbf{C}}}ge 0,~{{textbf{L}}}_{{textbf{T}}{textbf{C}}}ge 0,~{{textbf{I}}}_{{textbf{T}}{textbf{C}}}ge 0,~{{textbf{R}}}ge 0.)
Table 1 provides a description of the systems characteristics.
To help readers that are acquainted with fractional calculus, we provide the related summary herein (see21,22,23 comprehensive discussion on fractional calculus).
$$begin{aligned} ,_{0}^{c}{textbf{D}}_{tau }^{omega } {mathcal {G}}(tau )=frac{1}{Gamma (1-omega )}int limits _{0}^{tau }{mathcal {G}}^{prime }({textbf{q}})(tau -{textbf{q}})^{omega }d{textbf{q}},~~omega in (0,1]. end{aligned}$$
The index kernel is involved in the Caputo fractional derivative (CFD). Whenever experimenting with a particular integral transform, such as the Laplace transform36,37, the CFD accommodates regular ICs.
$$begin{aligned} ,_{0}^{CF}{textbf{D}}_{tau }^{omega } {mathcal {G}}(tau )=frac{bar{{mathcal {M}}}(omega )}{1-omega }int limits _{0}^{tau }{mathcal {G}}^{prime }({textbf{q}})exp bigg [-frac{omega }{1-omega }(tau -{textbf{q}})bigg ]d{textbf{q}},~~omega in (0,1], end{aligned}$$
where (bar{{mathcal {M}}}(omega )) indicates the normalization function (bar{{mathcal {M}}}(0)=bar{{mathcal {M}}}(1)=1.)
The non-singular kernel of the Caputo-Fabrizio fractional derivative (CFFD) operator has drawn the attention of numerous researchers. Furthermore, representing an assortment of prevalent issues that obey the exponential decay memory is best suited to utilize the CFFD operator38. With the passage of time, developing a mathematical model using the CFFD became a remarkable field of research. In recent times, several mathematicians have been busy with the development and simulation of CFFD DEs39.
The ABC fractional derivative operator is described as follows:
$$begin{aligned} ,_{0}^{ABC}{textbf{D}}_{tau }^{omega } {mathcal {G}}(tau )=frac{ABC(omega )}{1-omega }int limits _{0}^{tau }{mathcal {G}}^{prime }({textbf{q}})E_{omega }bigg [-frac{omega }{1-omega }(tau -{textbf{q}})^{omega }bigg ]d{textbf{q}},~~omega in (0,1], end{aligned}$$
where (ABC(omega )=1-omega +frac{omega }{Gamma (omega )}) represents the normalization function.
The memory utilized in AtanganaBaleanuCaputo fractional derivative (ABCFD) can be found intuitively within the index-law analogous for an extended period as well as exponential decay in a number of scientific concerns40,41. The broad scope of the connection and the non-power-law nature of the underlying tendency are the driving forces behind the selection of this version. The impact of the kernel, considered crucial in the dynamic BaggsFreedman framework, was fully produced by the GML function42.
To far better perceive the propagation of TB and COVID-19, we indicate a dynamic mechanism (2) that includes the co-infection within the context of CFD, CFFD and ABCFD, respectively. This is because FO algorithms possess inherited properties that characterize the local/non-local and singular/non-singular dynamics of natural phenomena, presented as follows:
$$begin{aligned} {left{ begin{array}{ll} ,^{c}{textbf{D}}_{tau }^{omega }{textbf{S}}=nabla -(psi _{{textbf{T}}}+psi _{{textbf{C}}}+beta ){textbf{S}},\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}}=psi _{{textbf{T}}}{textbf{S}}-(beta +mu +lambda psi _{{textbf{C}}}+varpi ){{textbf{L}}}_{{textbf{T}}},\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}}=mu {{textbf{L}}}_{{textbf{T}}}+varsigma _{2}eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{2}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta ){{textbf{I}}}_{{textbf{T}}},\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{E}}}_{{textbf{C}}}=psi _{{textbf{C}}}{textbf{S}}-(beta +epsilon psi _{{textbf{T}}}+varphi _{1}+varphi _{2}){{textbf{E}}}_{{textbf{C}}},~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~intercal _{1}le tau le intercal _{2},\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{C}}}=varphi _{1} {{textbf{E}}}_{{textbf{C}}}+rho eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{1}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +zeta _{{textbf{C}}}+nu +varphi _{3}){{textbf{I}}}_{{textbf{C}}},\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}{textbf{C}}}=lambda psi _{{textbf{C}}}{{textbf{L}}}_{{textbf{T}}}+epsilon psi _{{textbf{T}}}{{textbf{E}}}_{{textbf{C}}}-(beta +zeta _{{textbf{C}}}+rho +eta ){{textbf{L}}}_{{textbf{T}}{textbf{C}}},\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}{textbf{C}}}=rho {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+varsigma _{3}{{textbf{I}}}_{{textbf{T}}}+nu {{textbf{I}}}_{{textbf{C}}}-(beta +zeta _{{textbf{T}}{textbf{C}}}+xi ){{textbf{I}}}_{{textbf{T}}{textbf{C}}},\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{R}}}=varpi {{textbf{L}}}_{{textbf{T}}}+varphi _{2}{{textbf{E}}}_{{textbf{C}}}+delta {{textbf{I}}}_{{textbf{T}}}+varphi _{3}{{textbf{I}}}_{{textbf{C}}}+(1-(varsigma _{1}+varsigma _{2}))eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+(1-(theta _{1}+theta _{2}))xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-beta {textbf{R}},end{array}right. } end{aligned}$$
(3)
$$begin{aligned} {left{ begin{array}{ll} ,^{CF}{textbf{D}}_{tau }^{omega }{textbf{S}}=nabla -(psi _{{textbf{T}}}+psi _{{textbf{C}}}+beta ){textbf{S}},\ ,^{CF}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}}=psi _{{textbf{T}}}{textbf{S}}-(beta +mu +lambda psi _{{textbf{C}}}+varpi ){{textbf{L}}}_{{textbf{T}}},\ ,^{CF}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}}=mu {{textbf{L}}}_{{textbf{T}}}+varsigma _{2}eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{2}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta ){{textbf{I}}}_{{textbf{T}}},\ ,^{CF}{textbf{D}}_{tau }^{omega }{{textbf{E}}}_{{textbf{C}}}=psi _{{textbf{C}}}{textbf{S}}-(beta +epsilon psi _{{textbf{T}}}+varphi _{1}+varphi _{2}){{textbf{E}}}_{{textbf{C}}},~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~intercal _{1}le tau le intercal _{2},\ ,^{CF}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{C}}}=varphi _{1} {{textbf{E}}}_{{textbf{C}}}+rho eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{1}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +zeta _{{textbf{C}}}+nu +varphi _{3}){{textbf{I}}}_{{textbf{C}}},\ ,^{CF}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}{textbf{C}}}=lambda psi _{{textbf{C}}}{{textbf{L}}}_{{textbf{T}}}+epsilon psi _{{textbf{T}}}{{textbf{E}}}_{{textbf{C}}}-(beta +zeta _{{textbf{C}}}+rho +eta ){{textbf{L}}}_{{textbf{T}}{textbf{C}}},\ ,^{CF}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}{textbf{C}}}=rho {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+varsigma _{3}{{textbf{I}}}_{{textbf{T}}}+nu {{textbf{I}}}_{{textbf{C}}}-(beta +zeta _{{textbf{T}}{textbf{C}}}+xi ){{textbf{I}}}_{{textbf{T}}{textbf{C}}},\ ,^{CF}{textbf{D}}_{tau }^{omega }{{textbf{R}}}=varpi {{textbf{L}}}_{{textbf{T}}}+varphi _{2}{{textbf{E}}}_{{textbf{C}}}+delta {{textbf{I}}}_{{textbf{T}}}+varphi _{3}{{textbf{I}}}_{{textbf{C}}}+(1-(varsigma _{1}+varsigma _{2}))eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+(1-(theta _{1}+theta _{2}))xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-beta {textbf{R}},end{array}right. } end{aligned}$$
(4)
$$begin{aligned} {left{ begin{array}{ll} ,^{ABC}{textbf{D}}_{tau }^{omega }{textbf{S}}=nabla -(psi _{{textbf{T}}}+psi _{{textbf{C}}}+beta ){textbf{S}},\ ,^{ABC}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}}=psi _{{textbf{T}}}{textbf{S}}-(beta +mu +lambda psi _{{textbf{C}}}+varpi ){{textbf{L}}}_{{textbf{T}}},\ ,^{ABC}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}}=mu {{textbf{L}}}_{{textbf{T}}}+varsigma _{2}eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{2}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta ){{textbf{I}}}_{{textbf{T}}},\ ,^{ABC}{textbf{D}}_{tau }^{omega }{{textbf{E}}}_{{textbf{C}}}=psi _{{textbf{C}}}{textbf{S}}-(beta +epsilon psi _{{textbf{T}}}+varphi _{1}+varphi _{2}){{textbf{E}}}_{{textbf{C}}},~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~intercal _{1}le tau le intercal _{2},\ ,^{ABC}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{C}}}=varphi _{1} {{textbf{E}}}_{{textbf{C}}}+rho eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{1}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +zeta _{{textbf{C}}}+nu +varphi _{3}){{textbf{I}}}_{{textbf{C}}},\ ,^{ABC}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}{textbf{C}}}=lambda psi _{{textbf{C}}}{{textbf{L}}}_{{textbf{T}}}+epsilon psi _{{textbf{T}}}{{textbf{E}}}_{{textbf{C}}}-(beta +zeta _{{textbf{C}}}+rho +eta ){{textbf{L}}}_{{textbf{T}}{textbf{C}}},\ ,^{ABC}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}{textbf{C}}}=rho {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+varsigma _{3}{{textbf{I}}}_{{textbf{T}}}+nu {{textbf{I}}}_{{textbf{C}}}-(beta +zeta _{{textbf{T}}{textbf{C}}}+xi ){{textbf{I}}}_{{textbf{T}}{textbf{C}}},\ ,^{ABC}{textbf{D}}_{tau }^{omega }{{textbf{R}}}=varpi {{textbf{L}}}_{{textbf{T}}}+varphi _{2}{{textbf{E}}}_{{textbf{C}}}+delta {{textbf{I}}}_{{textbf{T}}}+varphi _{3}{{textbf{I}}}_{{textbf{C}}}+(1-(varsigma _{1}+varsigma _{2}))eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+(1-(theta _{1}+theta _{2}))xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-beta {textbf{R}}.end{array}right. } end{aligned}$$
(5)
The arrangement of this article is as follows: In Codynamics model and preliminaries section, explanations for fractional calculus, along with several key notions and model (2) details, are provided. Moreover, a detailed analysis of the FO co-infection systems (3) equilibrium stability is presented in Codynamics model and preliminaries section. In Stochastic configuration of codynamics of TB-COVID-19 model section, a probabilistic form of the TB and COVID-19 models (28) codynamics is proposed and a detailed description of the unique global positive solution for each positive initial requirement is presented. The dynamical characteristics of the mechanisms appropriate conditions for the presence of the distinctive stationary distribution are provided. The P.D.F enclosing a quasi-stable equilibrium of the probabilistic COVID-19 framework is presented in Stochastic COVID-19 model without TB infection section. Numerous numerical simulations in view of piecewise fractional derivative operators are presented in Numerical solutions of co-dynamics model using random perturbations section to validate the diagnostic findings we obtained in Stochastic configuration of codynamics of TB-COVID-19 model and Stochastic COVID-19 model without TB infection sections. In conclusion, we conceal our findings to conclude this study.
Since we interact with living communities, each approach ought to be constructive and centred on a workable area. We utilized the subsequent hypothesis that guarantees these.
Assume that the set ({tilde{Xi }}:=Big ({{textbf{S}}},{{textbf{L}}}_{{textbf{T}}},{{textbf{I}}}_{{textbf{T}}},{{textbf{E}}}_{{textbf{C}}},{{textbf{I}}}_{{textbf{C}}},{{textbf{L}}}_{{textbf{T}}{textbf{C}}},{{textbf{I}}}_{{textbf{T}}{textbf{C}}},{{textbf{R}}}Big )) is a positive invariant set for the suggested FO model (3).
In order to demonstrate whether the solution to a set of equations (3) is positive, then (3) yields
$$begin{aligned} {left{ begin{array}{ll} ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{S}}}big vert _{{{textbf{S}}}=0}=nabla ge 0,\ ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{{textbf{L}}}_{{textbf{T}}}}big vert _{{{textbf{L}}}_{{textbf{T}}}}=psi _{{textbf{T}}}{{textbf{S}}}ge 0,\ ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{{textbf{I}}}_{{textbf{T}}}}big vert _{{{textbf{I}}}_{{textbf{T}}}=0}=mu {{textbf{L}}}_{{textbf{T}}}ge 0,\ ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{{textbf{E}}}_{{textbf{C}}}}big vert _{{{textbf{E}}}_{{textbf{C}}}=0}=psi _{{textbf{C}}}{{textbf{S}}}ge 0,\ ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{{textbf{I}}}_{{textbf{C}}}}big vert _{{{textbf{I}}}_{{textbf{C}}}=0}=varphi _{1}{{textbf{E}}}_{{textbf{C}}}ge 0,\ ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{{textbf{L}}}_{{textbf{T}}{textbf{C}}}}big vert _{{{textbf{L}}}_{{textbf{T}}{textbf{C}}}=0}=lambda psi _{{textbf{C}}}{{textbf{L}}}_{{textbf{T}}}+epsilon psi _{{textbf{T}}}{{textbf{E}}}_{{textbf{C}}}ge 0,\ ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{{textbf{I}}}_{{textbf{T}}{textbf{C}}}}big vert _{{{textbf{I}}}_{{textbf{T}}{textbf{C}}}=0}=rho {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+varsigma _{3}{{textbf{I}}}_{{textbf{T}}}+nu {{textbf{I}}}_{{textbf{C}}}ge 0,\ ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{R}}}big vert _{{textbf{R}}=0}=varpi {{textbf{L}}}_{{textbf{T}}}+varphi _{2}{{textbf{E}}}_{{textbf{C}}}+delta {{textbf{I}}}_{{textbf{T}}}+varphi _{3}{{textbf{I}}}_{{textbf{C}}}+(1-(varsigma _{1}+varsigma _{2}))eta {L_{{textbf{T}}{textbf{C}}}}+(1-(theta _{1}+theta _{2}))xi {{{textbf{I}}}_{{textbf{T}}{textbf{C}}}}ge 0. end{array}right. } end{aligned}$$
(6)
Therefore, the outcomes related to the FO model (3) are positive. Finally, the variation in the entire community is described by
$$begin{aligned} ,_{0}^{c}{textbf{D}}_{tau }^{omega }{tilde{Xi }}{} & {} le nabla +zeta _{{textbf{T}}}{{textbf{I}}}_{{textbf{T}}}-zeta _{{textbf{C}}}({{textbf{I}}}_{{textbf{C}}}+{{textbf{L}}}_{{textbf{T}}{textbf{C}}})-zeta _{{textbf{T}}{textbf{C}}}{{textbf{I}}}_{{textbf{T}}{textbf{C}}}-beta {textbf{N}}nonumber \{} & {} le nabla -beta {{textbf{N}}}. end{aligned}$$
Addressing the variant previously mentioned, we get
$$begin{aligned} {tilde{Xi }}(tau )le bigg ({tilde{Xi }}(0)-frac{nabla }{beta }bigg )E_{omega }bigg (-beta tau ^{omega }bigg )+frac{nabla }{beta }. end{aligned}$$
Consequently, we derive the GML functions asymptotic operation43 as
$$begin{aligned} {tilde{Xi }}(tau )le frac{nabla }{beta }. end{aligned}$$
Adopting the same procedure for other systems of equations in the model (3), which indicates that the closed set ({tilde{Xi }}) is a positive invariant domain for the FO system (3).(square )
Assuming that every requirement is non-negative throughout time (tau ), we exhibit that the outcomes remain non-negative and bounded in the proposed region, (Pi ). Well look at the co-infection model (3) ({tilde{Xi }}:=Big ({{textbf{S}}},{{textbf{L}}}_{{textbf{T}}},{{textbf{I}}}_{{textbf{T}}},{{textbf{E}}}_{{textbf{C}}},{{textbf{I}}}_{{textbf{C}}},{{textbf{L}}}_{{textbf{T}}{textbf{C}}},{{textbf{I}}}_{{textbf{T}}{textbf{C}}},{{textbf{R}}}Big )) spreads in the domain, which is described as (Pi :=Big {{tilde{Xi }}in Re _{+}^{8}:0le {textbf{N}}le frac{nabla }{beta }Big }.)
According to the afflicted categories in co-infection model (3), disease-free equilibrium (DFE) and endemic equilibrium (EE) are the biologically significant steady states of FO model (3). We establish the fractional derivative to get the immune-to-infection steady state as ( ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{S}}},~,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}},~,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}},,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{E}}}_{{textbf{C}}},~,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{C}}}, ,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}{textbf{C}}},~,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}{textbf{C}}},~,_{0}^{c}{textbf{D}}_{tau }^{omega }{{textbf{R}}},) to zero of the FO model (3) have no infection, and get
$$begin{aligned} {mathcal {E}}_{0}=Big (frac{nabla }{beta },0,0,0,0,0,0,0Big ). end{aligned}$$
The dominating eigenvalue of the matrix ({textbf{F}}{textbf{G}}^{-1}) correlates with the basic reproductive quantity ({mathbb {R}}_{0}^{CT}) of structure (3), in accordance with the next generation matrix approach44. Thus, we find
$$begin{aligned}{mathcal {F}}= begin{pmatrix} psi _{{textbf{T}}}{{textbf{S}}}\ 0\ psi _{{textbf{C}}}{textbf{S}}\ 0\ 0\ 0 end{pmatrix},~~~Phi =begin{pmatrix} (beta +mu +lambda psi _{{textbf{C}}}+varpi ){{textbf{L}}}_{{textbf{T}}}\ -theta _{2}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-varsigma _{2}eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}-mu {{textbf{L}}}_{{textbf{T}}}+(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta ){{textbf{I}}}_{{textbf{T}}}\ (beta +epsilon psi _{{textbf{T}}}+varphi _{1}+varphi _{2}){{textbf{E}}}_{{textbf{C}}}\ -varphi _{1}{{textbf{E}}}_{{textbf{C}}}-varsigma _{1}eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}-theta _{1}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}+(beta +nu +zeta _{{textbf{C}}}+varphi _{3}){{textbf{I}}}_{{textbf{C}}}\ -lambda psi _{{textbf{C}}}{{textbf{L}}}_{{textbf{T}}}-epsilon psi _{{textbf{T}}}{{textbf{E}}}_{{textbf{C}}}+(beta +zeta _{{textbf{C}}}+rho +eta ){{textbf{L}}}_{{textbf{T}}{textbf{C}}}\ -rho {{textbf{L}}}_{{textbf{T}}{textbf{C}}}-varsigma _{3}{{textbf{I}}}_{{textbf{T}}}-nu {{textbf{I}}}_{{textbf{C}}}+(beta +zeta _{{textbf{T}}{textbf{C}}}+xi ) end{pmatrix}. end{aligned}$$
The next generation matrix at DEF can then be obtained by using the Jacobian of ({textbf{F}}) and ({textbf{G}}) examined at ({mathcal {E}}_{0}) as
$$begin{aligned} {textbf{F}}{textbf{G}}^{-1}=begin{pmatrix} frac{mu {mathcal {K}}_{1}}{(beta +mu +varpi ){mathcal {K}}_{7}}&{}frac{{mathcal {K}}_{1}}{{mathcal {K}}_{7}}&{}frac{varphi _{1}{mathcal {K}}_{3}}{(beta +omega +varphi _{2}){mathcal {K}}_{7}}&{}frac{{mathcal {K}}_{3}}{{mathcal {K}}_{7}}&{}frac{{mathcal {K}}_{5}}{(beta +zeta _{{textbf{C}}}+rho +eta ){mathcal {K}}_{7}}&{}frac{-alpha _{1}(beta +nu +zeta _{{textbf{C}}}+varphi _{3})(beta +varsigma _{3}+zeta _{{textbf{T}}}delta +theta _{2}xi )}{{mathcal {K}}_{7}}\ 0&{}0&{}0&{}0&{}0&{}0\ frac{mu {mathcal {K}}_{2}}{(beta +mu +varpi ){mathcal {K}}_{7}}&{}frac{{mathcal {K}}_{2}}{{mathcal {K}}_{7}}&{}frac{varphi _{1}{mathcal {K}}_{4}}{(beta +omega +varphi _{2}){mathcal {K}}_{7}}&{}frac{-alpha _{2}(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +xi +zeta _{{textbf{T}}{textbf{C}}}+nu )-theta _{2}varsigma _{3}xi }{{mathcal {K}}_{7}}&{}frac{{mathcal {K}}_{6}}{(beta +varphi _{1}+varphi _{2}){mathcal {K}}_{7}}&{}frac{-alpha _{2}(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +zeta _{{textbf{C}}}+rho +eta )}{{mathcal {K}}_{7}}\ 0&{}0&{}0&{}0&{}0&{}0\ 0&{}0&{}0&{}0&{}0&{}0\ 0&{}0&{}0&{}0&{}0&{}0 end{pmatrix}, end{aligned}$$
where
$$begin{aligned} {mathcal {K}}_{kappa }= {left{ begin{array}{ll} -alpha _{1}big ((beta +nu +zeta _{{textbf{C}}}+varphi _{3})(beta +xi +zeta _{{textbf{T}}{textbf{C}}})+(beta +nu +zeta _{{textbf{C}}}+varphi _{3})varsigma _{3}-theta _{1}nu xi big ),~~~~kappa =1,\ -alpha _{2}varsigma _{3}(theta _{1}xi +beta +nu +zeta _{{textbf{C}}}+varphi _{3}),~~~~kappa =2,\ -alpha _{1}nu (theta _{2}xi +beta +varsigma _{3}+zeta _{{textbf{T}}}+delta ),~~~~kappa =3,\ -alpha _{2}(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )big ((beta +nu +varphi _{3}+zeta _{{textbf{C}}})(beta +xi +zeta _{{textbf{T}}{textbf{C}}})+varphi _{1}(beta +xi +zeta _{{textbf{T}}{textbf{C}}})+nu varphi _{1}-theta _{1}nu xi big )\ qquad -theta _{2}varsigma _{3}xi (varphi _{1}+beta +nu +zeta _{{textbf{C}}}+varphi _{3}),~~~~kappa =4,\ nu rho xi (theta _{2}varsigma _{1}-theta _{1}varsigma _{2})+(beta +nu +zeta _{{textbf{C}}}+varphi _{3})big (-alpha _{1}rho (nu xi +beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )+eta varsigma _{2}(beta +xi +varsigma _{3}+zeta _{{textbf{T}}{textbf{C}}})big )\ qquad +varsigma _{1}nu eta (beta +varsigma _{3}+zeta _{{textbf{T}}}+delta ),~~~~kappa =5,\ -alpha _{2}big ((beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +nu +zeta _{C{1}}+varphi _{3})(beta +xi +zeta _{{textbf{T}}{textbf{C}}}+rho )+theta _{1}xi (rho -nu )(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )\ qquad +(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )eta varsigma _{1}(beta +xi +zeta _{{textbf{T}}{textbf{C}}}+nu )+varsigma _{2}eta varsigma _{3}(beta +nu +zeta _{{textbf{C}}}+varphi _{3}+theta _{1}xi )\ qquad -theta _{2}varsigma _{3}xi (varsigma _{1}eta +beta +nu +zeta _{{textbf{C}}}+varphi _{3})big ),~~~kappa =6,\ theta _{1}nu xi (beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )+(beta +zeta _{{textbf{C}}}+rho +eta )big (theta _{2}varsigma _{3}xi -(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta =xi +zeta _{{textbf{T}}{textbf{C}}})big ),~~~kappa =7. end{array}right. } end{aligned}$$
The fundamental reproducing quantity of the pairing system is shown by the highest spectral radius of the subsequent generations matrix. It is evident that the matrix ({textbf{F}}{textbf{G}}^{-1}) has four eigenvalues that are equivalent to zero. The truncated matrix yields the additional eigenvalues as
$$begin{pmatrix}frac{mu {mathcal {K}}_{1}}{(beta +mu +varpi ){mathcal {K}}}&frac{varphi _{1}{mathcal {K}}_{3}}{(beta +varphi _{1}+varphi _{2}){mathcal {K}}} frac{mu {mathcal {K}}_{2}}{(beta +mu +varpi ){mathcal {K}}}&frac{{mathcal {K}}_{4}}{(beta +varphi _{1}+varphi _{2}){mathcal {K}}}end{pmatrix}.$$
Consequently, by calculating the eigenvalues of ({textbf{F}}{textbf{G}}^{-1}), it is possible to simply determine that
$$begin{aligned} tilde{delta _{1}}{} & {} =frac{(beta +mu +varpi ){textbf{Q}}_{4}+mu (beta +varphi _{1}+varphi _{2}){textbf{Q}}_{1}-nabla _{1}^{2}}{2(beta +mu +varpi )(beta +varphi _{1}+varphi _{2})big ( theta _{1}nu xi (beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )+(beta +zeta _{{textbf{C}}}+rho +eta )big (theta _{2}varsigma _{3}xi -(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +xi +zeta _{{textbf{T}}{textbf{C}}})big )big )},nonumber \ tilde{delta _{2}}{} & {} =frac{(beta +mu +varpi ){textbf{Q}}_{4}+mu (beta +varphi _{1}+varphi _{2}){textbf{Q}}_{1}+nabla _{1}^{2}}{2(beta +mu +varpi )(beta +varphi _{1}+varphi _{2})big ( theta _{1}nu xi (beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )+(beta +zeta _{{textbf{C}}}+rho +eta )big (theta _{2}varsigma _{3}xi -(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +xi +zeta _{{textbf{T}}{textbf{C}}})big )big )}, end{aligned}$$
where
$$begin{aligned} nabla _{1}=sqrt{mu ^{2}{mathcal {K}}_{1}^{2}(beta +varphi _{1}+varphi _{2})^{2}-2mu (beta +mu +varpi )(beta +varphi _{1}+varphi _{2}){textbf{Q}}_{1}{textbf{Q}}_{2}+4varphi _{1}mu (beta +mu +varpi )(beta +varphi _{1}+varphi _{2}){mathcal {K}}_{2}^{2}+(beta +mu +varpi )^{2}{mathcal {K}}_{4}^{2}}. end{aligned}$$
Therefore, the co-dynamics structures (3) fundamental reproductive quantity ({mathbb {R}}_{0}) is provided by ({mathbb {R}}_{0}^{CT}=max {{mathbb {R}}_{0}^{C},{mathbb {R}}_{0}^{T}}.)
Here, we shall then demonstrate how transmission persists in the FO mechanism. It explains how widespread the virus is within the framework. From the viewpoint of biology, the virus continues in the bloodstream if the infectious proportion is elevated for a sufficiently long time (tau ).
However, the linearization technique is used to examine the local stabilization of the codynamics algorithms DFE state. At the DFE state ({mathcal {E}}_{0},) the Jacobean matrix of system (3) is displayed as
$$begin{aligned} {mathcal {J}}_{{mathcal {E}}_{0}}=begin{pmatrix} -beta &{}0&{}-alpha _{1}&{}-alpha _{2}&{}-alpha _{2}&{}-alpha _{2}&{}-(alpha _{1}+alpha _{2})&{}0\ 0&{}-(beta +mu +varpi )&{}alpha _{1}&{}0&{}0&{}0&{}alpha _{1}&{}0\ 0&{}mu &{}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )&{}0&{}0&{}varsigma _{2}eta &{}theta _{2}xi &{}0\ 0&{}0&{}0&{}alpha _{2}-beta -varphi _{1}-varphi _{2}&{}alpha _{2}&{}alpha _{2}&{}alpha _{2}&{}0\ 0&{}0&{}0&{}varphi _{1}&{}-beta -nu -zeta _{{textbf{C}}}-varphi _{3}&{}varsigma _{1}eta &{}theta _{1}xi &{}0\ 0&{}0&{}0&{}0&{}0&{}-(beta +zeta _{{textbf{C}}}+rho +eta )&{}0&{}0\ 0&{}0&{}varsigma _{3}&{}0&{}nu &{}rho &{}-(beta +xi +zeta _{{textbf{T}}{textbf{C}}})&{}0\ 0&{}varpi &{}delta &{}varphi _{2}&{}varphi _{3}&{}(1-(varsigma _{1}+varsigma _{2}))eta &{}(1-(theta _{1}+theta _{2}))eta &{}-beta . end{pmatrix} end{aligned}$$
(7)
The analysis of ({mathcal {E}}_{0})s localized temporal equilibrium relies upon the eigenvalues interpretation. Here, (tilde{delta _{1,2}}=-beta ) and (tilde{delta _{3}}=-(beta +rho +eta +zeta _{{textbf{C}}})) are obtained by broadening the following polynomial (vert {mathcal {J}}_{{mathcal {E}}_{0}}-delta {mathcal {I}}vert =0). Moreover, we get the additional (delta )s based on the simplified matrixs (vert {mathcal {J}}_{{mathcal {E}}_{0}}-delta {mathcal {I}}vert =0) described as
$$begin{aligned}{} & {} {mathcal {J}}-delta {mathcal {I}}_{5}nonumber \ {}{} & {} =begin{pmatrix} mu &{}-(beta +varsigma _{3}+delta +zeta _{{textbf{T}}}+{tilde{delta }})&{}0&{}0&{}theta _{2}xi \ 0&{}varsigma _{3}&{}0&{}nu &{}-({tilde{delta }}+beta +xi +zeta _{{textbf{C}}})\ 0&{}0&{}varphi _{1}&{}-({tilde{delta }}+beta +nu +varphi _{3}+zeta _{{textbf{C}}})&{}theta _{1}xi \ 0&{}0&{}0&{}alpha _{2}varphi _{1}+({tilde{delta }}+beta +nu +varphi _{3}+zeta _{{textbf{C}}})(alpha _{2}-{tilde{delta }}-beta -xi -varphi _{1})/varphi _{1}&{}Im _{1}\ 0&{}0&{}0&{}0&{}Im _{2} end{pmatrix}, end{aligned}$$
where (Im _{1}=alpha _{2}varphi _{1}+({tilde{delta }}+beta +nu +varphi _{3}+zeta _{{textbf{C}}})(alpha _{2}-{tilde{delta }}-beta -xi -varphi _{1})/varphi _{1},Im _{2}=alpha _{1}(varsigma _{3}+({tilde{delta }}+beta +xi +zeta _{{textbf{C}}}))/varsigma _{3}+big (beta +varsigma _{3}+zeta _{{textbf{T}}}+delta +{tilde{delta }}/mu big )big (theta _{2}xi varsigma _{3}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta +{tilde{delta }})(beta +xi +zeta _{{textbf{T}}{textbf{C}}}+{tilde{delta }})/varsigma _{3})big ).) After simple computations, the characteristic polynomial of the above matrix is presented as
$$begin{aligned} {textbf{U}}({tilde{delta }}){} & {} =-mu varsigma _{3}varphi _{1} frac{alpha _{2}varphi _{1}+({tilde{delta }}+beta +nu +varphi _{3}+zeta _{{textbf{C}}})(alpha _{2}-{tilde{delta }}-beta -xi -varphi _{1})}{varphi _{1}}Bigg {frac{alpha _{1}(varsigma _{3}+({tilde{delta }}+beta +xi +zeta _{{textbf{C}}}))}{varsigma _{3}}\{} & {} quad +frac{(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta +{tilde{delta }}}{mu }frac{theta _{2}xi varsigma _{3}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta +{tilde{delta }})(beta +xi +zeta _{{textbf{T}}{textbf{C}}}+{tilde{delta }})}{varsigma _{3}}Bigg }. end{aligned}$$
(8)
In other words, the outcomes to the ({textbf{U}}({tilde{delta }})) are the eigenvalues:
$$begin{aligned} {textbf{U}}({tilde{delta }})={tilde{delta }}^{5}+{textbf{d}}_{1}{tilde{delta }}^{4}+{textbf{d}}_{2}{tilde{delta }}^{3}+{textbf{d}}_{3}{tilde{delta }}^{2}+{textbf{d}}_{4}{tilde{delta }}+{textbf{d}}_{5}=0, end{aligned}$$
(9)
where
$$begin{aligned} {textbf{d}}_{1}{} & {} =alpha _{2}-beta -varphi _{1}-varphi _{2},nonumber \ {textbf{d}}_{2}{} & {} =alpha _{2}varphi _{1}+(beta +nu +zeta _{{textbf{C}}}+varphi _{3})(alpha _{2}-beta -varphi _{1}-varphi _{2})-(alpha _{2}-2beta -varphi _{1}-varphi _{2}-nu -zeta _{{textbf{C}}}-varphi _{3})nonumber \{} & {} quad times (beta +varsigma _{3}+zeta _{{textbf{T}}}+delta +xi +zeta _{{textbf{T}}{textbf{C}}}-mu -varpi )+big (mu alpha _{1}+theta _{2}xi varsigma _{3}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +xi +zeta _{{textbf{T}}{textbf{C}}})nonumber \{} & {} quad -(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +mu +varpi )-(beta +mu +varpi )(beta +xi +zeta _{{textbf{T}}{textbf{C}}})big ),nonumber \ {textbf{d}}_{3}{} & {} =mu alpha _{1}(varsigma _{3}+beta +xi +zeta _{{textbf{T}}{textbf{C}}})+(beta +mu +varpi )big (theta _{2}xi varsigma _{3}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +xi +zeta _{{textbf{T}}{textbf{C}}})big )nonumber \{} & {} quad -big (alpha _{2}varphi _{1}+(beta +nu +varphi _{3}+zeta _{{textbf{C}}})(alpha _{2}-beta -varphi _{1}-varphi _{2})big )(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta +varphi _{1}+varphi _{2}-xi -zeta _{{textbf{T}}{textbf{C}}})nonumber \ {}{} & {} quad -(alpha _{2}-2beta -varphi _{1}-varphi _{2}-nu -zeta _{{textbf{C}}}-varphi _{3})big (mu alpha _{1}+theta _{2}xi varsigma _{3}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +xi +zeta _{{textbf{T}}{textbf{C}}})nonumber \ {}{} & {} quad -(beta +mu +varpi )(2beta +varsigma _{3}+zeta _{{textbf{T}}}+delta +xi +zeta _{{textbf{T}}{textbf{C}}})big ),nonumber \{textbf{d}}_{4}{} & {} = -big (alpha _{2}varphi _{1}+(beta +nu +zeta _{{textbf{C}}}+varphi _{3})(alpha _{2}-beta -varphi _{1}-varphi _{2})big )big (mu alpha _{1}+theta _{2}xi varsigma _{3}-(beta +mu +varpi )(2beta +varsigma _{3}+zeta _{{textbf{T}}}+delta +xi +zeta _{{textbf{T}}{textbf{C}}})big )nonumber \ {}{} & {} quad -(alpha _{2}-2beta -varphi _{1}-varphi _{2}-nu -zeta _{{textbf{C}}}-varphi _{3})big (mu alpha _{1}(varsigma _{3}+beta +xi +zeta _{{textbf{T}}{textbf{C}}})+(beta +mu +varpi )nonumber \ {}{} & {} quad times (theta _{2}xi varsigma _{3}-(beta varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +xi +zeta _{{textbf{T}}{textbf{C}}}))big ),nonumber \{textbf{d}}_{5}{} & {} =big (alpha _{2}varphi _{1}+(beta +nu +varphi _{3}+zeta _{{textbf{C}}})(alpha _{2}-beta -varphi _{1}-varphi _{2})big )big (mu alpha _{1}(varsigma _{3}+beta +xi +zeta _{{textbf{T}}{textbf{C}}})nonumber \ {}{} & {} quad +(beta +mu +varpi )(theta _{2}xi varsigma _{3}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta )(beta +xi +zeta _{{textbf{T}}{textbf{C}}}))big ). end{aligned}$$
(10)
Therefore, if the subsequent requirements apply, the roots of expression (10) exhibit negative real portions according to the RouthHurwitz stability specifications as
$$begin{aligned} {left{ begin{array}{ll} {textbf{d}}_{jmath }>0,~~forall ~jmath =1,...,5,~{textbf{d}}_{1}{textbf{d}}_{2}{textbf{d}}_{3}>{textbf{d}}_{3}^{2}+{textbf{d}}_{1}^{2}{textbf{d}}_{4},\ ({textbf{d}}_{1}{textbf{d}}_{4}-{textbf{d}}_{5})({textbf{d}}_{1}{textbf{d}}_{2}{textbf{d}}_{3}-{textbf{d}}_{3}^{2}-{textbf{d}}_{1}^{2}{textbf{d}}_{4})>{textbf{d}}_{5}({textbf{d}}_{1}{textbf{d}}_{2}-{textbf{d}}_{3})^{2}+{textbf{d}}_{1}{textbf{d}}_{5}^{2}. end{array}right. } end{aligned}$$
(11)
Evolution of the basic reproduction number ({mathbb {R}}_{0}^{CT}) with the aid of ({mathbb {R}}_{0}^{C}) and ({mathbb {R}}_{0}^{T}).
Figure 4 is illustrated by depicting in 3D evolution of the threshold parameter ({mathbb {R}}_{0}^{CT}) of model (3) as a function of ({mathbb {R}}_{0}^{C}) and ({mathbb {R}}_{0}^{T}.)
The forthcoming result is established thanks to Theorem 2 in44.
The DFE point of the FO codynamics model (3) is locally asymptotically stable if the prerequisite specified in formula (12) is satisfied.
This section shows that there is only one solution for the system (3). Now, we demonstrate that the frameworks solution is distinctive. Initially, we construct framework (3) in the form of:
$$begin{aligned} {left{ begin{array}{ll} ,^{c}{textbf{D}}_{tau }^{omega }{textbf{S}}={mathcal {Q}}_{1}big (tau ,{textbf{S}}(tau )big ),\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}}={mathcal {Q}}_{2}big (tau ,{{textbf{L}}}_{{textbf{T}}}(tau )big ),\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}}={mathcal {Q}}_{3}big (tau ,{{textbf{I}}}_{{textbf{T}}}(tau )big ),\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{E}}}_{{textbf{C}}}={mathcal {Q}}_{4}big (tau ,{{textbf{E}}}_{{textbf{C}}}(tau )big ),\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{C}}}={mathcal {Q}}_{5}big (tau ,{{textbf{I}}}_{{textbf{C}}}(tau )big ),\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{L}}}_{{textbf{T}}{textbf{C}}}={mathcal {Q}}_{6}big (tau ,{{textbf{L}}}_{{textbf{T}}{textbf{C}}}(tau )big ),\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{I}}}_{{textbf{T}}{textbf{C}}}={mathcal {Q}}_{7}big (tau ,{{textbf{I}}}_{{textbf{T}}{textbf{C}}}(tau )big ),\ ,^{c}{textbf{D}}_{tau }^{omega }{{textbf{R}}}={mathcal {Q}}_{8}big (tau ,{{textbf{R}}}(tau )big ),\ end{array}right. } end{aligned}$$
(12)
where
$$begin{aligned} {left{ begin{array}{ll} {mathcal {Q}}_{1}big (tau ,{textbf{S}}(tau )big )=nabla -(psi _{{textbf{T}}}+psi _{{textbf{C}}}+beta ){textbf{S}},\ {mathcal {Q}}_{2}big (tau ,{{textbf{L}}}_{{textbf{T}}}(tau )big )=psi _{{textbf{T}}}{textbf{S}}-(beta +mu +lambda psi _{{textbf{C}}}+varpi ){{textbf{L}}}_{{textbf{T}}},\ {mathcal {Q}}_{3}big (tau ,{{textbf{I}}}_{{textbf{T}}}(tau )big )=mu {{textbf{L}}}_{{textbf{T}}}+varsigma _{2}eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{2}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta ){{textbf{I}}}_{{textbf{T}}},\ {mathcal {Q}}_{4}big (tau ,{{textbf{E}}}_{{textbf{C}}}(tau )big )=psi _{{textbf{C}}}{textbf{S}}-(beta +epsilon psi _{{textbf{T}}}+varphi _{1}+varphi _{2}){{textbf{E}}}_{{textbf{C}}},\ {mathcal {Q}}_{5}big (tau ,{{textbf{I}}}_{{textbf{C}}}(tau )big )=varphi _{1} {{textbf{E}}}_{{textbf{C}}}+rho eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+theta _{1}xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-(beta +zeta _{{textbf{C}}}+nu +varphi _{3}){{textbf{I}}}_{{textbf{C}}},\ {mathcal {Q}}_{6}big (tau ,{{textbf{L}}}_{{textbf{T}}{textbf{C}}}(tau )big )=lambda psi _{{textbf{C}}}{{textbf{L}}}_{{textbf{T}}}+epsilon psi _{{textbf{T}}}{{textbf{E}}}_{{textbf{C}}}-(beta +zeta _{{textbf{C}}}+rho +eta ){{textbf{L}}}_{{textbf{T}}{textbf{C}}},\ {mathcal {Q}}_{7}big (tau ,{{textbf{I}}}_{{textbf{T}}{textbf{C}}}(tau )big )=rho {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+varsigma _{3}{{textbf{I}}}_{{textbf{T}}}+nu {{textbf{I}}}_{{textbf{C}}}-(beta +zeta _{{textbf{T}}{textbf{C}}}+xi ){{textbf{I}}}_{{textbf{T}}{textbf{C}}},\ {mathcal {Q}}_{8}big (tau ,{{textbf{R}}}(tau )big )=varpi {{textbf{L}}}_{{textbf{T}}}+varphi _{2}{{textbf{E}}}_{{textbf{C}}}+delta {{textbf{I}}}_{{textbf{T}}}+varphi _{3}{{textbf{I}}}_{{textbf{C}}}+(1-(varsigma _{1}+varsigma _{2}))eta {{textbf{L}}}_{{textbf{T}}{textbf{C}}}+(1-(theta _{1}+theta _{2}))xi {{textbf{I}}}_{{textbf{T}}{textbf{C}}}-beta {textbf{R}}.end{array}right. } end{aligned}$$
(13)
Integral transform applied to both sides of equations (14) yields
$$begin{aligned} {left{ begin{array}{ll} {textbf{S}}(tau )-{textbf{S}}(0)=frac{1}{Gamma (omega )}int limits _{0}^{tau }(tau -{mathfrak {p}})^{omega -1}{mathcal {Q}}_{1}big ({mathfrak {p}},{textbf{S}}big )d{mathfrak {p}},\ {{textbf{L}}}_{{textbf{T}}}(tau )-{{textbf{L}}}_{{textbf{T}}}(0)=frac{1}{Gamma (omega )}int limits _{0}^{tau }(tau -{mathfrak {p}})^{omega -1}{mathcal {Q}}_{2}big ({mathfrak {p}},{{textbf{L}}}_{{textbf{T}}}big )d{mathfrak {p}},\ {{textbf{I}}}_{{textbf{T}}}(tau )-{{textbf{I}}}_{{textbf{T}}}(0)=frac{1}{Gamma (omega )}int limits _{0}^{tau }(tau -{mathfrak {p}})^{omega -1}{mathcal {Q}}_{3}big ({mathfrak {p}},{{textbf{I}}}_{{textbf{T}}}big )d{mathfrak {p}},\ {{textbf{E}}}_{{textbf{C}}}(tau )-{{textbf{E}}}_{{textbf{C}}}(0)=frac{1}{Gamma (omega )}int limits _{0}^{tau }(tau -{mathfrak {p}})^{omega -1}{mathcal {Q}}_{4}big ({mathfrak {p}},{{textbf{E}}}_{{textbf{C}}}big )d{mathfrak {p}},\ {{textbf{I}}}_{{textbf{C}}}(tau )-{{textbf{I}}}_{{textbf{C}}}(0)=frac{1}{Gamma (omega )}int limits _{0}^{tau }(tau -{mathfrak {p}})^{omega -1}{mathcal {Q}}_{5}big ({mathfrak {p}},{{textbf{E}}}_{{textbf{C}}}big )d{mathfrak {p}},\ {{textbf{L}}}_{{textbf{T}}{textbf{C}}}(tau )-{{textbf{L}}}_{{textbf{T}}{textbf{C}}}(0)=frac{1}{Gamma (omega )}int limits _{0}^{tau }(tau -{mathfrak {p}})^{omega -1}{mathcal {Q}}_{6}big ({mathfrak {p}},{{textbf{L}}}_{{textbf{T}}{textbf{C}}}big )d{mathfrak {p}},\ {{textbf{I}}}_{{textbf{T}}{textbf{C}}}(tau )-{{textbf{I}}}_{{textbf{T}}{textbf{C}}}(0)=frac{1}{Gamma (omega )}int limits _{0}^{tau }(tau -{mathfrak {p}})^{omega -1}{mathcal {Q}}_{7}big ({mathfrak {p}},{{textbf{I}}}_{{textbf{T}}{textbf{C}}}big )d{mathfrak {p}},\ {{textbf{R}}}(tau )-{{textbf{R}}}(0)=frac{1}{Gamma (omega )}int limits _{0}^{tau }(tau -{mathfrak {p}})^{omega -1}{mathcal {Q}}_{8}big ({mathfrak {p}},{{textbf{R}}}big )d{mathfrak {p}}.\ end{array}right. } end{aligned}$$
(14)
The kernels ({mathcal {Q}}_{iota },~(iota =1,...,8)) satisfies the Lipschitz condition and contraction, as demonstrated.
({mathcal {Q}}_{1}) satisfies the Lipschitz condition and contraction if the following condition holds: (0le alpha _{1}(sigma _{3}+sigma _{7})+alpha _{2}(sigma _{4}+sigma _{5}+sigma _{2}+sigma _{5})+beta <1.)
For ({textbf{S}}) and (mathbf {S_{1}},) we have
$$begin{aligned} big Vert {mathcal {Q}}_{1}big (tau ,{{textbf{S}}}big )-{mathcal {Q}}_{1}big (tau ,{{textbf{S}}}_{1}big )big Vert{} & {} =big Vert big (alpha _{1}({textbf{I}}_{{textbf{T}}}+{textbf{I}}_{textbf{TC}})+alpha _{2}({textbf{E}}_{{textbf{C}}}+{textbf{I}}_{{textbf{C}}}+{textbf{I}}_{textbf{TC}}+{textbf{L}}_{{textbf{T}}})+beta big )big ({{textbf{S}}}(tau )-{{textbf{S}}}_{1}(tau )big )big Vert nonumber \ {}{} & {} le big (alpha _{1}big (big Vert {textbf{I}}_{{textbf{T}}}big Vert +big Vert {textbf{I}}_{textbf{TC}})big Vert big )+alpha _{2}big (big Vert {textbf{E}}_{{textbf{C}}}big Vert +big Vert {textbf{I}}_{{textbf{C}}}big Vert +big Vert {textbf{I}}_{textbf{TC}}big Vert +big Vert {textbf{L}}_{{textbf{T}}}big Vert big )+beta big )big Vert {{textbf{S}}}(tau )-{{textbf{S}}}_{1}(tau )big Vert . end{aligned}$$
Suppose ({mathcal {V}}_{1}=alpha _{1}(sigma _{3}+sigma _{7})+alpha _{2}(sigma _{4}+sigma _{5}+sigma _{2}+sigma _{5})+beta ), where ({textbf{I}}_{{textbf{T}}}le sigma _{3},~{textbf{I}}_{textbf{TC}}le sigma _{7},~{textbf{E}}_{{textbf{C}}}le sigma _{4}~{textbf{I}}_{{textbf{C}}}le sigma _{5},~{textbf{I}}_{textbf{TC}}le sigma _{7},~{textbf{L}}_{{textbf{T}}}le sigma _{2}) are a bounded functions. So, we have
$$begin{aligned} big Vert {mathcal {Q}}_{1}big (tau ,{{textbf{S}}}big )-{mathcal {Q}}_{1}big (tau ,{{textbf{S}}}_{1}big )big Vert le {mathcal {V}}_{1}big Vert {{textbf{S}}}(tau )-{{textbf{S}}}_{1}(tau )big Vert . end{aligned}$$
(15)
After obtaining the Lipschitz criterion for ({mathcal {Q}}_{1}), hence, ({mathcal {Q}}_{1}) is a contraction if (0le alpha _{1}(sigma _{3}+sigma _{7})+alpha _{2}(sigma _{4}+sigma _{5}+sigma _{2}+sigma _{5})+beta <1).
In the same manner, ({mathcal {Q}}_{jmath }~(jmath =2,..,7)) satisfy the Lipschitz condition as follows:
$$begin{aligned}{} & {} big Vert {mathcal {Q}}_{2}big (tau ,{{textbf{L}}}_{{textbf{T}}}big )-{mathcal {Q}}_{2}big (tau ,{{{textbf{L}}}_{{textbf{T}}}}_{1}big )big Vert le {mathcal {V}}_{2}big Vert {{textbf{L}}}_{{textbf{T}}}(tau )-{{{textbf{L}}}_{{textbf{T}}}}_{1}(tau )big Vert ,nonumber \ {}{} & {} big Vert {mathcal {Q}}_{3}big (tau ,{{textbf{I}}}_{{textbf{T}}}big )-{mathcal {Q}}_{3}big (tau ,{{{textbf{I}}}_{{textbf{T}}}}_{1}big )big Vert le {mathcal {V}}_{3}big Vert {{textbf{I}}}_{{textbf{T}}}(tau )-{{{textbf{I}}}_{{textbf{T}}}}_{1}(tau )big Vert ,nonumber \ {}{} & {} big Vert {mathcal {Q}}_{4}big (tau ,{{textbf{E}}}_{{textbf{C}}}big )-{mathcal {Q}}_{4}big (tau ,{{{textbf{E}}}_{{textbf{C}}}}_{1}big )big Vert le {mathcal {V}}_{4}big Vert {{textbf{E}}}_{{textbf{C}}}(tau )-{{{textbf{E}}}_{{textbf{C}}}}_{1}(tau )big Vert ,nonumber \ {}{} & {} big Vert {mathcal {Q}}_{5}big (tau ,{{textbf{I}}}_{{textbf{C}}}big )-{mathcal {Q}}_{5}big (tau ,{{{textbf{I}}}_{{textbf{C}}}}_{1}big )big Vert le {mathcal {V}}_{5}big Vert {{textbf{L}}}_{{textbf{T}}}(tau )-{{{textbf{I}}}_{{textbf{C}}}}_{1}(tau )big Vert ,nonumber \ {}{} & {} big Vert {mathcal {Q}}_{6}big (tau ,{{textbf{L}}}_{textbf{TC}}big )-{mathcal {Q}}_{6}big (tau ,{{{textbf{L}}}_{textbf{TC}}}_{1}big )big Vert le {mathcal {V}}_{6}big Vert {{textbf{S}}}(tau )-{{{textbf{L}}}_{textbf{TC}}}_{1}(tau )big Vert ,nonumber \ {}{} & {} big Vert {mathcal {Q}}_{7}big (tau ,{{textbf{I}}}_{textbf{TC}}big )-{mathcal {Q}}_{T}big (tau ,{{{textbf{I}}}_{textbf{TC}}}_{1}big )big Vert le {mathcal {V}}_{7}big Vert {{textbf{S}}}(tau )-{{textbf{S}}}_{1}(tau )big Vert ,nonumber \ {}{} & {} big Vert {mathcal {Q}}_{8}big (tau ,{{textbf{r}}}big )-{mathcal {Q}}_{8}big (tau ,{{textbf{R}}}_{1}big )big Vert le {mathcal {V}}_{8}big Vert {{textbf{R}}}(tau )-{{textbf{R}}}_{1}(tau )big Vert ,end{aligned}$$
where ({mathcal {V}}_{2}=psi _{{textbf{T}}}sigma _{1}-(beta +mu +lambda psi _{{textbf{C}}}+varpi ),~{mathcal {V}}_{3}=mu sigma _{2}+varsigma _{2}eta sigma _{6}+theta _{2}xi sigma _{7}-(beta +varsigma _{3}+zeta _{{textbf{T}}}+delta ),~{mathcal {V}}_{4}=psi _{{textbf{C}}}sigma _{1}-(beta +epsilon psi _{{textbf{T}}}+varphi _{1}+varphi _{2}),~{mathcal {V}}_{5}=varphi _{1}sigma _{4}+rho eta sigma _{6}+theta _{1}xi sigma _{7}-(beta +zeta _{{textbf{C}}}+nu +varphi _{3}),~{mathcal {V}}_{6}=lambda psi _{{textbf{C}}}sigma _{2}+epsilon psi _{{textbf{T}}}sigma _{4}-(beta +zeta _{{textbf{C}}}+rho +xi ),~{mathcal {V}}_{7}=rho sigma _{6}+varsigma _{3}sigma _{3}+nu sigma _{5}-(beta +zeta _{textbf{TC}}+xi ),~{mathcal {V}}_{8}=varpi sigma _{2}+varphi _{2}sigma _{4}+delta sigma _{3}+varphi _{3}sigma _{5}+(1-(varsigma _{1}+varsigma _{2}))eta sigma _{6}+(1-(theta _{1}+theta _{2}))xi sigma _{7}-beta .)
For (jmath =2,...,8,) we find (0le {mathcal {V}}_{jmath }<1,) then ({mathcal {V}}_{jmath }) are contractions. Assume the following recursive pattern, as suggested by system (15):
The COVID-19 pandemic was associated with an increased use of neoadjuvant chemotherapy in US patients with advanced ovarian cancer (OC), according to a study published in Frontiers in Oncology.
The researchers explained that the COVID-19 pandemic caused delays in cancer diagnosis and treatment initiation. In terms of gynecologic cancers, there were cervical cancer screening service discontinuations, treatment initiation delays, and surgical procedure postponements; the pandemic also caused reductions in emergency visits and urgent referrals among patients with suspected cancer.
Because of pandemic-related shortages, the researchers explained that the American College of Surgeons categorized gynecological cancer cases as semi-urgent. Simultaneously, to reduce harm and accommodate delays in ovarian cancer surgery, the Society of Gynecologic Oncology recommended using neoadjuvant chemotherapy during the pandemic.
The researchers explained that although primary cytoreductive surgery is the first-line treatment choice for patients with ovarian cancer, another treatment option is neoadjuvant chemotherapy followed by interval cytoreductive surgery. However, evidence on the impact of neoadjuvant chemotherapy use among US patients with OC during the pandemic has not yet been reported. Consequently, the researchers aimed to assess the association of the COVID-19 pandemic with neoadjuvant chemotherapy use in patients with diagnosed OC.
To reduce harm and accommodate for delays in ovarian cancer surgery, the Society of Gynecologic Oncology recommended using neoadjuvant chemotherapy during the COVID-19 pandemic | Image Credit: catinsyrup - stock.adobe.com
To do so, the researchers analyzed patients who received a diagnosis of incident epithelial OC between January 1, 2017, and June 30, 2021, at Kaiser Permanente Southern California (KPSC), an integrated health care delivery system; they included patients aged 18 to 89 years whose cancer was diagnosed at stage II through stage IV and who were active members of the KPSC health plan at the time of diagnosis.
The researchers identified patients with epithelial type OC between 2017 and 2020 through KPSCs Surveillance, Endpoints, & End Resultsaffiliated cancer registry. Conversely, they identified patients who received their diagnosis in 2021 from KPSCs electronic medical records using International Classification of Diseases, Tenth Revision diagnosis codes and later confirmed by chart review.
Overall, their outcome of interest was neoadjuvant chemotherapy use, while the COVID-19 pandemic period was the exposure of interest; March 4, 2020, was the cut-off to define prepandemic and pandemic periods based on the date of implementation of Californias stay-at-home order. Also, the researchers' covariates of interest included age at cancer diagnosis, cancer stage, KPSC membership years before OC diagnosis, and race and ethnicity.
Of 566 patients identified with stage II through stage IV OC, 406 (71.7%) received their diagnosis during the prepandemic period and 160 (28.3%) during the pandemic period; most patients' (85.5%) cancer was diagnosed at either stage III or stage IV OC. The researchers noted that patients who received their diagnosis during the pandemic era were slightly younger than those who received their diagnosis during the prepandemic period (mean age, 62.7 vs 64.9 years; P = .07).
They found that 50.5% of the overall study population received neoadjuvant chemotherapy, which included 58.7% and 47.3% who received their diagnosis during the pandemic and prepandemic periods, respectively (P = .01). The mean (SD) time from diagnosis to neoadjuvant treatment initiation among the population was 22.3 (24.5) days, with no differences observed by pandemic periods (P = .17).
In the unadjusted model, the researchers found that patients who received their diagnosis in the pandemic period were 24% more likely to receive neoadjuvant chemotherapy (risk ratio [RR], 1.24; 95% CI, 1.04-1.47), as were those with stage III (RR, 5.42; 95% CI, 2.64-11.12) and stage IV (RR, 9.07; 95% CI, 4.44-18.50) OC compared with stage II OC.
However, after adjusting for age, cancer stage, comorbidity index, and race and ethnicity, the researchers reported that patients with a diagnosis in the pandemic period were 29% more likely to receive neoadjuvant chemotherapy (RR, 1.29; 95% CI, 1.12-1.49). Also, in terms of race, Hispanic (RR, 1.46; 95% CI, 1.13-1.88) and non-Hispanic White (RR, 1.27; 95% CI, 1.04-1.54) patients were 46% and 27%, respectively, more likely to receive neoadjuvant chemotherapy during the pandemic period.
The researchers acknowledged their studys limitations, one being that they did not have information on neoadjuvant therapy dose, meaning they were unable to assess if the COVID-19 pandemic affected the recommended neoadjuvant chemotherapy dose in patients with OC. Also, their study population consisted of insured patients within KPSC, so the findings may not be generalizable to other cohorts. Despite these limitations, the researchers suggested areas for future research based on their findings.
Future studies are needed to assess the impact of the pandemic on treatment patterns and cancer outcomes, including response to cancer treatments and survival in patients with ovarian cancers, the authors concluded.
Reference
Mukherjee A, Shammas N, Xu L, et al. Impact of the coronavirus disease 2019 pandemic on neoadjuvant chemotherapy use in patients diagnosed with epithelial type ovarian cancer.Front Oncol. 2024;14:1290719. doi:10.3389/fonc.2024.1290719
