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In this paper, we propose a general viral infection model to incorporate two infection modes (virus-to-cell mode and cell-to-cell mode), the CTL immune response, and the distributed intracellular delays during the processes of viral infection, viral production, and CTLs recruitment. We investigate the existence, the uniqueness, and the global stability of three equilibria: infection-free equilibrium E 0 , immune-inactivated equilibrium E 1 and immune-activated equilibrium E 2 , respectively. We prove that the viral dynamics are determined by two threshold parameters: the basic reproduction number for infection R 0 and the basic reproduction number for immune response R IM . We also numerically explore the viral dynamics beyond stability. We use bifurcation diagrams to show that increasing the delay in CTL immune cell recruitment can induce a switch in viral load from a stable constant level to sustained oscillations, and then back to a stable equilibrium. We also compare the contributions of the two infection modes to the total infection level and identify the key parameters that would affect the percentages of virus-to-cell infection and cell-to-cell infection. Finally, we explore how Filippov control can be applied in antiretroviral therapy to reduce the viral loads. [ABSTRACT FROM AUTHOR]

HIV preferentially infects activated CD4+ T cells. Current antiretroviral therapy cannot eradicate the virus. Viral infection of other cells such as macrophages may contribute to viral persistence during antiretroviral therapy. In addition to cell-free virus infection, macrophages can also get infected when engulfing infected CD4+ T cells as innate immune sentinels. How macrophages affect the dynamics of HIV infection remains unclear. In this paper, we develop an HIV model that includes the infection of CD4+ T cells and macrophages via cell-free virus infection and cell-to-cell viral transmission. We derive the basic reproduction number and obtain the local and global stability of the steady states. Sensitivity and viral dynamics simulations show that even when the infection of CD4+ T cells is completely blocked by therapy, virus can still persist and the steady-state viral load is not sensitive to the change of treatment efficacy. Analysis of the relative contributions to viral replication shows that cell-free virus infection leads to the majority of macrophage infection. Viral transmission from infected CD4+ T cells to macrophages during engulfment accounts for a small fraction of the macrophage infection and has a negligible effect on the total viral production. These results suggest that macrophage infection can be a source contributing to HIV persistence during suppressive therapy. Improving drug efficacies in heterogeneous target cells is crucial for achieving HIV eradication in infected individuals. [ABSTRACT FROM AUTHOR]

The purposes of this paper are twofold: to develop a rigorous approach to analyze the threshold behaviors of nonlinear virus dynamics models with impulsive drug effects and to examine the feasibility of virus clearance following the Manuals of National AIDS Free Antiviral Treatment in China. An impulsive system of differential equations is developed to describe the within-host virus dynamics of both wild-type and drug-resistant strains when a combination of antiretroviral drugs is used to induce instantaneous drug effects at a sequence of dosing times equally spaced while drug concentrations decay exponentially after the dosing time. Threshold parameters are derived using the basic reproduction number of periodic epidemic models, and are used to depict virus clearance/persistence scenarios using the theory of asymptotic periodic systems and the persistence theory of discrete dynamical systems. Numerical simulations using model systems parametrized in terms of the antiretroviral therapy recommended in the aforementioned Manuals illustrate the theoretical threshold virus dynamics, and examine conditions under which the impulsive antiretroviral therapy leads to treatment success. In particular, our results show that only the drug-resistant strain can dominate (the first-line treatment program guided by the Manuals) or both strains may be rapidly eliminated (the second-line treatment program), thus the work indicates the importance of implementing the second-line treatment program as soon as possible. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract  We present a simple mathematical model with six compartments for the interaction between HIV and TB epidemics. Using data from a township near Cape Town, South Africa, where the prevalence of HIV is above 20% and where the TB notification rate is close to 2,000 per 100,000 per year, we estimate some of the model parameters and study how various control measures might change the course of these epidemics. Condom promotion, increased TB detection and TB preventive therapy have a clear positive effect. The impact of antiretroviral therapy on the incidence of HIV is unclear and depends on the extent to which it reduces sexual transmission. However, our analysis suggests that it will greatly reduce the TB notification rate. [ABSTRACT FROM AUTHOR]