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The purpose of this work is to investigate an optimal control model of drug treatment of HIV infection of CD4 + T-cells. The optimal controls represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence for the optimal control pair is established and the Pon-tryagin's maximum principle is used to(More)
A delayed SIR epidemic model with a generalized incidence rate is studied. The time delay represents the incubation period. The threshold parameter, R 0 (τ) is obtained which determines whether the disease is extinct or not. Throughout the paper, we mainly use the technique of Lyapunov functional to establish the global stability of both the disease-free(More)
The aim of this work is to investigate a new mathematical model that describes the interactions between Hepatitis B virus (HBV), liver cells (hepatocytes), and the adaptive immune response. The qualitative analysis of this as cytotoxic T lymphocytes (CTL) cells and the antibodies. These outcomes are (1) a disease free steady state, which its local stability(More)
In this paper, we propose an HIV infection model with CTL immune response which includes the cure of infected cells and the effect of immune impairment caused by HIV infection. Both the infection transmission process and the proliferation of CTL immune response are modeled by two saturated functions. Moreover, the qualitative analysis of the model is(More)
In this paper, we propose two HIV infection models with specific nonlinear incidence rate by including a class of infected cells in the eclipse phase. The first model is described by ordinary differential equations (ODEs) and generalizes a set of previously existing models and their results. The second model extends our ODE model by taking into account the(More)
To better understand the dynamics of the hepatitis B virus (HBV) infection, we introduce an improved HBV model with standard incidence function, cytotoxic T lymphocytes (CTL) immune response, and take into account the effect of the export of precursor CTL cells from the thymus and the role of cytolytic and noncytolytic mechanisms. The local stability of the(More)