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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2507.09159 |
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| _version_ | 1866911052737806336 |
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| author | Trang, Cong-Bang Vo, Hoang-Hung |
| author_facet | Trang, Cong-Bang Vo, Hoang-Hung |
| contents | This paper is concerned with the spatio-temporal dynamics of an age-structured reaction-diffusion system of KPP-epidemic type (SIS), subject to Neumann boundary conditions and incorporating $L^1$ blow-up type death rate. We first establish the existence of time dependent solutions using age-structured semigroup theory. Afterward, the basic reproduction number $\mathcal{R}_0$ is derived by linearizing the system around the disease-free equilibrium state. In the case $\mathcal{R}_0<1$, the existence, uniqueness and stability of disease-free equilibrium are shown by using $ω$-limit set approach of Langlais \cite{langlais_large_1988}, combined with the technique developed in recent works of Zhao et al. \cite{zhao_spatiotemporal_2023} and Ducrot et al. \cite{ducrot_age-structured_2024}. We highlight that the absence of a general comparison principle for the age-structured SIS-model and non-separable variable mortality rate prevent the direct application of the semi-flow technique developed in \cite{ducrot_age-structured_2024} to study the long time dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spatio-temporal dynamics of an age-structured reaction-diffusion system of epidemic type subjected by Neumann boundary condition Trang, Cong-Bang Vo, Hoang-Hung Analysis of PDEs This paper is concerned with the spatio-temporal dynamics of an age-structured reaction-diffusion system of KPP-epidemic type (SIS), subject to Neumann boundary conditions and incorporating $L^1$ blow-up type death rate. We first establish the existence of time dependent solutions using age-structured semigroup theory. Afterward, the basic reproduction number $\mathcal{R}_0$ is derived by linearizing the system around the disease-free equilibrium state. In the case $\mathcal{R}_0<1$, the existence, uniqueness and stability of disease-free equilibrium are shown by using $ω$-limit set approach of Langlais \cite{langlais_large_1988}, combined with the technique developed in recent works of Zhao et al. \cite{zhao_spatiotemporal_2023} and Ducrot et al. \cite{ducrot_age-structured_2024}. We highlight that the absence of a general comparison principle for the age-structured SIS-model and non-separable variable mortality rate prevent the direct application of the semi-flow technique developed in \cite{ducrot_age-structured_2024} to study the long time dynamics. |
| title | Spatio-temporal dynamics of an age-structured reaction-diffusion system of epidemic type subjected by Neumann boundary condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.09159 |