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Traveling Wave Solutions in a Nonlocal Dispersal SIR Epidemic Model with General Nonlinear Incidence

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Abstract

In this paper, for a class of nonlocal dispersal SIR epidemic models with nonlinear incidence, we study the existence of traveling waves connecting the disease-free equilibrium with endemic equilibrium. We obtain that the existence of traveling waves depends on the minimal wave speed \(c^{*}\) and basic reproduction number \(\mathcal{R}_{0}\). That is, if \(\mathcal{R}_{0}>1\) and \(c> c^{*}\) then the model has a traveling wave connecting the disease-free equilibrium with endemic equilibrium. Otherwise, if \(\mathcal{R}_{0}>1\) and \(0< c< c^{*}\), then there does not exist the traveling wave connecting the disease-free equilibrium with endemic equilibrium. The numerical simulations verify the theoretical results. Our results improve and generalize some known results.

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  1. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Weixin Wu & Zhidong Teng

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  1. Weixin Wu
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  2. Zhidong Teng
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Correspondence to Zhidong Teng.

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This work was supported by the Natural Science Foundation of China (Grant No. 11771373, 11861065) and the Natural Science Foundation of Xinjiang Province of China (Grant No. 2016D03022).

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Wu, W., Teng, Z. Traveling Wave Solutions in a Nonlocal Dispersal SIR Epidemic Model with General Nonlinear Incidence. Acta Appl Math 175, 4 (2021). https://doi.org/10.1007/s10440-021-00432-3

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