Bifurcation analysis and chaos for a double-strains HIV coinfection model with intracellular delays, saturated incidence and Logistic growth

In this paper, a class of virus-to-cell HIV model with intracellular delays, saturated incidence and Logistic growth is proposed to characterize the interaction between two types HIV strains, i.e., wild-type and drug-resistant strains. First, a series of threshold criteria on the locally and globally asymptotic stability of (infection-free, dominant, coexistence) equilibria are discussed based on the basic reproduction number R0. Furthermore, a detailed Hopf bifurcation analysis is performed on the coexistence equilibrium using two delays as bifurcation parameters. We find that the Hopf bifurcations induced by double-strains are evidently different and more complicated than that of single strain, the former switches from stability (periodic branches) to un-stability (chaos) more frequently and earlier than the latter since double-strains would yield more pairs of imaginary roots in the characteristic equations. Meanwhile, the total viral load of double-strains would be higher than that of single-strain as well. The emergence of drug resistance imposes either negative or positive influences on the survival of wild-type strain, which would further facilitate the transmission of HIV.