Traveling waves for a diffusive SIR model with delay
Traveling waves for a diffusive SIR model with delay
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DOI：
10.1016/j.jmaa.2015.09.069
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发表时间：
2016-03
影响因子：
1.3
通讯作者：
Sheng-Chen Fu
中科院分区：
文献类型：
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作者：
Sheng-Chen Fu
本文研究了一类具有时滞和饱和传染率的SIR扩散模型的无病平衡态和地方病平衡态之间的行波解。由于该系统不具有比较原理，我们将使用迭代过程来构造一对上下解。借助于这对上下解，我们可以应用Schauder不动点定理构造截断问题的解族，通过极限变元，这些解族可以产生行波.证明了存在c ≠ 0使得该系统存在速度为c的行波解当且仅当c≥ c ≠ 0.
In this paper, we study traveling waves connecting the infection-free equilibrium state and the endemic equilibrium state for a diffusive SIR model with delay and saturated incidence rate. Since this system does not enjoy the comparison principle, we will use an iteration process to construct a pair of upper and lower solutions. With the aid of the pair of upper and lower solutions, we can apply the Schauder fixed point theorem to construct a family of solutions of the truncated problems, which, via the limiting argument, can generate the traveling wave. Indeed, we show that there exists c⁎> 0 such that this system admits a traveling wave solution with speed c iff c≥ c⁎.