Predator-Prey Dynamics in the Interaction of HIV Virus with CD4+T Cells

Mathematical modeling provides a powerful framework for understanding the complex dynamics of HIV infection within the human immune system. This review presents a dynamic modeling and stability assessment of HIV infection in CD4⁺ T-cells using systems of nonlinear differential equations. The model incorporates key biological processes, including viral replication, infection rate, immune response, and natural cell death, to describe the interaction between healthy T-cells, infected T-cells, and free virus particles. Stability analysis is performed to determine the equilibrium points—disease-free and endemic states—and their corresponding threshold conditions based on the basic reproduction number (R₀). Results indicate that when R₀ < 1, the infection-free equilibrium is stable, signifying viral clearance, whereas R₀ > 1 leads to instability and persistence of infection. Sensitivity analysis highlights the influence of parameters such as viral production rate, infection rate, and immune cell regeneration on system dynamics. This study emphasizes the significance of mathematical modeling in predicting disease progression, evaluating therapeutic interventions, and designing optimal control strategies against HIV infection.

In this paper, an SIS epidemic model with age of vaccination is investigated. Asymptotic smoothness of the semi-flow is proved. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state is discussed. It is shown that if the basic reproduction number is greater than unity, the system is permanent. By constructing two Lyapunov functionals, it is proved that the endemic steady state is globally asymptotically stable if the basic reproduction number is greater than unity, and sufficient conditions are derived for the global asymptotic stability of the disease-free steady state. Numerical simulations are given to illustrate the asymptotic stabilities of the disease-free steady state and endemic state.

An advanced version of a conformable mathematical model of Ebola virus disease in Africa

The Gastrointestinal Tract and AIDS Pathogenesis

Gastrointestinal Disease in Simian Immunodeficiency Virus-Infected Rhesus Macaques Is Characterized by Proinflammatory Dysregulation of the Interleukin-6-Janus Kinase/Signal Transducer and Activator of Transcription3 Pathway

Wonder of wonders, miracle of miracles: the unprecedented speed of COVID-19 science.

Generalized reproduction numbers, sensitivity analysis and critical immunity levels of an SEQIJR disease model with immunization and varying total population size

Human Immunodeficiency Virus – Acquired Immune Deficiency Syndrome HIV/AIDS stands as one of the most prevalent sexually transmitted disease globally and is regarded as one of the deadliest epidemic in human history. This study presents a mathematical model for understanding the dynamics of HIV/AIDS transmission, incorporating a saturated incidence rate. The model employs a system of ordinary differential equations, comprising various group of individuals including susceptible, asymptomatic infective, symptomatic infective, treated and AIDS class. The validity of the solution states affirms that the model is well-defined and holds epidemiological significance. The disease-free and endemic equilibrium states are identified, and their stability is analyzed using Routh Hurwitz criteria. Sensitivity analysis was carried out using normalized forward sensitivity index and result showed that the contact rate is the most sensitive parameter. However, it is observed from the numerical simulation that screening and treatment of the infective play a significant role in reducing the transmission of the disease. The outcome of the stability analysis for both disease-free and endemics equilibrium states indicates the potential for HIV/AIDS control.

Chronic immune activation and viral latency are among the main factors behind the persistence of Human Immunodeficiency Virus (HIV) and other viral diseases. Immune activation is chiefly lead by dendritic cells which detect the presence of Virus (HIV) and notify other immune cells particularly the helper T cells via the process called antigen presentation. However, antigen presentation process increases the chances of T cells to be infected by the viral particles trapped by dendritic cells. In this paper, a time-fractional diffusion model is proposed to investigate the impact of dendritic cells on the spread of HIV among susceptible T cells with respect to time and anomalous diffusion posed by cells crowding. The equilibrium points of the model are obtained and analysed. The disease free steady state proved to be stable both in spatially homogeneous case and in the presence diffusion and chemotaxis. The endemic steady state is stable in the absence of diffusion and chemotaxis, however the presence of diffusion induces instability if a thresshold value is exceeded. A priori estimates were also obtained in the appropriate Sobolev spaces. Furthermore, the numerical experiments were conducted to examine the dynamic behaviour of cells densities with respect to time and the sub-diffusion parameter.

This a basic report on the current status of acquired immune deficiency syndrome AIDS/HIV. It deals with the current status of this horrible disease. It defines the basic information and terminology and lists the method of management for non medical readers. This report would give the reader the primer to understand this disease. THE EPIDEMIOLOGICAL BACKGROUND The epidemiology and burden of HIV in the developing world had two distinct viruses. HIV types 1 and 2 (HIV-1/HIV-2) cause AIDS. HIV-1 is responsible for the great majority of infections globally. The life cycle of the virus can be viewed at web link http://www.aids.org/factSheets/400-HIV-Life-Cycle.html While HIV-2 is very rare outside West Africa, individual cases of HIV-2 infection have been described in other parts of Africa, Europe, the Americas, and Asia (India), but most people with HIV-2 infection have some epidemiological link to West Africa. Several reports published by international health agencies like the World Health Organization WHO and the United Nations agencies UNFPA conclude that AIDS is the leading cause of death in sub-Saharan Africa and the fourth biggest killer worldwide.[Table 1] Figure 1 The ranges around the estimates in this table define the boundaries within which the actual numbers lie. Since the epidemic began more than 24 years ago at least 60 million people worldwide have been infected with the virus and currently more than 45 million people live with HIV. The cumulative number can be read from UNFPA AIDS Clock at http://www.unfpa.org/aids_clock/main.htm These reports warn that the rates of infection are rising fastest in Eastern Europe and Russia. In 2001, there were an estimated 250000 new infections in this region. Russia has seen a 15-fold increase in infections over the years. Most of Basic Facts About HIV And AIDS 2 of 5 these cases are related to illegal drug use. Sub-Saharan Africa continues to be the worst affected area. The report says that AIDS killed 2.3 million people in 2001 and that there were 3.4 million new HIV infections. The region is the only one where more women than men are infected by the virus. More than 28 million people in the region currently live with HIV, a prevalence of 8%. Most of these people, the report says, do not know they have the virus. The epidemic also “threatens human welfare, developmental progress, and social stability on an unprecedented scale.” Hardest hit countries could lose 20% of their gross domestic product by 2020. Steep drops in life expectancies are now beginning to occur. If it were not for HIV and AIDS, the average life expectancy in sub-Saharan Africa would be 62 years; it currently stands at 47 years. The report says that marked increases in rates of infection in Asia and the Pacific, which have some of the world's most populous countries, are also of “particular concern.” Reported HIV infections in China rose by 67% in the first six months of 2001, compared with the previous year. India has a prevalence of about 1% representing an estimated 3.86 million peo.[3] HUMAN IMMUNODEFICIENCY VIRUS AND ACQUIRED IMMUNODEFICIENCY SYNDROME HUMAN IMMUNODEFICIENCY VIRUS (HIV) The abbreviations HIV stands for the virus named 'human immunodeficiency virus'. HIV is a member of retroviruses that infect cells of the human immune system (mainly CD4 positive T cells and macrophages—key components of the cellular immune system), and destroy or impair their function. Infection with this virus results in the progressive depletion of the immune system, leading to 'immune deficiency'. The immune system is considered deficient when it can no longer fulfill its role of fighting off infection and diseases. Immunodeficient people are much more vulnerable to a wide range of infections, most of which are very rare among people without immune deficiency. Diseases associated with severe immunodeficiency are known as 'opportunistic infections', because they take advantage of a weakened immune system. ACQUIRED IMMUNODEFICIENCY SYNDROME (AIDS) AIDS stands for 'acquired immunodeficiency syndrome' and describes the collection of symptoms and infections associated with acquired deficiency of the immune system. Infection with HIV has been established as the underlying cause of AIDS. The level of HIV in the body and the appearance of certain infections are used as indicators that HIV infection has progressed to AIDS. MANIFESTATION OF AIDS THE SYMPTOMS OF HIV INFECTION Most people infected with HIV do not know that they have become infected because no symptoms develop immediately after the initial infection. Some people have a glandular fever-like illness (with fever, rash, joint pains and enlarged lymph nodes), which can occur at the time of development of antibodies to HIV and usually takes place between six weeks and three months after an infection has occurred this is called seroconversion. Despite the fact that HIV infection does not cause any initial symptoms, an HIV-infected person is highly infectious and can transmit the virus to another person. The only way to determine whether HIV is present in a person's body is by taking an HIV test. HIV infection causes a gradual depletion and weakening of the immune system. This results in an increased susceptibility of the body to infections and can lead to the development of AIDS. WHEN WE CAN SAY THAT A PERSON DOES HAVE AIDS? The term AIDS applies to the most advanced stages of HIV infection. The majority of people infected with HIV, if not treated, develop signs of AIDS within 8-10 years. MEDICAL MANAGEMENT OF AIDS AIDS is identified on the basis of certain infections, grouped by the (WHO): Stage 1 HIV disease is asymptomatic and not categorized as AIDS Stage II (includes minor mucocutaneous manifestations and recurrent upper respiratory tract infections) Stage III (includes unexplained chronic diarrhea Basic Facts About HIV And AIDS 3 of 5 for longer than a month, severe bacterial infections and pulmonary tuberculosis) or Stage IV (includes Toxoplasmosis of the brain, Candidiasis of the esophagus, trachea, bronchi or lungs and Kaposi's Sarcoma) HIV diseases are used as indicators of AIDS. Most of these conditions are opportunistic infections that can be treated easily in healthy The length of time taken by infected patient to show signs of the disease can vary widely between individuals. With a healthy lifestyle, the time between infection with HIV and becoming ill with AIDS can be 10–15 years, sometimes longer. Antiretroviral therapy can slow down the progression of AIDS by decreasing viral load in an infected body. There is no cure for HIV/AIDS. Progression of the disease can be slowed down but cannot be stopped completely. The right combination of antiretroviral drugs can slow down the damage that HIV causes to the immune system and delay the onset of AIDS. The available treatment and care consist of a number of different elements, including voluntary counseling and testing (VCT), support for the prevention of onward transmission of HIV, follow-up counseling, advice on food and nutrition, treatment of STIs, management of nutritional effects, prevention and treatment of opportunistic infections (OIs), and the provision of antiretroviral drugs. They are used in the treatment of HIV infection. Antiretroviral drugs work as follow: Inside an infected cell, HIV produces new copies of itself, which can then go on to infect other healthy cells within the body. The more cells HIV infects, the greater its impact on the immune system (immunodeficiency). Antiretroviral drugs slow down the replication and, therefore, the spread of the virus within the body, by interfering with its replication process in different ways. NUCLEOSIDE REVERSE TRANSCRIPTASE INHIBITORS: HIV needs an enzyme called reverse transcriptase to generate new copies of itself. This group of drugs inhibits reverse transcriptase by preventing the process that replicates the virus's genetic material. NON-NUCLEOSIDE REVERSE TRANSCRIPTASE INHIBITORS: This group of drugs also interferes with the replication of HIV by binding to the reverse transcriptase enzyme itself. This prevents the enzyme from working and stops the production of new virus particles in the infected cells.

IN THE MODERN ERA OF HIGHLY ACTIVE ANTIRETROVIRAL therapy (HAART), hepatitis C virus (HCV) has emerged as a major cause of morbidity and death in human immunodeficiency virus (HIV) infection. An estimated 15% to 30% of HIV-infected individuals are coinfected with HCV, representing 150000 to 300000 patients in the United States alone. The prevalence of anti-HCV antibodies in HIVinfected persons differs significantly according to the HIVexposure risk category, ranging from less than 10% in homosexual men to more than 85% in injecting drug users. In the vast majority of immunocompetent non–HIVinfected persons, chronic hepatitis C usually takes a relatively mild course, leading to liver cirrhosis in 2% to 25% after 20 to 25 years depending on the individual risk factor profile. Liver-related death is only slightly more frequent in HCV-infected individuals. In contrast, hepatitis C may take a much more severe course in HIV-infected patients. In men with hemophilia, the prevalence of cirrhosis as well as liver-related deaths is significantly higher in HCV-HIV– coinfected individuals than in patients infected with HIV alone. However, these findings may not necessarily reflect the situation in other cohorts in which HCV infection has not been shown to increase the risk of death. Since antiretroviral therapy can be associated with significant hepatotoxicity, there has been some concern that HAART, specifically protease inhibitors, may promote progression of fibrosis in HCV-RNA–positive patients. Fortunately, this has not been the case, and antiretroviral therapy has even been shown to reduce long-term liver-related mortality in HIV-HCV–coinfected patients. In contrast, HCV infection appears to influence the natural history of HIV disease. In the Swiss HIV cohort, among more than 3000 HIVinfected individuals, those also infected with HCV had a modestly increased risk for developing AIDS and a less robust increase in CD4 cell counts after initiation of antiretroviral therapy compared with patients infected with HIV alone. On the other hand, a study from Baltimore found that HCV coinfection had no influence on developing AIDS or response to HAART. These differences highlight the problem that different cohorts may be difficult to compare because both HIV and HCV disease may have different trajectories depending on the route of infection (eg, blood transfusions vs community acquired) and other factors. Interactions between HCV and HIV are difficult to investigate. Although the primary site of replication differs (for HCV, the liver; for HIV, T cells, monocytes, and dendritic cells), HCV may also replicate in dendritic cells and monocytes, while HIV can cause hepatitis. Thus, both viruses may directly interact with the other’s replication and influence the host’s immune response to the other virus. Hepatitis C virus replication is much more rapid in HIV-infected patients than in patients infected with HCV alone, indicating decreased immune function. On the other hand, HCV proteins may directly inhibit the function of dendritic cells and natural killer cells and thus alter the anti-HIV–specific immune response. Thus, coinfection with HIV and HCV may influence viral load and immune responses and thereby affect efficacy of antiviral treatment against both HIV and HCV. Treatment options for patients infected with hepatitis C have significantly improved only in recent years. Acute hepatitis C as well as chronic HCV genotype 2 or 3 infection is now considered a curable disease in immunocompetent patients. Even patients infected with the more difficult-to-treat HCV genotypes 1 and 4 can achieve sustained clearance rates of HCV-RNA in about 50%. Three

HIV and sickle cell disease (SCD) are significant causes of morbidity and mortality in sub-Saharan Africa. Given their separate roles in immune dysregulation, our objective was to characterise the impact that SCD has on the presentation and progression of paediatric HIV. The study was a retrospective cohort study (study period 2004-2018). Cases of HIV+and SCD-afflicted patients (HIV+/SCD+) were obtained via electronic chart review from a paediatric HIV clinic in Kampala, Uganda and matched 1:3 with HIV+controls without SCD (HIV+/SCD-). Thirty-five HIV+/SCD+subjects and 95 HIV+/SCD- controls were analysed (39% female (51/130), age 3.6years (SD3.9)). At baseline, WHO clinical stage (64% total cohort Stage III/IV) and nutritional status (9.4% severe acute malnutrition) were similar for both groups, whereas HIV+/SCD+had higher though non-significant baseline CD4 count (1036 (SD713) vs 849 (SD638) cells/microlitre, P=0.20, two-tailed t-test). There were 19 deaths, 6 (17%) HIV+/SCD+and 13 (14%) HIV+/SCD-, with unadjusted/adjusted models showing no significant difference. Nutritional progression and clinical stage progression showed no significant differences between groups. Kaplan-Meier analysis showed a slower rate of treatment failures in the HIV+/SCD+cohort (P=0.11, log-rank survival test). Trajectory analysis showed that in the time period analysed, the HIV+/SCD+cohort showed a more rapid rise and higher total CD4 count (P=0.012, regression analysis). The study suggests that SCD does not adversely affect the progression of HIV in patients on ART. Further, HIV+/SCD+achieved higher CD4 counts and fewer HIV treatment failures, suggesting physiological effects due to SCD might mitigate HIV progression.

Addressing HIV-1 latency with Flow-FISH: Finding, characterizing and targeting HIV-1 infected cells.

We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.

Approximately 30 years ago, in June 1981, it was reported from theCenter forDiseaseControl andPrevention (CDC) that five, otherwise healthy, homosexual men in California had presented with pneumonia caused by Pneumocystis jiroveci pneumonia, a rare disease seen exclusively in individualswith a severely suppressed immune system. Several reports confirmed the initial observation and lent support to the possibility that a new sexually transmitted, infectious agent was circulating within the gay community in the United States. The clinical condition was named acquired immunodeficiency syndrome (AIDS). Two years later, a research team at the Institut Pasteur under the guidance of Francoise Barre-Sinoussi and Luc Montagnier isolated human immunodeficiency virus (HIV), the causative agent of AIDS, from a lymph node biopsy of a French patient. The isolation and characterization of HIV paved the way for the design of diagnosticmethods to identify the virus in blood andbloodproducts and towards the development of novel antiretroviral treatment (ART) to control HIV replication in infected patients. For their discoveries, Barre-Sinoussi and Montagnier were awarded the Nobel Prize in Physiology and Medicine in 2008.