Asymptotic behavior of traveling waves for a nonlocal epidemic model with delay
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Date
2017-06-30
Authors
Zhao, Haiqin
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we study the traveling wave solutions of a monostable nonlocal reaction-diffusion system with delay arising from the spread of an epidemic by oral-faecal transmission. From [23], there exists a minimal wave speed c* > 0 such that a traveling wave solution exists if and only if the wave speed is above c*. In this article, we first establish the exact asymptotic behavior of the traveling waves at ±∞. Then, we construct some annihilating-front entire solutions which behave like a traveling wave front propagating from the left side (or the right side) on the x-axis or two traveling wave fronts propagating from both sides on the x-axis as t → -∞ and converge to the unique positive equilibrium as t → +∞. From the viewpoint of epidemiology, these results provide some new spread ways of the epidemic.
Description
Keywords
Traveling wave front, Epidemic model, Reaction-diffusion system, Monostable nonlinearity
Citation
Zhao, H. (2017). Asymptotic behavior of traveling waves for a nonlocal epidemic model with delay. Electronic Journal of Differential Equations, 2017(160), pp. 1-19.
Rights
Attribution 4.0 International