具有非线性发生率的SIR模型的全局吸引性Global Attractivity for SIR Model with Nonlinear Incidence
王建军,张晋珠
摘要(Abstract):
研究一类具有非线性发生率的传染病模型。确定了疾病是否流行的阈值R0.当R0≤1时,通过构造Lyapunov泛函,证明了无病平衡点的全局吸引性。
关键词(KeyWords): 时滞;SIR模型;全局吸引性
基金项目(Foundation): 山西省自然科学基金(2007011019)
作者(Author): 王建军,张晋珠
参考文献(References):
- [1]马知恩,周义仓,王稳地,靳祯.传染病动力学的数学建模与研究[M].北京:科学出版社,2004.
- [2]COOKE K.Stability Analysis for A Vector Disease Model[J].Rocky Mount,J.Math.,1979(9):31-42.
- [3]ANDERSON R M,MAY R M.Regulation and Stability of Host-parasite Population Interactions[J].Journal of Animal Ecology,1978,47:219-267.
- [4]KUANG Y.Delay Differential Equations with Applications in Population Dynamics[M].NewYork:Academic Press,1993.
- [5]YANG X,CHEN L,CHEN J.Permanence and Positive Periodic Solution for the Single Species Nonautonomous Delay Diffusive Model[J].Comp.Math.Appl.,1996,32:109-116.