DYNAMICS OF AN ALMOST PERIODIC EPIDEMIC MODEL WITH NON-LOCAL INFECTIONS AND LATENCY IN A PATCHY ENVIRONMENT

Based on the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of population may disperse, combined with seasonal factors, an almost periodic SIR model with non-local infections and latency in a patchy environment is investigated. Draw support from the idea of the next generation operator, the definition of the basic reproduction number R-0 is given. Furthermore, the global dynamical theory of the model is studied using the basic regeneration number R-0 as a threshold parameter. It is shown that the disease will die out in the sense that the disease-free almost periodic solution of the model is globally attractive if R-0 < 1, while the disease is uniformly persistent when R-0 > 1. Finally, this paper numerically simulates the model in a two patch environment, and verifies the propagation mechanism of the almost periodic infectious disease model. Moreover, Some numerical simulations indicate that population distribution between patches has a significant impact on the spread of diseases and show that the periodic epidemic models may overestimate or underestimate the disease risk comparing with the almost periodic model.