摘要
传染病模型易受外界随机因素的干扰.该文提出一类具有非单调发生率的时滞随机传染病模型.利用Lyapunov方法及伊藤公式,证明了该模型具有唯一一个正全局解和该模型的无病平衡点是随机稳定的,并且得到了相应的确定型模型地方病平衡点在随机扰动下的渐近性.最后,利用数值仿真图例对理论结果加以验证说明.
Epidemic models are often subject to random perturbations. This article proposes a stochastic delayed epidemic model with a non-monotonic incidence rate. By the Lyapunov method and ItS＇s formula, the existence of a unique global positive solution of the model and the stability of the disease-free equilibrium of the model are proved. The asymptotic behavior around the endemic equilibrium of the associated definite model is obtained. Finally, numerical simulations are presented to illustrate the results.
作者
孟笑莹
Meng Xiaoying(The School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 43007)
出处
《数学物理学报（A辑）》
CSCD
北大核心
2017年第6期1162-1175,共14页
Acta Mathematica Scientia
基金
国家自然科学基金(61503415)~~
