一类带有扩散与时滞的流行性传染病模型的行波解

讨论了一类带有扩散与时滞的流行性传染病模型的行波解的存在性.首先,将系统的行波解的存在性问题转化为一个二阶常微分方程组的单调解的存在性问题;应用单调方法和不动点方法,进一步地将问题转化为方程组的上下解的构造问题;应用所建立的引理与定理,通过构造适合的上下解,证明了系统单调行波解的存在性.

Traveling Waves in a Diffusive and Temporal Delayed Epidemic Model

In this paper,the existence of the travelling waves in a diffusive and temporal delayed epidemic model has been discussed.First,the discussion on the travelling waves in the reaction-diffusion system with which this model corresponds is turned into one problem on upper and lower solutions in second order ordinary differential equations;then,the existence condition is established via the method of upper and lower solutions.Second,based on the above estiblished lemmas and theorem,we construct appropriate upper and lower solutions to prove the existence of the traveling waves.