Epidemic reaction-diffusion systems with two types of boundary conditions
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Date
2018-10-11
Authors
Li, Kehua
Li, Jiemei
Wang, Wei
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
SIRS model, Reaction-diffusion system, Global dynamics, Neumann boundary condition, Free boundary condition
Citation
Li, K., Li, J., & Wang, W. (2018). Epidemic reaction-diffusion systems with two types of boundary conditions. <i>Electronic Journal of Differential Equations, 2018</i>(170), pp. 1-21.
Rights
Attribution 4.0 International