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Threshold Dynamics for Infection Age-Structured Epidemic Models with Spatial Diffusion and Degenerate Diffusion

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Abstract

This paper is devoted to studying the threshold dynamics for infection age-structured epidemic models with non-degenerate diffusion and degenerate diffusion. For general infection age-structured epidemic models with non-degenerate diffusion, we establish the basic reproduction number \(R_0\) by using non-densely defined operators and prove that \(R_0\) equals the spectral radius of \(-{\mathscr {F}}{\mathscr {A}}^{-1}\). For a class of infection age-structured epidemic models with non-degenerate diffusion or degenerate diffusion, we give a general method to prove that \(R_0\) plays the role of the threshold for the extinction or persistence of the disease. Finally, we apply our methods to the infection age-structured SIR, SEIR epidemic models and obtain the threshold results on their global dynamics. Our results on \(R_0\) for the general infection age-structured epidemic models extend the cases of ODE and reaction–diffusion epidemic models. In addition, our method in this paper improves some previous results and is applicable to the Neumann, Dirichlet, and Robin boundary conditions.

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Acknowledgements

The authors would like to thank the referee for many valuable comments which helped to improve the manuscript. This work was supported by the National Natural Science Foundation of China (No. 11771044, 12171039 and 11871007).

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  1. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Jiawei Huo, Qiang Huo & Rong Yuan

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  1. Jiawei Huo
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Huo, J., Huo, Q. & Yuan, R. Threshold Dynamics for Infection Age-Structured Epidemic Models with Spatial Diffusion and Degenerate Diffusion. J Dyn Diff Equat (2023). https://doi.org/10.1007/s10884-023-10288-w

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