Dynamical Behavior of an Epidemic Model with Coinfection Of Two Diseases

We have formulated a simple epidemiological model with two diseases that can coinfect a single host. The first disease is assumed to be chronic, the second one acute. For infectives infected only by the first disease, we introduce the age of infection, For these two diseases, we obtain their reproduction numbers, respectively, and establish conditions for the existence and stability of the disease-free equilibrium, the boundary equilibrium, and the positive (coexistent) equilibrium. For infectious individuals infected only by the first disease, when some transfer rates depend on the age of infection and the corresponding model is governed by partial differential equations (PDEs), we give a sufficient condition for the existence of positive equilibrium, and its stability is determined by a transcendental equation; when all the associated rates are independent of the age of infection, the corresponding models are ordinary differential equations (ODEs). We obtain complete results on dynamics, find that the coexistent equilibrium of two diseases is globally stable if they exist, and find that the boundary equilibrium is globally stable if it is locally stable. Finally, we find that there is a difference between PDE and ODE models.