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Concentration behavior of endemic equilibrium for a reaction-diffusion-advection SIS epidemic model with mass action infection mechanism. (English) Zbl 1480.35380

Summary: We are concerned with a reaction-diffusion-advection SIS epidemic model with mass action infection mechanism in a one dimensional bounded domain. We first prove the existence of endemic equilibrium (EE) whenever the basic reproduction number is greater than unity. We then focus on the asymptotic behavior of EE in three cases: large advection; small diffusion of the susceptible population; small diffusion of the infected population. Our main results show that the asymptotic profiles of the susceptible and infected populations obtained here are very different from that of the corresponding system without advection and that of the system with standard incidence infection mechanism. Thus, the effects of advection and different infection mechanisms are substantial on the spatial distribution of infectious disease; our findings bring novel insight into the disease control strategy.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
92D30 Epidemiology
92D25 Population dynamics (general)
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