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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 * 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 * is unstable.
MSC:
34D23Global stability of ODE
92D30Epidemiology
34C11Qualitative theory of solutions of ODE: growth, boundedness
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