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Global boundedness of a density-dependent SIRS epidemic model with nonlinear infection mechanism.
- Source :
- Evolution Equations & Control Theory; Oct2024, Vol. 13 Issue 5, p1-13, 13p
- Publication Year :
- 2024
-
Abstract
- In this paper, we study the following density-dependent SIRS epidemic model with power-like infection mechanism$ \begin{align*} \left\{ \begin{aligned} &u_t = \Delta(d_1(v)u)-\beta(x) u^qv^p+\gamma w, \quad &&x\in\Omega, t>0, \\ &v_t = d_2\Delta v+\beta(x) u^qv^p-(\delta+\alpha)v, \quad &&x\in\Omega, t>0, \\ &w_t = \Delta(d_3(v)w)+\delta v-\gamma w, \quad &&x\in\Omega, t>0, \end{aligned} \right. \end{align*} $in a bounded smooth domain $ \Omega\subset \mathbb{R}^n (n\geq2) $. Here $ p $, $ q $, $ \gamma $, $ \delta $, $ \alpha>0 $ are constants. We prove that the problem possesses a global classical solution in $ n $ dimension $ (n\geq2) $ when $ q<\frac{2}{n} $, $ p\leq1 $. Moreover, we show that the above solution will converge to the steady state $ (u^*, 0, 0) $, where $ u^* = \vert\Omega\vert^{-1}\left(\int_{\Omega}(u_0+v_0+w_0)-\alpha\int_{0}^{\infty}\int_{\Omega} v\right) $. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 21632472
- Volume :
- 13
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Evolution Equations & Control Theory
- Publication Type :
- Academic Journal
- Accession number :
- 179092053
- Full Text :
- https://doi.org/10.3934/eect.2024027