Epidemic reaction-diffusion systems with two types of boundary conditions
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We investigate an epidemic reaction-diffusion system with two different types of boundary conditions. For the problem with the Neumann boundary condition, the global dynamics is fully determined by the basic reproduction number R0. For the problem with the free boundary condition, the disease will vanish if the basic reproduction number R0 < 1 or the initial infected radius g0 is sufficiently small. Furthermore, it is shown that the disease will spread to the whole domain if R0 > 1 and the initial infected radius g0 is suitably large. Main results reveal that besides the basic reproduction number, the size of initial epidemic region and the diffusion rates of the disease also have an important influence to the disease transmission.
CitationLi, K., Li, J., & Wang, W. (2018). Epidemic reaction-diffusion systems with two types of boundary conditions. Electronic Journal of Differential Equations, 2018(170), pp. 1-21.
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