Bifurcation and Global Stability of a SEIRS Model With a Modified Nonlinear Incidence Rate

In this work, a SEIRS (susceptible–exposed–infected–recovered–susceptible) model with modified nonlinear incidence rate is considered. The incidence rate illustrates how the number of infected individuals initially increases at the onset of a disease, subsequently decreases due to the psychological effect, and ultimately reaches saturation due to the crowding effect. Firstly, we determine the existence criteria for the model equilibrium points, followed by the identification of the threshold quantity for disease survival; R0 determines whether the disease dies out or not. We analyze both the local and global stability of the associated equilibria. The dynamics of the model are complex due to its forward and backward bifurcations. Finally, we perform some numerical simulations to illustrate the impact of the analytical findings observed in the works.