具有时滞和旅途过程中有传染的两斑块SIS模型的全局动力学

摘要

We formulate a delayed SIS model to describe the effect of transport-related infec-tion. The basic reproduction number is obtained. By the linearization method and comparison principle, it is proved that the disease-free equilibrium is globally asymptotically stable and the disease always dies out if the basic reproduction number is less than unity. While there exists a unique endemic equilibrium which is globally attractive and the disease persists if the basic reproduction number is greater than unity. The simulation results show the influence of travel rates on the disease spread. The dependence of the basic reproduction number on the travel rates during travel is also analyzed.%本文建立了一个具有时滞的SI S模型,研究了旅途过程中疾病的传染.得到了基本再生数.通过线性化方法和比较原理,证明了当基本再生数小于1时无病平衡点是全局渐近稳定的,疾病绝灭.当基本再生数大于1时,系统存在唯一的全局吸引的地方病平衡点,且疾病持续生存.数值模拟验证了扩散率对疾病传播的影响.分析了基本再生数对扩散率的依赖性.