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arXiv · 2002.02586

Traveling wave solutions for a class of discrete diffusive SIR epidemic model

Ran Zhang·Jinliang Wang·Shengqiang Liu
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Abstract

This paper is concerned with the conditions of existence and nonexistence of traveling wave solutions (TWS) for a class of discrete diffusive epidemic models. We find that the existence of TWS is determined by the so-called basic reproduction number and the critical wave speed: When the basic reproduction number R0 greater than 1, there exists a critical wave speed c* > 0, such that for each c >= c * the system admits a nontrivial TWS and for c < c* there exists no nontrivial TWS for the system. In addition, the boundary asymptotic behaviour of TWS is obtained by constructing a suitable Lyapunov functional and employing Lebesgue dominated convergence theorem. Finally, we apply our results to two discrete diffusive epidemic models to verify the existence and nonexistence of TWS.

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Ran Zhang, Jinliang Wang, Shengqiang Liu. 2020-02-07. Traveling wave solutions for a class of discrete diffusive SIR epidemic model. https://doi.org/10.1007/s00332-020-09656-3

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