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The aim of this work is the application of optimal control for the system of ordinary differential equations modeling a tuberculosis disease with exogenous reinfection. Seeking to reduce the infectious group by the reduction of the contact between infectious and exposed individuals, we use control representing the prevention of exogenous reinfection. The(More)
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)
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)
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)
We investigate a stochastic SIR epidemic model with specific nonlinear incidence rate. The stochastic model is derived from the deterministic epidemic model by introducing random perturbations around the endemic equilibrium state. The effect of random perturbations on the stability behavior of endemic equilibrium is discussed. Finally, numerical simulations(More)
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