Bifurcation Analysis of a Delayed Infection Model with General Incidence Function

In this paper, an infection model with delay and general incidence function is formulated and analyzed. Theoretical results reveal that positive equilibrium may lose its stability, and Hopf bifurcation occurs when choosing delay as the bifurcation parameter. The direction of Hopf bifurcation and the stability of the periodic solutions are also discussed. Furthermore, to illustrate the numerous changes in the local stability and instability of the positive equilibrium, we conduct numerical simulations by using four different types of functional incidence, i.e., bilinear incidence, saturation incidence, Beddington–DeAngelis response, and Hattaf–Yousfi response. Rich dynamics of the model, such as Hopf bifurcations and chaotic solutions, are presented numerically.