Dynamics Of An Infectious Model Of Vector-borne Disease In An Almost Periodic Environment

Epidemic has always been an important problem in human society,it has threatened our life and wealth since human existed.Dynamics analysis is a powerful tool in math to predict the spreading of epidemic.In this article,we concern on a kind of nonlocal epidemic model in an almost periodic environment.Based on its biology character,we establish a model with spatial homo-geneous、time-delay（age structure of population and the incubation period of disease）.Because of the influence of seasons and the negative movement of vectors,we consider this model under almost periodic environments and its diffusion is nonlocal.Then we discuss the well-posedness of our model and get its limiting reaction-diffusion system.Further-more,we define the upper Lyapunov exponentλ^*as the threshold to by skew-product semiflow theory.Based on this,we can see that the disease will disappear whenλ^*<0but persist whenλ^*>0.At last we calculateλ^*numerically and discuss the influence of parameters on it.