Global stability of an HIV pathogenesis model with cure rate

In this paper, 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 NN be the number of virus released by each productive infected CD4+ T cell. The critical number Ncrit that ensures the existence of the positive equilibrium is obtained. We further show that if N≤Ncrit, then there exists a unique uninfected equilibrium point E0E0 that is locally asymptotically stable. If N>Ncrit, then the system is persistent and the only infected steady state E∗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∗E∗ is unstable.