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Global Dynamics of a Reaction–Diffusion Model of Zika Virus Transmission with Seasonality

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Abstract

In this paper, we propose a periodic reaction–diffusion model of Zika virus with seasonal and spatial heterogeneous structure in host and vector population. We introduce the basic reproduction ratio \(R_0\) for this model and show that the disease-free periodic solution is globally asymptotically stable if \(R_0\le 1\), while the system admits a globally asymptotically stable positive periodic solution if \(R_0 >1\). Numerically, we study the Zika transmission in Rio de Janeiro Municipality, Brazil, and investigate the effects of some model parameters on \(R_0\). We find that the neglect of seasonality underestimates the value of \(R_0\) and the maximum carrying capacity affects the spread of Zika virus.

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Fig. 1

Source: https://www.citypopulation.de/php/brazil-rio.php. b Density of susceptible host \(H_u(x)\) in Rio de Janeiro Municipality

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Acknowledgements

This work was supported in part by the Fundamental Research Funds for the Central Universities (2652020012), the China Scholarship Council (201506460020) and the Natural Science and Engineering Research Council of Canada. We are grateful to the referees for their valuable comments and suggestions which led to an improvement of our original manuscript.

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Correspondence to Fuxiang Li.

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Li, F., Zhao, XQ. Global Dynamics of a Reaction–Diffusion Model of Zika Virus Transmission with Seasonality. Bull Math Biol 83, 43 (2021). https://doi.org/10.1007/s11538-021-00879-3

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