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Immune response in HIV epidemics for distinct transmission rates and for saturated CTL response. (English) Zbl 1421.35375

Summary: In this paper, we study the immune response in a fractional order model for HIV dynamics, for distinct disease transmission rates and saturated cytotoxic T-lymphocyte (CTL) response. Our goal is twofold: (i) to analyze the role of the order of the fractional derivative, \(\alpha\), on the efficacy of the immune response, (ii) to examine the immune response for distinct transmission functions, in the presence of saturated CTL response. We compute the reproduction number of the model and state the stability of the disease-free equilibrium. We discuss the results of the model from an epidemiological point of view.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
34A08 Fractional ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
92C60 Medical epidemiology
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