Threshold dynamics of an age-structured infectious disease model with limited medical resources

In this paper, an age-structured infectious disease dynamical model that considers two diseases simultaneously but with limited medical resources is proposed and analyzed. The asymptotic smoothness and persistence of the solution semi-flow are investigated. Then conditions for the existence of a global attractor are derived, which means that disease persists when ℜ0>1. By using a Lyapunov function, it is shown that the infection-free equilibrium is globally asymptotically stable if ℜ0<1 and the infection equilibrium is globally asymptotically stable if ℜ0>1. In the presence of limited medical resources, the results suggest that equitable distribution for the limited medical resources is significant when treating low-risk and high-risk diseases and that keeping a resource sharing coefficient at a moderate level helps to eliminate the disease.