Bifurcation analysis of HIV infection model with cell-to-cell transmission and non-cytolytic cure

Abstract

Abstract A mathematical model is proposed and discussed to study the effect of cell-to-cell transmission, the non-cytolytic process, and the effect of logistic growth on the dynamics of HIV in vivo. The model system consists of one disease-free steady state and another endemic steady state. The disease-free steady state is globally asymptotically stable and the disease eradicated if the basic reproduction number is smaller than one. However, the endemic steady state is globally stable under specific parametric conditions, when it exists. At R 0 = 1 {R}_{0}=1 , the forward transcritical bifurcation is obtained. Also, by considering proliferation rate as bifurcation parameter, we get Hopf and Hopf–Hopf bifurcations. We have performed numerical simulations using MATLAB to support our analytical results and show the effects of cell-to-cell infection, proliferation rate, and non-cytolytic cure on all three populations. In the end, we have performed data fitting and note the same behaviour of observed data with predicted data.