Backward bifurcation arising from decline of immunity against emerging infectious diseases

Decline of immunity is a phenomenon characterized by immunocompromised host and plays a crucial role in the epidemiology of emerging infectious diseases (EIDs) such as COVID-19. In this paper, we propose an age-structured model with vaccination and reinfection of immune individuals. We prove that the disease-free equilibrium of the model undergoes backward and forward transcritical bifurcations at the critical value of the basic reproduction number for different values of parameters. We illustrate the results by numerical computations, and also find that the endemic equilibrium exhibits a saddle-node bifurcation on the extended branch of the forward transcritical bifurcation. These results allow us to understand the interplay between the decline of immunity and EIDs, and are able to provide strategies for mitigating the impact of EIDs on global health.