摘要
【目的】研究由SIR和SIS组合的三维传染病模型行波解的存在性。【方法】利用Routh-Hurwitz判据,运用Schauder不动点定理构造合适的上下解,讨论该模型中无病平衡点和地方病平衡点在一定条件下的稳定性以及连接两个平衡点的行波解的存在性。【结果】当R_(0)>1时,对任意的c>c^(*),该传染病模型存在连接无病平衡点和地方病平衡点的行波解,且最小波速为c^(*)。【结论】该传染病模型的行波解是存在的。
[Purposes]In order to study the existence of travelling wave solutions in a three-dimensional infectious disease model composed of SIR and SIS.[Methods]The stabilities,under certain conditions,of disease-free equilibrium point and endemic disease equilibrium point in this model are discussed by means of Routh-Hurwitz criterion.Moreover,using Schauder fixed point theorem,the existence of travelling wave solutions connecting those two equilibrium points is investigated via constructing appropriate upperlower solutions.[Findings]When R_(0)>1,for any c>c^(*),there exists travelling wave solution with the minimum wave speed c^(*),which connect the disease-free equilibrium point and endemic equilibrium point in the epidemic model.[Conclusions]The existence of travelling wave solutions in this infectious disease model has been verified.
作者
杨三艳
李庶民
YANG Sanyan;LI Shumin(College of Science,Kunming University of Science and Technology,Kunming 650500,China)
出处
《重庆师范大学学报（自然科学版）》
CAS
北大核心
2021年第3期84-93,共10页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金(No.11561034)。
关键词
行波解
局部渐进稳定
SCHAUDER不动点定理
上下解
最小波速
travelling wave solution
locally asymptotic stability
Schauder fixed point theorem
upper-lower solution
minimum wave speed
