Traveling wave solutions for a delayed diffusive SIR epidemic model with nonlinear incidence rate and external supplies |
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| Authors: | Kai Zhou Maoan Han Qiru Wang |
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| Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai, China;2. School of Mathematics and Computer, Chizhou University, Chizhou, China;3. School of Mathematics and Computational Science, Sun Yat‐Sen University, Guangzhou, China |
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| Abstract: | In this paper, we study the traveling wave solutions of a delayed diffusive SIR epidemic model with nonlinear incidence rate and constant external supplies. We find that the existence of traveling wave solutions is determined by the basic reproduction number of the corresponding spatial‐homogenous delay differential system and the minimal wave speed. The existence is proved by applying Schauder's fixed point theorem and Lyapunov functional method. The non‐existence of traveling waves is obtained by two‐sided Laplace transform. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | traveling wave solutions Schauder's fixed point theorem SIR model upper and lower solutions external supplies subclass 92D30 35K57 35C07 |
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