Dynamics of solutions to a multi-patch epidemic model with a saturation incidence mechanism
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910609533042688 |
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| author | Ezunkpe, Yawo Nnolum, Cynthia T. Salako, Rachidi B. Xue, Shuwen |
| author_facet | Ezunkpe, Yawo Nnolum, Cynthia T. Salako, Rachidi B. Xue, Shuwen |
| contents | This study examines the behavior of solutions in a multi-patch epidemic model that includes a saturation incidence mechanism. When the fatality rate due to the disease is not null, our findings show that the solutions of the model tend to stabilize at disease-free equilibria. Conversely, when the disease-induced fatality rate is null, the dynamics of the model become more intricate. Notably, in this scenario, while the saturation effect reduces the basic reproduction number $\mathcal{R}_0$, it can also lead to a backward bifurcation of the endemic equilibria curve at $\mathcal{R}_0=1$. Provided certain fundamental assumptions are satisfied, we offer a detailed analysis of the global dynamics of solutions based on the value of $\mathcal{R}_0$. Additionally, we investigate the asymptotic profiles of endemic equilibria as population dispersal rates tend to zero. To support and illustrate our theoretical findings, we conduct numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11443 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of solutions to a multi-patch epidemic model with a saturation incidence mechanism Ezunkpe, Yawo Nnolum, Cynthia T. Salako, Rachidi B. Xue, Shuwen Populations and Evolution 34D05, 34D23, 92D25, 92D30, 37N25 This study examines the behavior of solutions in a multi-patch epidemic model that includes a saturation incidence mechanism. When the fatality rate due to the disease is not null, our findings show that the solutions of the model tend to stabilize at disease-free equilibria. Conversely, when the disease-induced fatality rate is null, the dynamics of the model become more intricate. Notably, in this scenario, while the saturation effect reduces the basic reproduction number $\mathcal{R}_0$, it can also lead to a backward bifurcation of the endemic equilibria curve at $\mathcal{R}_0=1$. Provided certain fundamental assumptions are satisfied, we offer a detailed analysis of the global dynamics of solutions based on the value of $\mathcal{R}_0$. Additionally, we investigate the asymptotic profiles of endemic equilibria as population dispersal rates tend to zero. To support and illustrate our theoretical findings, we conduct numerical simulations. |
| title | Dynamics of solutions to a multi-patch epidemic model with a saturation incidence mechanism |
| topic | Populations and Evolution 34D05, 34D23, 92D25, 92D30, 37N25 |
| url | https://arxiv.org/abs/2409.11443 |