论文标题
一类离散扩散SIR流行模型的行驶波解决方案
Traveling wave solutions for a class of discrete diffusive SIR epidemic model
论文作者
论文摘要
本文涉及一类离散扩散流行模型的行驶波解（TWS）的存在和不存在的条件。我们发现，TWS的存在取决于所谓的基本繁殖数和关键波速度：当基本复制号r0大于1时，存在一个临界波速度C*> 0，因此对于每个C> = C*，该系统承认C <c*对系统而言，对于系统而言，对于系统而言，则不存在非琐事。另外，通过构建合适的Lyapunov功能并采用Lebesgue主导的收敛定理来获得TWS的边界渐近行为。最后，我们将结果应用于两个离散的扩散流行模型，以验证TWS的存在和不存在。
This paper is concerned with the conditions of existence and nonexistence of traveling wave solutions (TWS) for a class of discrete diffusive epidemic models. We find that the existence of TWS is determined by the so-called basic reproduction number and the critical wave speed: When the basic reproduction number R0 greater than 1, there exists a critical wave speed c* > 0, such that for each c >= c * the system admits a nontrivial TWS and for c < c* there exists no nontrivial TWS for the system. In addition, the boundary asymptotic behaviour of TWS is obtained by constructing a suitable Lyapunov functional and employing Lebesgue dominated convergence theorem. Finally, we apply our results to two discrete diffusive epidemic models to verify the existence and nonexistence of TWS.
