Speaker
Description
In this work, we explore the dynamics of a hybrid differential–difference system with delay describing a HIV SI-model with protected compartment (PrEP treatment) and a nonmonotonic recruitment rate. The limited protection duration offered induces a delay in the system. First, we study the existence of equilibria. Under our assumption, we show that the system exhibits several steady states without infection which challenges the study. After a local stability analysis of each equilibrium, we study the existence of Hopf bifurcation around the endemic equilibrium. Our results show that the delay may destabilize the endemic steady state and lead to the existence of recurrent periodic epidemic waves. Each situation is illustrated illustrate each situation.
