Category: Covid-19

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Cognitive decline ‘measurable’ in those with lasting COVID symptoms – Medical News Today

March 11, 2024

People who had an infection with SARS-CoV-2, the virus that causes COVID-19, showed measurable cognitive impairment compared with those who have not had COVID-19, a new study from Imperial College of London in the United Kingdom shows.

While the cognitive and memory deficits were small for people who had mild infections or did not go on to develop long COVID, the effect of more severe infections that resulted in admission to intensive care units was associated with a more pronounced effect.

The researchers found that vaccination had a protective effect, however.

The study, published in The New England Journal of Medicine, used a multiple regression analysis to focus on the results of 112,964 adults in England.

Study participants who had recovered from COVID-19 and whose symptoms resolved in less than 4 weeks or at least 12 weeks had small cognitive deficits compared with those in the noCOVID-19 group, who had not ever been infected with the SARS-CoV-2 virus, or had unconfirmed infection.

People who had symptoms occurring over 12 weeks after recovery from the initial infection such as chronic fatigue, respiratory difficulty, or neurological issues had greater cognitive deficits, as did people who had become infected with early variants of the SARS-CoV-2 virus.

Even though the researchers did not attach a long COVID diagnosis to these participants, such persistent symptoms are common in people with this post-viral condition.

By using an innovative cognitive test which has also been completed by people who did not have COVID-19, this important and well-conducted study provides the first accurate quantification of the scale of cognitive deficits in people who had COVID-19, Dr. Maxime Taquet, NIHR Academic Clinical Fellow in Psychiatry, University of Oxford, who was not involved with the study, commented.

Dr. Taquet added that the disparity was the most obvious at the extremes:

The risk of having more severe cognitive problems was almost twice as high in those who had COVID-19 compared to those who did not, and three times as high in those who were hospitalised with COVID-19. A few key questions remain open: Do these cognitive problems persist or improve in the years after infection? What is their biological explanation? How does it affect peoples everyday life and their ability to work?

The mental and psychological effects of COVID-19 have been the focus of study since evidence emerged they were linked to SARS-CoV-2 infections in 2020.

Long COVID has been associated with longer periods of anxiety, poor memory, or struggles with concentration or thinking, but this study did not draw any significant conclusions about the neurocognitive impact of long COVID.

The authors emphasize that further study is required here.

We focused on symptoms that had persisted for at least 12 weeks, and we did not depend on a diagnosis of long Covid, which may require clinical assessment, the study authors wrote. In the absence of baseline cognitive data before infection, we could not assess cognitive change, and the observational nature of the data means that we could not infer causality.

Dr. Scott Kaiser, MD, a board-certified geriatrician and director of Geriatric Cognitive Health for the Pacific Neuroscience Institute at Providence Saint Johns Health Center in Santa Monica, CA, who was not involved in the study, told Medical News Today that it helps fill out some of the ongoing uncertainty around brain fog.

This study reinforces the idea that the experience of cognitive impairment following COVID is quite frequent and is striking in the extent to which this impairment may persists for many months following infection, even in cases that were not that severe, Dr. Kaiser said.

As far as the true long-term consequences its just too soon to tell. While it appears that most cases gradually resolve even if it takes several months its unclear if a subset of people may continue to have lingering symptoms across an even longer time horizon. Similarly, it remains unknown whether this could actually increase ones ultimate risk of a major neurocognitive disorder dementia later in life.

Dr. Scott Kaiser

The study found that participants who had received two or more vaccinations and had minimal repeat infections of COVID-19 had less cognitive decline.

Similarly, those who were infected with later variants of SARS-CoV-2 had better cognitive abilities than those who were infected during the alpha stage of the pandemic.

The authors of the study also note that the delta variant occurred in a highly vaccinated population.

Dr. Kaiser advised that anyone experiencing brain fog should reach out to a medical professional and seek guidance, given that at this stage in the pandemic there are more resources available and better opportunities to understand what long-term effects the SARS-CoV-2 virus has on cognition.

Because this is all a relatively new phenomena the overall understanding continues to evolve. There are many potential pathways reduced oxygen delivery, reduced blood flow, an attack by the immune system on healthy brain cells or an actual invasion of infectious cells into the brain, or inflammation affecting brain cells and a combination of multiple factors may be at play, Dr. Kaiser said.

Additional factors associated with having COVID may indirectly contribute as well increased stress and anxiety, depressed mood, changes in diet, medications, decreased physical activity, poor sleep quality, or even social isolation and feelings of loneliness, he added.

And while its possible that certain cases have very different causes, overall, there does appear to be a clear physiologic pathway by which infection with the virus induces an inflammatory response which actually causes inflammation in the brain neuroinflammation which can, in turn, can cause cognitive dysfunction.

Dr. Scott Kaiser

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Today Is Your Last Chance to Order Free COVID-19 Tests – TIME

March 11, 2024

March 8, 2024 1:33 PM EST

March 8 is your last day to order free rapid COVID-19 tests, as the U.S. government prepares to suspend its at-home test program. Households in the U.S. can receive at least four rapid antigen tests, free of charge, simply by entering a name and address.

The federal government has been shipping free tests since early 2022. The program was suspended for a few months in 2023, after the U.S. government stopped considering COVID-19 a public-health emergency, but was reinstated this past fall, as new variants began to spread and cause upticks in infections and hospitalizations. Now, the free testing initiative is again coming to an end.

Today is the last day the U.S. Postal Service will accept orders, here. Households that have not ordered any tests since the program was reinstated in September 2023 can place two orders of four tests each, while those that have ordered more recently can get one set of four tests.

Rapid tests will also remain for sale in retail stores, and may be available for free through certain community organizations, after March 8.

The end of the government's free testing program is the latest in a string of public-health decisions that signal officials are moving on from COVID-19. On March 1, the U.S. Centers for Disease Control and Prevention ended its long-standing recommendation that people isolate themselves from others for at least five days when they have COVID-19. Instead, the agency now recommends that people stay home until theyve been fever-free for at least 24 hours and their other symptoms are improvingan approach that brings COVID-19 guidance in line with that of the flu and other common respiratory diseases.

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Today Is Your Last Chance to Order Free COVID-19 Tests - TIME

COVID-19, the virus that shut down everything | Cochise County – myheraldreview.com

March 11, 2024

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COVID-19, the virus that shut down everything | Cochise County - myheraldreview.com

COVID-19 outbreak at SVPD during pandemic affected personnel, procedures – myheraldreview.com

March 11, 2024

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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, 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COVID-19 outbreak at SVPD during pandemic affected personnel, procedures - myheraldreview.com

It’s been 4 years since COVID hit Michigan. For Long COVID patients, the pandemic isn’t over. Michigan Advance – Michigan Advance

March 11, 2024

Four years have passed since Gov. Gretchen Whitmer declared a state of emergency to address the COVID-19 pandemic on March 10, 2020. But the disease remains more than a memory, especially for those whose lives are continually impacted by the illness.

Robert McCann, 46, was exposed to COVID-19 at a Lansing-area veterinary clinic which was tied to an outbreak of the disease in June 2020. About a day after testing positive, McCann, the executive director of the K-12 Alliance of Michigan, said he started to feel sick.

At the time, it wasnt anything, like, horrible and the symptoms went away probably after a week or so, McCann said. I figured, OK, that wasnt too bad, Ive moved on.

In the fall, McCanns symptoms returned and persisted, despite testing negative for the illness. More than three and a half years later, McCann says he still faces issues with severe fatigue, nerve pain and brain fog from Long COVID.

Overall, you know, I consider myself one of the more fortunate ones, McCann said.

Theres days I struggle a little more than others to be sure, but you know, Im able to function reasonably well the majority of the time and theres people out there that arent, McCann said.

But describing his fatigue symptoms to others has proved difficult.

Theres a connotation there, or at least that you worry about sometimes, that people just think youre lazy, McCann said.

There are nights where I will be so tired that I will sleep for 15 hours, and I still cant wake up in the morning. Just I have no energy and its hard to really describe that to people, McCann said. There are days where its hard to do your job. Theres days where its hard to, you know, do the things you enjoy doing.

Prior to developing Long COVID, McCann said hed done quite a bit of traveling and hiking.

Ive been fortunate to kind of get all over the world, he said. In like 2019, I did a hike through the Austrian Alps that was pretty astonishing, quite frankly.

Im still fortunate that I can do some of that, but there are days where its like, yeah, thats not going to happen today, McCann said.

As far as seeking solutions for Long COVID, You name it. Ive probably tried it, McCann said. From clinical treatments, to supplements to prescription medication, none have had a major impact on his condition.

While McCann has received his COVID-19 vaccine and boosters, he said it has not helped relieve his symptoms in the way others with Long COVID have reported.

There are some people that do seem to have found some relief from that from various things, and Im certainly glad to see that. But for me, it just wasnt the case, McCann said.

According to the World Health Organization, there have been more than 7 million reported deaths worldwide from COVID-19 since Dec. 31, 2019, with 1.2 million deaths in the United States. As of March 5, Michigan has reported 44,654 deaths from the disease.

Vaccines became widely available by spring 2021, and now 70% of the Michigan population is fully vaccinated, the same as the U.S. rate.

Visible signs of the pandemic have all but disappeared. Its been almost three years since Whitmer removed capacity limits on indoor and outdoors events and ended the states masking requirement in June 2021.

And thankfully, the number of COVID deaths has been ramping down. Although the state recorded more than 9,000 deaths among confirmed cases of COVID-19 in 2022, that number dropped to just over 2,300 in 2023.

But while the World Health Organization declared an end to the global emergency posed by the virus on May 5, 2023, the body noted this does not mean the pandemic is over.

Long COVID continues to present challenges for medical professionals working to treat the condition, despite breakthroughs in vaccines and antiviral medications since the pandemic began. An August 2022 Brookings Institution report, which analyzed Census Bureau survey information, estimated that 16 million people of working age in the U.S. suffer from Long COVID.

Arianna Perra, a psychologist for Mary Free Bed at Munson Healthcare in Traverse City who leads a Long COVID recovery group, said the tricky thing about treating the condition is that it has around 200 documented symptoms.

Everyones profile is slightly different. The most common ones that we see in the COVID rehab setting and psychology setting are related to fatigue and brain fog, like cognitive dysfunction, Perra said.

According to an article published in Nature Reviews Microbiology, many Long COVID patients experience dozens of symptoms across multiple organ systems. The condition also encompasses a number of adverse outcomes, with common new-onset conditions including Type 2 diabetes, myalgic encephalomyelitis/chronic fatigue syndrome, cardiovascular, thrombotic and cerebrovascular disease and dysautonomia, particularly POTS, a condition that can cause a fast heart rate, dizziness and fatigue while transitioning from laying down to standing up.

A 2024 University of Michigan study also found that individuals with a chronic overlapping pain condition were at greater risk for developing Long COVID conditions.

According to the National Institutes of Health (NIH), individuals who experienced severe illness from COVID-19, people who experienced multisystem inflammatory syndrome during or after their illness, and people with underlying health conditions like diabetes, asthma, autoimmune diseases or obesity are more likely to develop Long COVID. Women, people of color, sexual and gender minorities and people without college degrees are also more likely to have Long COVID.

Studies have also found that the COVID-19 vaccine dramatically lowers the risk of developing Long COVID.

In treating Long COVID, Megan Jabin, an occupational therapist for Mary Free Bed, emphasized the importance of a multidisciplinary approach.

Even if maybe the patient is coming in and then only, originally, has a referral for physical therapy, the other disciplines are always looking out for can we have speech therapy or occupational therapy or psychology involved based on what the patients main concerns are, based on what their goals are, and what their symptoms are, Jabin said.

While every Long COVID patient presents symptoms differently, one of the main attributes is that patients are often deconditioned, have a difficult time maintaining their stamina and have overall weakness, Jabin said.

In a multidisciplinary treatment, physical therapists will usually focus on strengthening and endurance as it relates to a patients mobility, while a speech-language pathologist will focus on cognition and brain fog and memory issues. An occupational therapist will focus more on helping patients achieve their day to day independence including dressing, bathing and grocery shopping, Jabin said. In some cases, getting back to driving has also been an issue.

All of these disciplines, including psychology, work together, especially when a patient is more receptive to a particular treatment, or education from their therapists, Jabin said.

For psychological treatment, Perra said Long COVID is approached from a rehabilitation perspective similar to treatment for a stroke or a major car accident.

That also includes helping patients who may be frustrated with the lifestyle changes included as part of their treatment.

Figuring out how to pace is a really important part of the rehab process. And that is tackled with [physical therapy], right, so figuring out how to find the right dose of movement so that we can get stronger and build our tolerance for exercise and our energy stores, Perra said.

From a psychological perspective, how do I deal with the fact that I might be really annoyed or irritated that I have to pace myself, or I might fall into the trap of thinking, Well, Ill just push myself through it and then Ill deal with it later, and then being in an extreme amount of fatigue and being down for the count for a few days also impacts my mental health and my relationships with other people, Perra added.

Its not just finding the right dose of movement to help people build their strength and stamina. Addressing barriers and thought processes, and looking at how treatment can impact relationships with others, and how to receive support from people when a patient may need to rest, Perra said.

The hardest thing about making any behavioral change is not the act. It is what is between our ears, right? Its our cognitive processes, its our expectations, assumptions, predictions, how we compare ourselves to our pre-COVID lives. And so psychology has a lot of skills to be able to recognize when were caught in unhelpful loops and to manage that, Perra said.

When treating brain fog, treatment focuses on strategies to address sympathetic nervous system responses, Perra said.

A lot of folks were told or given the message that it can't be that bad, or it's all in your head or you know, I had COVID too and I recovered just fine. So I think there's a lot of folks that were coming to our program feeling like they weren't believed.

Arianna Perra, psychologist for Mary Free Bed at Munson Healthcare in Traverse City

Were understanding more and more about how the nervous system is affected by COVID in the long run. Its not just that people are anxious, right? This isnt caused by anxiety. There are functional changes in how our body regulates itself. So learning strategies to downshift, how to stimulate our rest and digest response, those are really specific health psychology strategies we can learn, Perra said.

One of the most effective ways someone can counteract their bodys stress response is through controlling the rate and rhythm of their breath through breathing exercises and learning how to decrease muscle tension, Perra said.

The life-changing nature of Long COVID can also bring mental health symptoms, Perra said. Depression is fairly common in patients, as well as anxiety, in regard to symptoms getting worse or being reexposed to COVID-19.

Its also not uncommon to see traumatic responses from being hospitalized or from the active illness phase, Perra said.

From a mental health perspective, not only are we sort of mourning the loss of the life we thought we would have, at this point after COVID were also dealing with some of the mood changes, sleep changes, how we think about things changes. So psychology is an integral part to that treatment plan, Perra said.

How Long COVID has become the silent pandemic

Additionally, research suggests COVID-19 may impact serotonin production, so the illness is not only disrupting peoples lives in functional ways, but changing the way their bodies produce hormones and chemicals needed to effectively manage their mood, Perra said.

While theres still a lack of research surrounding Long COVID, Perra said one of the biggest changes that has changed since she began treating the condition in 2021 was the amount of evidence in support of symptoms reported by patients.

A lot of folks were told or given the message that it cant be that bad, or its all in your head or you know, I had COVID, too, and I recovered just fine. So I think theres a lot of folks that were coming to our program feeling like they werent believed, Perra said.

We still lack evidence. We still lack research. Theres more and more coming out. And Im really heartened by that, Perra said. Being able to tell someone, yes, this is why we think this is happening for you and theres research to support that, its really relieving and validating for patients to hear that.

Looking at the Long COVID recovery group, theres a powerful aspect to being around others who may not share the exact same story, but can understand someones frustration in not being able to get up from the couch and load a dishwasher when they were previously able to run a household, Perra said.

While we continue to understand Long COVID better, McCann said there are likely more people realizing they have some form of the illness.

As we start figuring this out, you know, I think the best thing that people can do is just have empathy for those struggling with things, McCann said.

Everybodys going through something, right? If someones just like, You know, Im not feeling like Ive got the energy for it today, they dont need a motivational speech from you. They just need, You know, I get it. No problem, McCann said.

One of the most difficult parts of treating Long COVID is the slow progression and the different impacts the condition has on people, Jabin said.

Perra also noted that the rate of improvement differs between patients because of how their symptom profile may be impacted by other health conditions.

This is what I tell folks at the beginning of our group treatments too: People get better. It takes time. Its up and down. Its different. I mean, this is a major medical event in your life, and we have to treat it as such. So its not that theres no guarantee that we can go back to being the same person that we were before you had COVID, just like theres no guarantee that youre going to get back the same level of functioning that you had before your stroke, but there could be, Perra said.

If there's a way to be any less empathetic than denying the very thing that causes so many people to be suffering right now, I don't know what that is.

In her treatment sessions, Jabin said she works with patients on what they enjoy doing before they began experiencing Long COVID symptoms, using small goals to build toward a larger goal, like walking around their neighborhood, going shopping or seeing a movie.

McCann said he is grateful he has been able to find a middle ground with his body to where he is able to travel and go hiking.

There are days where, yeah, Im not climbing a mountain, but I can at least enjoy the atmosphere of where Im at, wander around the city a little bit or something. And, you know, on a good day, I can do more, McCann said.

Its not 100% of how you used to live your life and the things you used to enjoy, but you get to still do them at a level that still makes you happy, McCann said.

McCann also shared frustration at COVID-19 denial.

If theres a way to be any less empathetic than denying the very thing that causes so many people to be suffering right now, I dont know what that is, he said.

On March 1, the Centers for Disease Control and Prevention (CDC) updated its isolation recommendations for COVID-19 and other respiratory viruses, reducing isolation to 24 hours if symptoms have improved and if a fever is no longer present without the use of fever-reducing medication.

With the decision drawing concern and criticism from medically vulnerable individuals, with Long COVID activists arguing the decision ignoring the risk of post-COVID-19 symptoms and the lack of a clear cure.

While it is a laudable goal to have guidelines that are streamlined across common respiratory viruses that are easier to understand, these new guidelines fail to accurately reflect the reality of some of the key differences between COVID, the flu, and RSV, Maria Town, president and CEO of the American Association of People with Disabilities said in a statement.

Efforts to treat COVID more like the flu fail to recognize that COVID is not the flu, COVID is COVID a virus that, per the CDCs own resources, is more contagious than the flu, can cause more severe illness than the flu, causes more post-viral illness than the flu, and is infectious to others longer than the flu, Town said.

There's days I struggle a little more than others to be sure, but you know, I'm able to function reasonably well, you know, the majority of the time and there's people out there that aren't.

As researchers continue to search for a treatment for Long COVID, McCann said another big question was the long term impact. He also called for a reevaluation of the health care system.

I cant tell you how frustrating its been to have doctors want to do various tests on me and my insurance company say, Well, you can do it, but were not paying for it because you dont have a disease that meets the criteria for that, McCann said

I am fortunate that Im in a position where I can still move forward and pay things out of pocket if I need to, but if I were to total up the bills that I pay in the last three years dealing with this, it would be shocking, McCann said.

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It's been 4 years since COVID hit Michigan. For Long COVID patients, the pandemic isn't over. Michigan Advance - Michigan Advance

A mathematical model for the transmission of co-infection with COVID-19 and kidney disease | Scientific Reports – Nature.com

March 11, 2024

We studied how COVID-19 and kidney disease impact each other by examining them separately first. After understanding each individually, theyre combined to see the overall effect. The goal is to ensure the combined results are accurate and logical.

COVID-19-only model: when we exclude kidney disease infections, we can formulate a COVID-19-specific sub-model from the full disease model; we get ({I}_{k}=0,{I}_{kc}=0,{I}_{kd}=0,{I}_{kdc}=0)

$$begin{gathered} frac{dS}{{dt}} = Delta - frac{{phi_{1} I_{c} }}{N}S - mu S hfill \ frac{{dI_{c} }}{dt} = frac{{phi_{1} I_{c} }}{N}S - tau_{1} I_{c} - mu I_{c} hfill \ frac{dR}{{dt}} = tau_{1} I_{c} - mu R hfill \ end{gathered}$$

(2)

All the populations of the system with positive initial conditions are nonnegative.

Assume ({text{S}}left(0right)>0,{{text{I}}}_{{text{C}}}(0)>0,{text{R}}(0)>0) are positive for time ({text{t}}> 0) and for all nonnegative parameters.

From the initial condition, all the state variables are nonnegative at the initial time; then, (mathrm{t }> 0)

To show the solutions of the model, as it is positive, first, we take (frac{{text{dS}}}{{text{dt}}}) from equation

$$frac{{text{dS}}}{{text{dt}}}=Delta -frac{{upphi }_{1}{{text{I}}}_{{text{c}}}}{{text{N}}}{text{S}}-mathrm{mu S}$$

$$frac{{text{ds}}}{{text{dt}}}=Delta -left(frac{{upphi }_{1}{{text{I}}}_{{text{c}}}}{{text{N}}}+upmu right){text{s}}$$

$${text{S}}left({text{t}}right)={text{S}}(0){text{exp}}left(-underset{0}{overset{{text{t}}}{int }}left{frac{{upphi }_{1}{{text{I}}}_{{text{c}}}}{{text{N}}}+upmu right}{text{du}}right)+underset{0}{overset{{text{t}}}{int }}Delta mathrm{ exp}(underset{0}{overset{{text{x}}}{int }}left{frac{{upphi }_{1}{{text{I}}}_{{text{c}}}}{{text{N}}}+upmu right}{text{du}})mathrm{dx }times {text{exp}}left(-underset{0}{overset{{text{t}}}{int }}left{frac{{upphi }_{1}{{text{I}}}_{{text{c}}}}{{text{N}}}+upmu right}{text{du}}right)>0$$

Accordingly, all the variables are nonnegative in ([0,{text{t}}]), so ({text{S}}left(0right)>0,) similarly we can show ({{text{I}}}_{{text{C}}}(0)>0,{text{R}}(0)>0).

The dynamical system represented by the COVID-19 submodel remains positively invariant within the closed invariant set defined by ({rm Z}_{c} = left{left( S,{I}_{c},Rright)epsilon {R}^{3}+ : Nle frac{Delta }{mu }right})

An invariant region is identified to demonstrate that the solution remains within certain bounds. This invariant region provides a constraint ensuring that the solution does not exceed these limits; we have

$$frac{dN}{dt}=frac{dS}{dt}+frac{{dI}_{C}}{dt}+frac{dR}{dt}$$

$$frac{dN}{dt}=Delta -frac{{phi }_{1}{I}_{c}}{N}S-mu S+frac{{phi }_{1}{I}_{c}}{N}S-{tau }_{1}{I}_{c}-mu {I}_{c}+{tau }_{1}{I}_{c}-mu R$$

$$frac{dN}{dt}=Delta -left(S+{I}_{c}+Rright)mu$$

$$frac{dN}{dt}=Delta -Nmu$$

$$Nleft(tright)=Nleft(0right){e}^{-mu t}+frac{Delta }{mu }(1-{e}^{-mu t})$$

As,(tto infty), we get (0le Nle frac{Delta }{mu }), the theory of differential equation27 in the region.

({rm Z}_{c} = {left( S,{I}_{c},Rright)epsilon {R}^{3}+ : Nle frac{Delta }{mu } }), For the autonomous system representing the COVID-19-only model, given by (2), any solution that starts in ({Z}_{c}) will stay within ({Z}_{c}) for all (tge 0.) Based on Cheng et al., this means that ({Z}_{c}) acts as a stable and attractive region. Therefore, according to Naicker et al., the dynamics of model (2) are both mathematically sound and relevant to epidemiology, and it is appropriate to study its tabiliz within ({Z}_{c}.)

Stability analysis of equilibrium states: In the only COVID-19 sub-model, the equilibrium state is reached when the following conditions are met

$$frac{dS}{dt}=frac{{dI}_{c}}{dt}=frac{dR}{dt}=0$$

For the isolated COVID-19 model represented by the system (2), the state without any active disease (termed the disease-free equilibrium or DFE) is derived by setting each component of the system (2) to zero. At this DFE, neither infections nor recoveries are present.

Therefore, for the stand-alone COVID-19 model (2), the DFE is described ({Omega }_{c}=left(S,{I}_{C},Rright)=(frac{Delta }{mu },mathrm{0,0}))

The sub-models basic reproduction number is the average number of secondary infections caused by a single COVID-19-infected person in a totally susceptible population. The system (2) calculates it using the next-generation matrix.

$${R}_{oc}=frac{{phi }_{1}}{({tau }_{1}+mu )}$$

(3)

The basic reproduction number, ({R}_{0c}), represents the average number of people one infected individual is expected to infect over their entire infectious period within a completely susceptible population.

For the kidney disease sub-model, the point of equilibrium without the disease is represented as ({Omega }_{0c}), remains stable as long as the basic reproduction number ({R}_{oc}) is less than 1.

The Jacobian matrix is tabiliz to ascertain the equilibrium points local stability. For sub-model (2), the Jacobian matrix is formulated as (J=left(begin{array}{c}frac{partial {f}_{1}}{partial S} frac{partial {f}_{1}}{partial {I}_{C}} frac{partial {f}_{1}}{R}\ frac{partial {f}_{2}}{partial S} frac{partial {f}_{2}}{partial {I}_{C}} frac{partial {f}_{2}}{R} \ frac{partial {f}_{3}}{partial S} frac{partial {f}_{3}}{partial {I}_{C}} frac{partial {f}_{3}}{R}end{array}right))

$$J=left(begin{array}{c}-frac{{varnothing }_{1}{I}_{c}}{N}-mu frac{{varnothing }_{1}S}{N} ,,,,,,,0\ frac{{varnothing }_{1}{I}_{c}}{N} -{tau }_{1}-mu ,,,,,,,,,,0 \ 0 ,,,,,,,,,,{tau }_{1} -mu end{array}right)$$

The Jacobian matrix for the sub-model, when evaluated at the disease-free equilibrium point ({Omega }_{0c}), is expressed as

$$J({Omega }_{0c})=left(begin{array}{c}-mu ,,,,,,,,frac{{varnothing }_{1}Delta }{mu N} ,,,,,,,0 \ 0 ,,,,,-left({tau }_{1}+mu right) ,,,,,,,0\ 0 ,,,,,,,,{tau }_{1} -mu end{array}right)$$

In this context, one of the eigenvalues for ({Omega }_{0c}) is (lambda =-mu). The other eigenvalues can be conveniently derived from the associated submatrix.

$${J}_{1}=left(begin{array}{cc}-left({tau }_{1}+mu right)& 0\ {tau }_{1}& -mu end{array}right)$$

To confirm the local stability of the disease-free equilibrium point, two conditions need to be met:

(i) The trace of ({J}_{1}) should be less than zero. (ii) The determinant of ({J}_{1}) should be greater than zero.

The trace is Trc (left({J}_{1}right)=-({tau }_{1}+2mu ),) which is less than zero.

$${text{det}}left({J}_{1}right)=left({tau }_{1}+mu right)mu >0$$

As a result, the COVID-19 sub-models disease-free equilibrium point is asymptotically stable.

Theorem 5. The COVID-19 submodel has an isolated endemic equilibrium point if ({R}_{0c}>1).

The endemic equilibrium point of the COVID-19 sub-model is the solution of the system of equation in (4).

$$Delta -left({{text{f}}}_{{text{c}}}+mu right)S=0$$

$${f}_{c}S-left({tau }_{1}+mu right){I}_{c}=0$$

$${tau }_{1}{I}_{c}-mu R=0$$

To solve this system of equations,

we express it in terms of

$${f}_{c}^{*}=frac{{phi }_{1}{I}_{c}^{*}}{N}$$

(4)

$${S}^{*}=frac{Delta }{{f}_{c}^{*}+mu }, {I}_{c}^{*}=frac{{f}_{c}^{*}S}{({tau }_{1}+mu )}, {R}^{*}=frac{{tau }_{1}{I}_{c}*}{mu },$$

(5)

Now,

$${I}_{c}^{*}=frac{{f}_{c}^{*}S}{({tau }_{1}+mu )}$$

$${I}_{c}^{*}=frac{Delta {f}_{c}^{*}}{({tau }_{1}+mu )({f}_{c}^{*}+mu )}$$

So, using (4)

$${f}_{c}^{*}=frac{{phi }_{1}{I}_{c}^{*}}{N}$$

$${f}_{c}^{*}=frac{{phi }_{1}mu }{left({tau }_{1}+mu right)}-mu$$

$${f}_{c}^{*}=mu (frac{{phi }_{1}}{left({tau }_{1}+mu right)}-1)$$

$${f}_{c}^{*}=mu ({R}_{0c}-1)$$

The conclusion drawn is that the infection force ({f}_{c}^{*}) will be positive at the endemic equilibrium point ({Omega }_{0c}) only when ({R}_{oc}>1). With this, we have effectively demonstrated the related theorem.

Analysis of the Global Stability Analysis for the Endemic Equilibrium Point.

The endemic equilibrium point ({Omega }_{c}) undergoes a global stability analysis using the Lyapunov function method. To facilitate this analysis, we establish the

$$L=frac{1}{2}((S-{S}^{*})+left({I}_{c}-{I}_{c}^{*}right)+{left(R-{R}^{*}right))}^{2}$$

(6)

The Lyapunov function L consistently maintains a positive value and only becomes zero at the endemic equilibrium point and differentiating with respect to time (t)

$$begin{gathered} frac{{{text{dL}}}}{{{text{dt}}}} = left{ {left( {{text{S}} - {text{S}}^{*} } right) + left( {{text{I}}_{{text{c}}} - {text{I}}_{{text{c}}}^{*} } right) + left( {{text{R}} - {text{R}}^{*} } right)} right}left( {frac{{{text{dS}}}}{{{text{dt}}}} + frac{{{text{dI}}_{{text{c}}} }}{{{text{dt}}}} + frac{{{text{dR}}}}{{{text{dt}}}}} right) hfill \ = left{ {left( {{text{S}} + {text{I}}_{{text{c}}} + {text{R}}} right) - left( {{text{S}}^{*} + {text{I}}_{{text{c}}}^{*} + {text{R}}^{*} } right)} right}left( {Delta - {mu N}} right) hfill \ = frac{{left( {{mu N} - Delta } right)}}{{upmu }}left( {Delta - {mu N}} right) hfill \ = - frac{{left( {Delta - {mu N}} right)^{2} }}{{upmu }} hfill \ frac{{{text{dL}}}}{{{text{dt}}}} le 0 hfill \ end{gathered}$$

For ({R}_{oc}>1), the endemic equilibrium point exists, leading to (frac{dL}{dt}) is less than zero. It seems that the function L appears as a clear-cut Lyapunov function, suggesting that the endemic equilibrium point reaches asymptotic and global stability. From a biological perspective, this signifies that COVID-19 has remained prevalent in the community over a prolonged duration.

We conducted a sensitivity analysis of parameters within the COVID-19 sub-model. The behavior of the model in response to modest changes in a parameters value is known as the parameters sensitivity and is tabilize by the symbol ({phi }_{1}). It can be expressed as

$${R}_{oc}=frac{{phi }_{1}}{left({tau }_{1}+mu right)}$$

$${S}_{{phi }_{1}}=frac{partial {R}_{0c}}{partial {varnothing }_{1}} frac{{phi }_{1}}{{R}_{0c}}=frac{1}{left({tau }_{1}+mu right)} frac{{phi }_{1}}{frac{{phi }_{1}}{left({tau }_{1}+mu right)}}=+1$$

$${S}_{mu }=frac{partial {R}_{0c}}{partial mu } frac{mu }{{R}_{0c}}= - frac{{phi }_{1}}{{left({tau }_{1}+mu right)}^{2}} frac{mu }{frac{{phi }_{1}}{left({tau }_{1}+mu right)}}=-frac{mu }{(mu +{tau }_{1})}$$

$${S}_{{tau }_{1} }=frac{partial {R}_{0c}}{partial {tau }_{1}} frac{{tau }_{1}}{{R}_{0c}}=-frac{{phi }_{1}}{{left({tau }_{1}+mu right)}^{2}} frac{{tau }_{1}}{frac{{phi }_{1}}{left({tau }_{1}+mu right)}}=-frac{{tau }_{1}}{left({tau }_{1}+mu right)}$$

Table 1 displays the data for the sensitivity indices related to the sole COVID-19 sub-model. This sub-model analysis reveals that the COVID-19 contact rate is ({phi }_{1}), play a significant role in intensifying the viruss spread. This trend results from an upsurge in secondary infections when these parameters increase, as highlighted by (Martcheva 2015). Conversely, parameters such as ({tau }_{1}) and (mu) have a diminishing effect, meaning an uptick in their values could reduce the infection rate. A visual depiction of the sensitivity indices for ({R}_{oc}) is showcased in Fig.2.

The graphical depiction of the sensitivity indices concerning the primary reproduction number (({R}_{oc})) parameters are shown in the COVID-19 sub-model.

Kidney disease-only sub-model from the co-infection model, we get ({I}_{c}=0,{I}_{kc}=0,{I}_{kdc}=0,R=0)

$$begin{gathered} frac{dS}{{dt}} = Delta - f_{k} S - mu S hfill \ frac{{dI_{k} }}{dt} = f_{k} S - sigma_{1} I_{k} - mu I_{k} hfill \ frac{{dI_{kd} }}{dt} = sigma_{1} I_{k} - mu I_{kd} hfill \ end{gathered}$$

(7)

All the populations of the system with positive initial conditions are nonnegative.

Assume ({text{S}}(0) > 0,{{text{I}}}_{{text{k}}}(0) >0,{{text{I}}}_{{text{k}}}(0) > 0) are positive for time (mathrm{t }>0) and all nonnegative parameters.

From the initial condition, all the state variables are nonnegative at the initial time; then, (mathrm{t }>0).

To show the solutions of the model, as it is positive, first, we take (frac{{text{dS}}}{{text{dt}}}) from equation

$$begin{gathered} frac{{{text{dS}}}}{{{text{dt}}}} = Delta - frac{{phi_{2} {text{I}}_{{text{k}}} }}{{text{N}}}{text{S}} - {mu S} hfill \ frac{{{text{dS}}}}{{{text{dt}}}} = Delta - left( {frac{{phi_{2} {text{I}}_{{text{k}}} }}{{text{N}}} + {upmu }} right){text{S}} hfill \ {text{S}}left( {text{t}} right) = {text{S}}left( 0 right)exp left( { - mathop smallint limits_{0}^{{text{t}}} left{ {frac{{phi_{2} {text{I}}_{{text{k}}} }}{{text{N}}} + {upmu }} right}{text{du}}} right) + mathop smallint limits_{0}^{{text{t}}} Delta {text{ exp}}(mathop smallint limits_{0}^{{text{x}}} left{ {frac{{phi_{2} {text{I}}_{{text{k}}} }}{{text{N}}} + {upmu }} right}{text{du}}){text{dx }} times exp left( { - mathop smallint limits_{0}^{{text{t}}} left{ {frac{{phi_{2} {text{I}}_{{text{k}}} }}{{text{N}}} + {upmu }} right}{text{du}}} right) > 0 hfill \ end{gathered}$$

(8)

Hence ({text{S}}(0)>0), similarly we can prove ({{text{I}}}_{{text{k}}}(0) >0,{mathrm{ I}}_{{text{k}}}(0) > 0).

The dynamical system (7) is positively invariant in the closed invariant set.

$${rm Z}_{k} = {left( S,{I}_{k},{I}_{kd}right)epsilon {R}^{3}+ : Nle frac{Delta }{mu } }$$

To obtain an invariant region that shows that the solution is bounded, we have

$$begin{gathered} N = S + I_{k} + I_{kd} hfill \ frac{dN}{{dt}} = frac{dS}{{dt}} + frac{{dI_{k} }}{dt} + frac{{dI_{kd} }}{dt} hfill \ frac{dN}{{dt}} = Delta - f_{k} S - mu S + f_{k} S - sigma_{1} I_{k} - mu I_{k} + sigma_{1} I_{k} - mu I_{kd} hfill \ frac{dN}{{dt}} = Delta - left( {S + I_{k} + I_{kd} } right)mu hfill \ frac{dN}{{dt}} = Delta - Nmu hfill \ Nleft( t right) = Nleft( 0 right)e^{ - mu t} + frac{Delta }{mu }left( {1 - e^{ - mu t} } right) hfill \ end{gathered}$$

As,(tto infty), we get (0le Nle frac{Delta }{mu }), the theory of differential equation27 in the region.

({rm Z}_{k} = {left( S,{I}_{k},{I}_{kd}right)epsilon {R}^{3}+ : Nle frac{Delta }{mu } }) For the autonomous system representing the Kidney disease-only model, given by (7), any solution that starts in ({Z}_{k}) will stay within ({Z}_{k}) for all (tge 0)

By equating Eq.(10) to zero (frac{dS}{dt}=frac{{dI}_{k}}{dt}=frac{d{I}_{kd}}{dt}=0)

The disease-free equilibrium (DFE) of the COVID-19-only model system (7) is obtained by setting each of the systems of model system (10) to zero. Also, at the DFE, there are no infections. Thus, the DFE of the COVID-19-only model (10) is given by ({Omega }_{0k}=left( S,{I}_{k},{I}_{kd}right)=(frac{Delta }{mu },mathrm{0,0}))

Employing the next-generation matrix method outlined in (Yang 2014), we derive the related next-generation matrix as

$$begin{gathered} F = left[ {begin{array}{*{20}c} {frac{{phi_{2} left( {I_{k} + theta I_{kd} } right)}}{N}S} \ 0 \ end{array} } right] hfill \ V = left[ {begin{array}{*{20}c} {left( {sigma_{1} + mu } right)I_{k} } \ { - sigma_{1} I_{k} + mu I_{kd} } \ end{array} } right] hfill \ end{gathered}$$

Consequently, the terms for new infections, F and the subsequent transfer components, V are provided as follows:

$$begin{gathered} F = left[ {begin{array}{*{20}c} {phi_{2} } & {phi_{2} theta } \ 0 & 0 \ end{array} } right] hfill \ V = left[ {begin{array}{*{20}c} {left( {sigma_{1} + mu } right)} & 0 \ { - sigma_{1} } & mu \ end{array} } right] hfill \ {text{So}},,,V^{ - 1} = frac{1}{{left( {sigma_{1} + mu } right)mu }}left[ {begin{array}{*{20}c} mu & 0 \ {sigma_{1} } & {left( {sigma_{1} + mu } right)} \ end{array} } right] hfill \ end{gathered}$$

The next-generation matrix (F{V}^{-1})s leading eigenvalue, which is also known as the spectral radius, represents the fundamental reproductive number and is defined as:

$${R}_{ok}=frac{{phi }_{2}(mu +theta {sigma }_{1})}{left({sigma }_{1}+mu right)mu }$$

(9)

More here:

A mathematical model for the transmission of co-infection with COVID-19 and kidney disease | Scientific Reports - Nature.com

This week in CHS history | DeLuxe ‘development,’ COVID-19 eviction moratorium, the last video store on Broadway – CHS Capitol Hill Seattle News

March 11, 2024

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This week in CHS history | DeLuxe 'development,' COVID-19 eviction moratorium, the last video store on Broadway - CHS Capitol Hill Seattle News

Pop-up locations in Louisville are offering free COVID-19 testing – Louisville Public Media

March 11, 2024

Two locations in Louisville will offer free COVID-19 testing on Thursdays to early June.

On the first Thursday of every month, The Salvation Army at 911 Brook Street will offer free COVID testing from 9 a.m. to 11 a.m. Testing will last until June 6.

Open Hands Kitchen at 1026 South Jackson Street will offer free COVID testing from 3:30 p.m. to 5:30 p.m. every second and fourth Thursday of each month. Pop-up testing at this location will last until June 13.

Participants are encouraged to wear masks at both locations, and masks will be provided if necessary. Rapid testing and PCR testing will be available.

The free testing is offered through partnerships with the Louisville Department of Public Health and Wellness, the Kentucky Nurses Association and Family Health Centers.

Louisville Metro Parks and Recreation has free, at-home testing kits available at its community center locations while supplies last. The federal government also offers free, at-home COVID tests to order online.

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Pop-up locations in Louisville are offering free COVID-19 testing - Louisville Public Media

COVID-19 Linked to Increased Risk of Rheumatic Disease – MD Magazine

March 11, 2024

Min Seo Kim, MD

Credit: X.com

A SARS-CoV-2 infection was linked to an increased risk for incident autoimmune inflammatory rheumatic disease (AIRD) when compared with patients with influenza infection or those without SARS-CoV-2 infection, according to a study published in Annals of Internal Medicine.1 The risk of AIRD was higher in patients with greater COVID-19 severity.

Emerging data suggest a higher risk for AIRDs among patients with a history of COVID-19, wrote a team of investigators led by Min Seo Kim, MD, associated with the Medical and Population Genetics and Cardiovascular Disease Initiative, Broad Institute of MIT and Harvard, Cambridge, Massachusetts. However, these findings are based entirely on comparisons between groups infected with SARS-CoV-2 and those that are not, which might be biased by differences in health-seeking behavior and inherent risk factors within the groups. In addition, studies have not explored the effect of vaccination and other modifiable factors on prevention of long-term COVID-19 complications.

Although the clinical definition of long COVID, the term commonly used for patients who experience long-term sequelae, is still evolving, it is generally defined as new or persistent symptoms lasting for > 4 weeks post-diagnosis which cannot be attributed to another cause. Common symptoms can range from fatigue, depression, and dyspnea to diabetes, neurologic disease, and cardiovascular disease.2

To evaluate the effect of COVID-19 infection on the long-term risk for incident AIRD, investigators used data from nationwide claims-based databases in South Korea (K-COV-N) and Japan (JMDC). The binational, longitudinal, propensity-matched cohort study included 10,027,506 Korean and 12,218,680 Japanese patients aged 20 years, including those with a COVID-19 diagnosis, between January 1, 2020 and December 31, 2021 and matched them to patients with either influenza infection or uninfected controls.

As both cohorts were from countries with universal health insurance, data included information on when patients visited multiple facilities, switched hospitals, or died outside of the health care systems. The definitions of exposure and outcomes, general health examinations, and diagnoses codes were the same among Korean and Japanese groups.

The primary endpoint was the onset of AIRD at 1, 6, and, 12 months after COVID-19 or influenza infection or a matched index date of uninfected controls.

The mean age of Korean patients was 48.4 years and 50.1% were male. Among this cohort, 3.9% (n = 394,274) experienced a COVID-19 infection and .98 (n = 98,596) had influenza. Among the Japanese cohort, 8.2% (n = 1,002,525) were diagnosed with COVID-19 and .99 (n = 121,543) were diagnosed with influenza during the study period.

After matching, 225,313 were included in the comparison cohort between those with COVID-19 infection (n = 115,003) and those with influenza (n = 110,310). The median follow-up for comparison between patients with COVID-19 and influenza was 11.3 and 12.1 months, respectively, while the median follow-up for comparison between patients with COVID-19 and the general population was 11.2 months in both groups.

After propensity score matching, patients with COVID-19 were at a significantly increased risk for all-cause AIRD, untreated AIRD, treated AIRD, and connective tissue disease when compared with uninfected controls (adjusted hazard ratio [aHR], 1.25 [95% confidence interval (CI), 1.18 to 1.31]) and influenza-infected controls (aHR, 1.30 [CI, 1.02 to 1.59]). This risk was higher among patients with more severe acute COVID-19 infection.

Investigators noted limitations including residual confounding and a potential referral bias due to the pandemic. Additionally, results may not be generalizable as the sample population was comprised of all Asian patients diagnosed prior to the Omicron variant.

This population-based cohort study shows that the increased risk for incident AIRD extends up to 12 months after SARS-CoV-2 infection, investigators concluded. Care strategies for patients who survive COVID-19 should pay close attention to manifestations of AIRD, particularly after severe COVID-19.

References

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COVID-19 Linked to Increased Risk of Rheumatic Disease - MD Magazine

Free at-home COVID-19 test kit distribution to stop after March 8. How to get your tests – The News Journal

March 11, 2024

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