Analysis of an HIV model with distributed delay and behavior change

Abstract

We develop and analyze a mathematical model for the transmission dynamics of HIV that accounts for behavioral change. The contact rate is modeled by a decreasing function (response function) of HIV prevalence to reflect a reduction in risky behavior that results from the awareness of individuals to a higher HIV prevalence. The model also includes a distributed delay representing the time needed for individuals to reduce their risky behavior. We study mathematically and numerically the impact of the response function and the distributed delay on the model's dynamics. Threshold values for the delay at which the system destabilizes and periodic solutions can arise through Hopf bifurcation are determined.