## 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.

### MSC:

 34D23 Global stability of solutions to ordinary differential equations 92D30 Epidemiology 34C11 Growth and boundedness of solutions to ordinary differential equations
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### References:

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