Monotonicity,uniqueness, and stability of traveling waves in a nonlocal reaction‐diffusion system with delay |
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| Authors: | Hai‐Qin Zhao |
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| Affiliation: | School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi, P.R. China |
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| Abstract: | The purpose of this paper is to study the traveling wave solutions of a nonlocal reaction‐diffusion system with delay arising from the spread of an epidemic by oral‐faecal transmission. Under monostable and quasimonotone it is well known that the system has a minimal wave speed c* of traveling wave fronts. In this paper, we first prove the monotonicity and uniqueness of traveling waves with speed c ?c ?. Then we show that the traveling wave fronts with speed c >c ? are exponentially asymptotically stable. |
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| Keywords: | epidemic model monostable nonlinearity reaction‐diffusion system traveling waves |
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