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Cytotoxic T lymphocytes eliminate infected or malignant cells, safeguarding surrounding tissues. Although experimental and systems-immunology studies have cataloged many molecular and cellular actors involved in an immune response, the…

Coarse structural nested mean models are used to estimate treatment effects from longitudinal observational data. Coarse structural nested mean models lead to a large class of estimators. It turns out that estimates and standard errors may…

Assessment of circulating CD4 count change over time in HIV-infected subjects on antiretroviral therapy (ART) is a central component of disease monitoring. The increasing number of HIV-infected subjects starting therapy and the limited…

In people infected with HIV the RNA viral load is a good predictor of the rate of loss of CD4 cells at a population level but there is still great variability in the rate of decline of CD4 cells among individuals. Here we show that the…

Retaining persons living with HIV (PLWH) in medical care is paramount to preventing new transmissions of the virus and allowing PLWH to live normal and healthy lifespans. Maintaining regular appointments with an HIV provider and taking…

Intrahost simian immunodeficiency virus (SIV) evolution is marked by repeated viral escape from cytotoxic T-lymphocyte (CTLs) response. Typically, the first such CTL escape occurs in a matter of days, starting around the time of peak viral…

Tuberculosis (TB) and human immunodeficiency virus (HIV) can be considered a deadly human syndemic. In this article, we formulate a model for TB and HIV transmission dynamics. The model considers both TB and acquired immune deficiency…

Cytotoxic T lymphocytes (CTLs) are immune system cells that are thought to play an important role in controlling HIV infection. We develop a stochastic ODE model of HIV-CTL interaction that extends current deterministic ODE models. Based on…

This paper studies an optimal control problem for a class of SIR epidemic models, in scenarios in which the infected population is constrained to be lower than a critical threshold imposed by the ICU (intensive care unit) capacity. The…

When highly active antiretroviral therapy is administered for long periods of time to HIV-1 infected patients, most patients achieve viral loads that are ``undetectable'' by standard assay (i.e., HIV-1 RNA $ < 50$ copies/ml). Yet despite…

An optimal dynamic treatment regime (DTR) is a sequence of decision rules aimed at providing the best course of treatments individualized to patients. While conventional DTR estimation uses longitudinal data, such data can also be…

In this paper, we study the optimal control for an SEIR model adapted to the vaccination strategy of susceptible individuals. There are factors associated with a vaccination campaign that make this strategy not only a public health issue…

In this work we develop a stochastic model of acute HIV infection, based on the well-known standard model, that allows us to simulate the complex mutation pathways of HIV escape from multiple CTL responses. Under this model, we describe two…

Intra-tumour heterogeneity (ITH) has a strong impact on the efficacy of the immune response against solid tumours. The number of sub-populations of cancer cells expressing different antigens and the percentage of immunogenic cells (i.e.…

In this article, the feasibility of using optimal control theory will be studied to develop control theoretic methods for personalized treatment of HCV patients. The mathematical model for HCV progression includes compartments for healthy…

In this paper, we investigate a novel 3-compartment model of HIV infection of CD4$^+$ T-cells with a mass action term by including two versions: one baseline ODE model and one delay-differential equation (DDE) model with a constant discrete…

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions, considering reinfection and post-exposure…

Hepatitis C virus (HCV) coinfection has become one of the most challenging clinical situations to manage in HIV-infected patients. Recently the effect of HCV coinfection on HIV dynamics following initiation of highly active antiretroviral…

A mathematical model from a previous work was re-fitted and analyzed for experimental data regarding the cellular immune response to the lymphocytic choriomeningitis virus. Specifically, the $CD8^{+}$ T cell response to six MHC class…

We analyze a within-host model of virus infection with antibody and CD8+ cytotoxic T lymphocyte (CTL) responses proposed by Schwartz et al. (2013). The goal of this work is to gain an overview of the stability of the biologically-relevant…