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Epidemic waves of a spatial SIR model in combination with random dispersal and non-local dispersal

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  • Wu, Chufen
  • Yang, Yong
  • Zhao, Qianyi
  • Tian, Yanling
  • Xu, Zhiting

Abstract

In this paper, a spatial SIR model in combination with random dispersal and non-local dispersal is proposed. We establish the existence and non-existence of the traveling wave solutions connecting the disease-free equilibrium and the endemic equilibrium for the model. The main difficulties lie in the fact that the semiflow generated here does not admit the order-preserving property and the solutions lack of regularity. We use a proper iteration scheme to construct a pair of upper and lower solutions and then apply the Schauder’s fixed-point theorem, polar coordinates transform to study the threshold dynamics of the model. That is, we show that if the basic reproduction number of the model R0>1, there is a positive constant critical number c* such that for each c ≥ c*, the model admits a non-trivial and positive traveling wave with wave speed c; and if R0>1 and 0 < c < c*, the model admits no non-trivial and non-negative traveling waves. In view of the numerical simulations, we see that the epidemic waves are not monotone and the non-local dispersal may cause them to oscillate more frequently.

Suggested Citation

  • Wu, Chufen & Yang, Yong & Zhao, Qianyi & Tian, Yanling & Xu, Zhiting, 2017. "Epidemic waves of a spatial SIR model in combination with random dispersal and non-local dispersal," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 122-143.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:122-143
    DOI: 10.1016/j.amc.2017.05.068
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    References listed on IDEAS

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    1. Li, Wan-Tong & Wu, Shi-Liang, 2008. "Traveling waves in a diffusive predator–prey model with holling type-III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 476-486.
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    Cited by:

    1. Burgos, C. & Cortés, J.-C. & Debbouche, A. & Villafuerte, L. & Villanueva, R.-J., 2019. "Random fractional generalized Airy differential equations: A probabilistic analysis using mean square calculus," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 15-29.
    2. Bisin, Alberto & Moro, Andrea, 2022. "JUE insight: Learning epidemiology by doing: The empirical implications of a Spatial-SIR model with behavioral responses," Journal of Urban Economics, Elsevier, vol. 127(C).

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