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Basic reproduction ratio of a mosquito-borne disease in heterogeneous environment

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Abstract

To explore the influence of spatial heterogeneity on mosquito-borne diseases, we formulate a reaction–diffusion model with general incidence rates. The basic reproduction ratio \(\mathcal {R}_0\) for this model is introduced and the threshold dynamics in terms of \(\mathcal {R}_0\) are obtained. In the case where the model is spatially homogeneous, the global asymptotic stability of the endemic equilibrium is proved when \(\mathcal {R}_0>1\). Under appropriate conditions, we establish the asymptotic profiles of \(\mathcal {R}_0\) in the case of small or large diffusion rates, and investigate the monotonicity of \(\mathcal {R}_0\) with respect to the heterogeneous diffusion coefficients. Numerically, the proposed model is applied to study the dengue fever transmission. Via performing simulations on the impacts of certain factors on \(\mathcal {R}_0\) and disease dynamics, we find some novel and interesting phenomena which can provide valuable information for the targeted implementation of disease control measures.

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Acknowledgements

The authors are grateful to the editor and the anonymous reviewers for their careful reading and valuable suggestions which led to substantial improvements of the manuscript. HZ is partially supported by the National Natural Science Foundation of China (No. 11971013). KW is partially supported by the Postgraduate Research  & Practice Innovation Program of Jiangsu Province (No. KYCX20_0169) and the Nan**g University of Aeronautics and Astronautics PhD short-term visiting scholar Project (No. ZDGB2021026) at the University of Alberta. HW is partially supported by the Natural Sciences and Engineering Research Council of Canada (Individual Discovery Grant RGPIN-2020-03911 and Discovery Accelerator Supplement Award RGPAS-2020-00090).

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Authors and Affiliations

  1. School of Mathematics, Nan**g University of Aeronautics and Astronautics, Nan**g, 211106, China

    Hongyong Zhao & Kai Wang

  2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nan**g, 211106, China

    Hongyong Zhao & Kai Wang

  3. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Kai Wang & Hao Wang

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  1. Hongyong Zhao
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Zhao, H., Wang, K. & Wang, H. Basic reproduction ratio of a mosquito-borne disease in heterogeneous environment. J. Math. Biol. 86, 32 (2023). https://doi.org/10.1007/s00285-023-01867-y

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