摘要
研究了一类含时滞具有垂直传染的SIR传染病模型,得到了系统的基本再生数R0,利用特征理论分析了系统的局部渐近稳定性,证明了R0〉1时系统是持久的;通过构造Lyapunov函数讨论了R0〉1时地方病平衡点的全局渐近稳定性,并且利用比较定理讨论了R0〈1时无病平衡点的全局渐近稳定性;最后利用MATLAB软件分析了时滞在SIR模型中的影响.
A delayed SIR model with vertical transmission is researched and the basic regeneration number R0 of the system is obtained.By analyzing the characteristic theory,we discuss the local asymptotical stability of the system.The system is permanent if R0〉1.By Lyapunov functional method,if R0〉1,then the endemic equilibrium is globally asymptotical stability,and by comparison theorem,if R0〈1,then the disease-free equilibrium is globally asymptotical stability.Finally,the impact of delayed SIR model by MATLAB software is analyzed.
出处
《北华大学学报（自然科学版）》
CAS
2011年第5期497-504,共8页
Journal of Beihua University（Natural Science）
