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Spreading Speed of a Cholera Epidemic Model in a Periodic Environment

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Abstract

This paper is devoted to the spreading speed of a cholera epidemic model, which is built upon a time-periodic reaction-diffusion system that is not necessarily monotonic. When the initial distribution of infected hosts and bacteria appears on a compact domain, we derive a rough expansion speed of the infection and the bacteria over space. Our results indicate that the disease may spread at an almost constant average speed. Although our approach can not give an explicit threshold in general, our conclusions imply that there exists a constant spreading speed and the numerical simulation is applicable to estimate the spreading ability of the disease in further application. Furthermore, if the parameters are constants, we obtain an explicit formulation of spreading speed. When incidence functions take the special form, the spreading speed is the minimal wave speed of traveling wave solutions in earlier works. Additionally, the theoretical findings of this work highlight that the movement of infected hosts and bacteria, and direct and indirect transmission routes are important factors affecting the spatial spreading ability of cholera.

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Acknowledgements

We are grateful to anonymous referees for their careful reading and valuable comments.

Funding

The first author is partially supported by NSF of China (11971213) and Natural Science Foundation of Gansu Province (No. 21JR7RA535).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    Guo Lin

  2. School of Science, Lanzhou University of Technology, Lanzhou, 730050, Gansu, People’s Republic of China

    Shuxia Pan

  3. Department of Mathematics and Statistics, Washington State University, Pullman, WA, 99164, USA

    Xueying Wang

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  1. Guo Lin
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Lin, G., Pan, S. & Wang, X. Spreading Speed of a Cholera Epidemic Model in a Periodic Environment. Qual. Theory Dyn. Syst. 22, 52 (2023). https://doi.org/10.1007/s12346-023-00753-8

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