Analysis of HIV models with multiple target cell populations and general nonlinear rates of viral infection and cell death

Xia Wang, Xinyu Song, Sanyi Tang and Libin Rong

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 124, issue C, 87-103

Abstract: HIV can infect different cell populations such as CD4+ T cells and macrophages. In this paper, we study the global property of the solution of an HIV model with two target cell populations. The model includes general nonlinear rates of viral infection and cell death. For each class of target cells, the time delay between viral entry into cells and viral production is included in the model. We obtain the basic reproductive number of the model, which is shown to provide a threshold condition determining the long-term behavior of the solution of the model. Specifically, we show that the infection-free equilibrium is globally asymptotically stable when the basic reproductive number is less than or equal to 1, and that the infected equilibrium is globally asymptotically stable when the basic reproductive number is greater than 1. We also extend the model with two target cell populations to a general model with n populations. Similar global properties are obtained for the general model. Numerical simulations are performed to illustrate the stability results and to evaluate the relative contribution to viral production from the two cell populations.

Keywords: Virus dynamics; Delay; Multiple target cells; Global stability; Lyapunov functional (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:124:y:2016:i:c:p:87-103

DOI: 10.1016/j.matcom.2015.11.011

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