一类具有扩散项的流行性传染病模型中的行波解  

Traveling Waves in a Diffusive Epidemic Model

作　　者：张国胜[1] 孙庆利[1] 曹志军[1] 赵冠华[2] 

机构地区：[1]石家庄学院数学系,河北石家庄050035 [2]邯郸学院数学系,河北邯郸056005

出　　处：《数学的实践与认识》2008年第9期92-101,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10401006);石家庄学院自然科学基金重点资助

摘　　要：讨论了一类具有扩散项的流行性传染病模型中的行波解的存在性.首先,将对该模型所对应的反应扩散系统的行波解的讨论转化为对二阶常微分系统的上下解的讨论;然后,通过上下解方法建立了这个具有扩散项的传染病模型中行波解的存在性条件,并进一步讨论了扩散因素对行波解的波速的影响,得到被感染人群的流动对病毒的传播有一定的影响.The existence of the travelling waves in an epidemic model with diffusion items has been discussed. First, the discussion on the travelling waves in reaction-diffusion system with which this model corresponds is turned into one 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, and then the influence upon travelling wave speed is further discussed. In this view, the mobility of the infective human population has a certain influence on the spread of the virus.

关 键 词：传染病模型 行波解 上下解 单调方法 

分 类 号：O175.2[理学—数学]