Stability Results for an Age-Structured SIS Epidemic Model with Vector Population

We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Frechet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system.