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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University of Newfoundland, Saint John’s, NL, A1C 5S7, Canada

    Ruiwen Wu & Xiao-Qiang Zhao

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  1. Ruiwen Wu
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  2. Xiao-Qiang Zhao
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Correspondence to Ruiwen Wu.

Additional information

Communicated by Sue Ann Campbell.

Research supported in part by the NSERC of Canada.

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Wu, R., Zhao, XQ. A Reaction–Diffusion Model of Vector-Borne Disease with Periodic Delays. J Nonlinear Sci 29, 29–64 (2019). https://doi.org/10.1007/s00332-018-9475-9

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  • DOI: https://doi.org/10.1007/s00332-018-9475-9

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