摘要
研究了一类非线性随机非自治SIRS传染病模型的动力学行为.首先,利用Lyapunov函数方法得到了疾病灭绝的充分条件.然后,通过Has′minskii的周期解理论,分成3个区域证明了该系统至少存在1个非平凡的正周期解.最后,利用Matlab进行了数值模拟来说明理论结果.
In this paper,we investigate the dynamic behavior of a nonlinear stochastic non-autonomous SIRS model.Firstly,by using the Lyapunov function method,sufficient conditions for extinction of the disease are established.Secondly,we prove that there exists at least one nontrivial positive periodic solution of the system by employing Has′minskii′s theory of periodic solution under three cases.Finally,we use the Matlab to provide a series of numerical simulations to illustrate the analytical results.
作者
吕学进
孟新柱
LV Xuejin,MENG Xinzhu(College of Mathematics and Systems Science,Shandong University of Science and Technology, Qingdao, Shandong 266590, Chin)
出处
《数学建模及其应用》
2018年第1期16-23,F0003,共9页
Mathematical Modeling and Its Applications
基金
国家自然科学基金项目(11371230)
山东科技大学科研创新团队支持计划项目(2014TDJH102)
关键词
随机SIRS模型
饱和发生率
灭绝
周期解
stochastic SIRS model
saturation incidence
extinction
periodic solution
