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Journal of Nonlinear Science

, Volume 29, Issue 1, pp 29–64 | Cite as

A Reaction–Diffusion Model of Vector-Borne Disease with Periodic Delays

  • Ruiwen WuEmail author
  • Xiao-Qiang Zhao
Article
  • 246 Downloads

Abstract

A vector-borne disease is caused by a range of pathogens and transmitted to hosts through vectors. To investigate the multiple effects of the spatial heterogeneity, the temperature sensitivity of extrinsic incubation period and intrinsic incubation period, and the seasonality on disease transmission, we propose a nonlocal reaction–diffusion model of vector-borne disease with periodic delays. We introduce the basic reproduction number \(\mathfrak {R}_0\) for this model and then establish a threshold-type result on its global dynamics in terms of \(\mathfrak {R}_0\). In the case where all the coefficients are constants, we also prove the global attractivity of the positive constant steady state when \(\mathfrak {R}_0>1\). Numerically, we study the malaria transmission in Maputo Province, Mozambique.

Keywords

Vector-borne disease Reaction–diffusion model Periodic delays Basic reproduction number Threshold dynamics 

Mathematics Subject Classification

35K57 37N25 92D25 

Notes

Acknowledgements

We sincerely thank Dr. Zhenguo Bai and Lei Zhang for helpful discussions on mathematical modeling and numerical computation of \(\mathfrak {R}_0\). We are also grateful to two referees for their careful reading and valuable suggestions which led to an improvement of our original manuscript.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMemorial University of NewfoundlandSaint John’sCanada

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