Traveling waves for a diffusive SEIR epidemic model
Traveling waves for a diffusive SEIR epidemic model
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DOI：
10.3934/cpaa.2016.15.871
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发表时间：
2016-02
影响因子：
1
通讯作者：
Zhiting Xu
中科院分区：
文献类型：
--
作者：
Zhiting Xu
本文提出了一个具有饱和传染率的SEIR传染病扩散模型。我们首先研究了模型的适定性，并给出了基本再生数$\mathcal{R}_0$的显式表达式。因此，我们证明了，如果$\mathcal{R}_0>1$，则存在一个正常数$c^*>0$，使得对于每个$c>c^*$，该模型允许一个非平凡行波解，并且如果$\mathcal{R}_0\leq1$和$c\geq 0$（或，$\mathcal{R}_0>1$和$c\in[0，c ^*）$），则该模型没有非平凡行波解。因此，我们确认常数c^*$确实是最小波速。主要结果的证明主要基于Schauder不动点定理和拉普拉斯变换。
In this paper, we propose a diffusive SEIR epidemic model with saturating incidence rate. We first study the well posedness of the model, and give the explicit formula of the basic reproduction number $\mathcal{R}_0$. And hence, we show that if $\mathcal{R}_0>1$, then there exists a positive constant $c^*>0$ such that for each $c>c^*$, the model admits a nontrivial traveling wave solution, and if $\mathcal{R}_0\leq1$ and $c\geq 0$ (or, $\mathcal{R}_0>1$ and $c\in[0,c^*)$), then the model has no nontrivial traveling wave solutions. Consequently, we confirm that the constant $c^*$ is indeed the minimal wave speed. The proof of the main results is mainly based on Schauder fixed theorem and Laplace transform.