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Global stability of an HIV pathogenesis model with cure rate. (English) Zbl 1231.34094
Summary: We consider an HIV pathogenesis model including cure rate and the full logistic proliferation term of \(CD4^{+}\) T cells in healthy and infected populations. Let \(N\) be the number of virus released by each productive infected \(CD4^{+}\) T cell. The critical number that ensures the existence of the positive equilibrium is obtained. We further show that if , then there exists a unique uninfected equilibrium point \(E_{0}\) that is locally asymptotically stable. If , then the system is persistent and the only infected steady state \(E^{\ast }\) is globally asymptotically stable in the feasible region. Numerical simulations are presented to illustrate the obtained main results. Moreover, we find that there exist periodic solutions when the infected steady state \(E^{\ast }\) is unstable.

34D23 Global stability of solutions to ordinary differential equations
92D30 Epidemiology
34C11 Growth and boundedness of solutions to ordinary differential equations
Full Text: DOI
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