Spatial profiles of a reaction-diffusion epidemic model with nonlinear incidence mechanism and varying total population
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910741727019008 |
|---|---|
| author | Peng, Rui Salako, Rachidi B. Wu, Yixiang |
| author_facet | Peng, Rui Salako, Rachidi B. Wu, Yixiang |
| contents | This paper considers a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and varying total population. The interaction of the susceptible and infected people is describe by the nonlinear transmission mechanism of the form $S^qI^p$, where $0<p\le 1$ and $q>0$. In [39], we have studied a model with a constant total population. In the current paper, we extend our analysis to a model with a varying total population, incorporating birth and death rates. We investigate the asymptotic profiles of the endemic equilibrium when the dispersal rates of susceptible and/or infected individuals are small. Our work is motivated by disease control strategies that limit population movement. To illustrate the main findings, we conduct numerical simulations and provide a discussion of the theoretical results from the view of disease control. We will also compare the results for the models with constant or varying total population. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatial profiles of a reaction-diffusion epidemic model with nonlinear incidence mechanism and varying total population Peng, Rui Salako, Rachidi B. Wu, Yixiang Analysis of PDEs 35J57, 35B40, 35Q92, 92D30 This paper considers a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and varying total population. The interaction of the susceptible and infected people is describe by the nonlinear transmission mechanism of the form $S^qI^p$, where $0<p\le 1$ and $q>0$. In [39], we have studied a model with a constant total population. In the current paper, we extend our analysis to a model with a varying total population, incorporating birth and death rates. We investigate the asymptotic profiles of the endemic equilibrium when the dispersal rates of susceptible and/or infected individuals are small. Our work is motivated by disease control strategies that limit population movement. To illustrate the main findings, we conduct numerical simulations and provide a discussion of the theoretical results from the view of disease control. We will also compare the results for the models with constant or varying total population. |
| title | Spatial profiles of a reaction-diffusion epidemic model with nonlinear incidence mechanism and varying total population |
| topic | Analysis of PDEs 35J57, 35B40, 35Q92, 92D30 |
| url | https://arxiv.org/abs/2411.00582 |