How to Have Theory in an Epidemic: Cultural Chronicles of AIDS.

Modeling antiretroviral drug responses for HIV-1 infected patients using differential equation models.

Recent development in antiretroviral treatment against HIV can help AIDS patients to fight against HIV. But the question that whether the disease is to be partially or totally eradicated from HIV infected individuals still remains unsolved. Usually, the most effective treatment for the disease is HAART which can only control the disease progression. But as the immune system becomes weak, the patients can not fight against other diseases. Immune cells are activated and proliferated by IL-2 after the identification of antigen. IL-2 production is impaired in HIV positive patients and intermitted administration of immune activator IL-2 together with HAART which is a more effective treatment to fight against the disease. Thus, its expediency is essential and is yet to be explored. In this article we anticipated a mathematical model of the effect of IL-2 together with RTIs therapy in HIV positive patients. Our analytical as well as numerical study shows that the optimal schedule of treatment for best result is ...

Anti-viral drug treatment along with immune activator IL-2: a control-based mathematical approach for HIV infection

Background: Induction-maintenance therapy is a treatment regime where patients are prescribed an intense course of treatment for a short period of time (the induction phase), followed by a simplified long-term regimen (maintenance). Since induction therapy has a significantly higher chance of pill fatigue than maintenance therapy, patients might take drug holidays during this period. Without guidance, patients who choose to stop therapy will each be making individual decisions, with no scientific basis. Methods: We use mathematical modelling to investigate the effect of imperfect adherence during the inductive phase. We address the following research questions: 1. Can we theoretically determine the maximal length of a possible drug holiday and the minimal number of doses that must subsequently be taken while still avoiding resistance? 2. How many drug holidays can be taken during the induction phase? Results: For a 180 day therapeutic program, a patient can take several drug holidays, but then has to follow each drug holiday with a strict, but fairly straightforward, drug-taking regimen. Since the results are dependent upon the drug regimen, we calculated the length and number of drug holidays for all fifteen protease-sparing triple-drug cocktails that have been approved by the US Food and Drug Administration. Conclusions: Induction therapy with partial adherence is tolerable, but the outcome depends on the drug cocktail. Our theoretical predictions are in line with recent results from pilot studies of short-cycle treatment interruption strategies and may be useful in guiding the design of future clinical trials.

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Modelling imperfect adherence to HIV induction therapy

The current emergence of coronavirus (SARS-CoV-2) puts the world in threat. The structural research on the receptor recognition by SARS-CoV-2 has identified the key interactions between SARS-CoV-2 spike protein and its host (epithelial cell) receptor, also known as angiotensin-converting enzyme 2 (ACE2). It controls both the cross-species and human-to-human transmissions of SARS-CoV-2. In view of this, we propose and analyze a mathematical model for investigating the effect of CTL responses over the viral mutation to control the viral infection when a postinfection immunostimulant drug (pidotimod) is administered at regular intervals. Dynamics of the system with and without impulses have been analyzed using the basic reproduction number. This study shows that the proper dosing interval and drug dose both are important to eradicate the viral infection.

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A Model for SARS-CoV-2 Infection with Treatment.

The majority of cells infected with the human immunodeficiency virus are activated CD4+ T cells, which can be treated with antiretoviral drugs. However, an obstacle to eradication is the presence of viral reservoirs, such as latently infected CD4+ T cells. Such cells may be less susceptible to antiretroviral drugs and may persist at low levels during treatment. We introduce a model of impulsive differential equations that describe T cell and drug interactions. We make the extreme assumption that latently infected cells are unaffected by drugs, in order to answer the research question: Can the viral reservoir of latently infected cells be eradicated using current antiretroviral therapy? We analyse the model in both the presence and absence of drugs, showing that, if the frequency of drug taking is sufficiently high, then the number of uninfected CD4+ T cells approaches the number of T cells in the uninfected immune system. In particular, this implies that the latent reservoir will be eliminated. It follows that, with sufficient application of drugs, latently infected cells cannot sustain a viral reservoir on their own. We illustrate the results with numerical simulations.

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Can the viral reservoir of latently infected CD4+ T cells be eradicated with antiretroviral HIV drugs?

We argue that the HIV epidemic in the United States is considerably more widespread than is officially reported. The occasional reports of outbreaks in cities like Washington DC, comparison with other countries in the developed world and our mathematical models, all point to the conclusion that the number of people living with HIV, but not AIDS, in the United States is more than four times larger than the current estimate. Although there are many reasons that HIV-positive individuals may not be aware of their serostatus, we argue that the United States healthcare system provides an additional pressure that simultaneously discriminates against and ignores the very people it should be targeting most.

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B. D. Aggarwala

Papers

Can the viral reservoir of latently infected CD4+ T cells be eradicated with antiretroviral HIV drugs?

HIV: The invisible epidemic of the United States healthcare system