The Dynamics Of Two Epidemic Models In An Almost Periodic Environment

The interaction of mixed factors leads to the outbreak of a infectious disease.Spatial diffusion and temporal heterogeneity are important factors that influence the spread of infectious diseases. Considering the seasonal factors, researchers tend to think the coefficients that affect the spread of diseases in epidemic models are periodic functions with the same period. For the population living in a complex environment, however, periodic system is not universal. Especially, if the periods of these coefficients functions have no common integer multiple, then the model is not a periodic system. Mathematically, we can treat such a model as an almost periodic system. This paper will explore the global dynamics of two epidemic models in an almost periodic environment.Considering the time factor, we first explore a within-host virus model with almost periodic multidrug therapy. First, we define the spectral radius of next generation operator as the basic reproduction number R0. Then, a threshold type result for uniform persistence and global extinction of the disease is obtained in terms of R0. Lastly, we illustrate the theoretical results by means of numerical simulations.Considering population diffusion and temporal heterogeneity, then we study a reaction-diffusion susceptible-infected-susceptible(SIS) epidemic model in an almost periodic environment. We first present the theory of abstract linear almost periodic parabolic equations. Next, by using the idea of the next generation operator, we establish the definition and the theories of the basic reproduction number R0, and obtain its computation formula. In particular, we get some quantitative properties for R0. Finally, we establish a threshold type result on the global dynamics in terms of R0.