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Dynamics of a reaction–diffusion dengue fever model with incubation periods and vertical transmission in heterogeneous environments

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Abstract

In this paper, we incorporate incubation periods of dengue virus, vertical transmission of dengue virus and climate factors into the spread of dengue fever, and propose a reaction–diffusion model with time delays of dengue fever in heterogeneous environments. We introduce the basic reproduction number \(R_0\) to describe the threshold dynamics of the model. Some sufficient conditions for the existence and attractivity of periodic solutions of the model are obtained. Our numerical simulation and analytical results show that small incubation periods and big probability of vertical transmission tend to enhance the spread of dengue fever in heterogeneous environments.

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Acknowledgements

We are grateful to the reviewers and editors for their constructive comments, which gave the manuscript an opportunity to be further refined. The work is supported by National Natural Science Foundation of China under Grant 11971013. The work is also sponsored by Foundation of Graduate Innovation Center in NUAA under Grant Kfjj20190802.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 29 General Road, Nanjing, 211106, Jiangsu, China

    Mingshan Li & Hongyong Zhao

  2. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, 29 General Road, Nanjing, 211106, Jiangsu, China

    Mingshan Li

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  1. Mingshan Li
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Correspondence to Hongyong Zhao.

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Li, M., Zhao, H. Dynamics of a reaction–diffusion dengue fever model with incubation periods and vertical transmission in heterogeneous environments. J. Appl. Math. Comput. 68, 3673–3703 (2022). https://doi.org/10.1007/s12190-021-01676-w

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  • DOI: https://doi.org/10.1007/s12190-021-01676-w

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