摘要
具有非线性影响率βI^p,0<p<1,的传染病数学模型常表现为非线性微分-差分方程.当研究该方程在疾病不发生的平衡态附近的解的性态时,方程的右端函数是不可微的.本文用李亚普诺夫泛函方法证明了这类方程的这种平微态是不稳定的.
The difference-differential equations with undifferentiable right sides arise in the models for epidemiological diseases when the incidence rates of the diseases are nonlinear functions with forms g(I)= βI′o<p<1,and the dynamical behavior of the models,near the disease-free-equilibrium points need to be examined.In these cases the disease-free states should be unstable.The instability of the equilibrium point (1,0,0) for the ■ mobel is proved with the method of Liapunov functional.The proofs for the other models are analogous.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
1992年第2期163-165,共3页
Journal of Inner Mongolia University：Natural Science Edition
关键词
种群
传染病模型
微-差分方程
Epidemiological model
Nonlinear incidence rate
Instability
Liapunov functional
