一类具有时滞的反应扩散登革热传染病模型的行波解

Traveling Wave of a Reaction-Diffusion Dengue Epidemic Model with Time Delays

该文研究了一类时滞反应扩散登革热传染病模型行波解的存在性与不存在性.首先,利用辅助系统并结合Schauder不动点定理,证明了当基本再生数R_(0)>1,c>c_(*)时,系统存在单调有界正行波解.其次,当R_(0)>1,0<C<c_(*)时,借助双边Laplace变换,得到行波的不存在性;运用比较原理和反证法,证明了当R_(0)≤1,c>0时行波的不存在性.最后,从理论和数值方面探讨了潜伏期和扩散率对阈值速度c_(*)的影响.结论表明:适当延长潜伏期或减少个体扩散可降低疾病传播速度.

In this paper,we investigate the existence and nonexistence of traveling wave solution(TWS)for a reaction-diffusion dengue epidemic model with time delays.Firstly,by introducing an auxiliary system and combining with Schauder’s fixed-point theorem,it is proved that when the basic reproduction number R_(0)>1,c>c_(*),the system admits a positive bounded monotone TWS.Secondly,when R_(0)>1,00 with the aid of comparison principle and contradictory arguments.Lastly,the effects of incubation period and individual diffusion on the threshold speed c_(*)are studied theoretically and numerically.The conclusion shows that prolonging the length of incubation period or decreasing the individual diffusion will reduce the speed of disease transmission.