Periodic Solutions of an Infected-Age Structured HIV Model with the Latent Factor and Different Transmission Modes

Abstract

In this paper, we mainly investigate an infected-age structured HIV model with logistic growth for target cells, which simultaneously takes the latent factor and different transmission modes into consideration. On the basis of integrated semigroup theory and Hopf bifurcation theory for semilinear equations in a nondense domain, we reach a conclusion that the system undergoes a Hopf bifurcation around the positive equilibrium, which implies that there exists a nontrivial periodic oscillation phenomenon when the Hopf bifurcation parameter [Formula: see text] passes through some critical values. Namely, the HIV infection will periodically erupt when the mature period [Formula: see text] crosses the critical value [Formula: see text] ([Formula: see text]), that is, HIV virus will always survive in the patient’s body. In order to verify the fact that the biological maturation period [Formula: see text] does play an essential role in our system, we also offer the relevant numerical simulation results by selecting several decisive parameters.