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Time-periodic traveling wave solutions of a reaction–diffusion Zika epidemic model with seasonality

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Abstract

In this paper, the full information about the existence and nonexistence of a time-periodic traveling wave solution of a reaction–diffusion Zika epidemic model with seasonality, which is non-monotonic, is investigated. More precisely, if the basic reproduction number, denoted by \(R_{0}\), is larger than one, there exists a minimal wave speed \(c^* > 0\) satisfying for each \(c > c^*\), the system admits a nontrivial time-periodic traveling wave solution with wave speed c, and for \(c<c^*\), there exist no nontrivial time-periodic traveling waves such that if \(R_0 \leqslant 1\), the system admits no nontrivial time-periodic traveling waves.

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Data Availability

The authors declare that the data are available on request from the authors.

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Funding

Researcher was supported by National Natural Science Foundation of China (12161052) and Natural Science Foundation of Gansu, China (21JR7RA240).

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  1. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, China

    Lin Zhao

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Zhao, L. Time-periodic traveling wave solutions of a reaction–diffusion Zika epidemic model with seasonality. Z. Angew. Math. Phys. 75, 32 (2024). https://doi.org/10.1007/s00033-023-02173-9

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