摘要
建立和研究一类具有非线性发生率的传染病模型,得到该模型基本再生数R_0的表达式,运用Lyapunov函数和第二加性复合矩阵理论证明了当R_0<1时无病平衡点全局渐近稳定,此时疾病消失,当R_0>1时地方病平衡点全局渐近稳定,此时疾病在人群中流行.
An epidemic model with nonlinear incidence rate is formulated, and studied in this paper. The explicit expression of the basic reproduction number is obtained, by using the Lyapunov function method and the geometric method, the globally asymptotical stabilities of diseaseqfree and endemic equilibria are proved under certain conditions.
出处
《数学的实践与认识》
CSCD
北大核心
2012年第12期112-117,共6页
Mathematics in Practice and Theory
基金
河南省自然科学基金(112300410238
112300410058
关键词
传染病模型
非线性发生率
地方病平衡点
全局渐近稳定性
endemic model
nonlinear incidence rate
endemic equilibrium
globally asymp-totical stability
