Stability and Bifurcation in an SI Epidemic Model with Additive Allee Effect and Time Delay

In this paper, we consider an SI epidemic model incorporating additive Allee effect and time delay. The primary purpose of this paper is to study the dynamics of the above system. Firstly, for the model without time delay, we demonstrate the existence and stability of equilibria for three different cases, i.e. with weak Allee effect, with strong Allee effect, and in the critical case. We also investigate the existence and uniqueness of Hopf bifurcation and limit cycle. Secondly, for the model with time delay, the stability of equilibria and the existence of Hopf bifurcation are discussed. All the above show that both additive Allee effect and time delay have vital effects on the prevalence of the disease.

Automated summary

This paper investigates the dynamics of an SI epidemic model incorporating additive Allee effect and time delay. The existence and stability of equilibria, the presence of Hopf bifurcation, and the impact of both the Allee effect and time delay on disease prevalence are explored, highlighting their vital effects on the system dynamics.