具有常数输入的非自治SIR流行病模型周期解的存在性The existence of periodic solutions for a SIR epidemic model with constant birth rate
胡新利;
摘要(Abstract):
利用MAWHIN重合度理论中的延拓定理研究了一类具有常数输入的非自治SIR流行病模型的非平凡周期解的存在性.并用MatLab对其进行了数值模拟,作出了模型的相图和解曲线图形.
关键词(KeyWords): 传染病模型;周期解;重合度
基金项目(Foundation): 陕西省自然科学基金资助项目(07JK267);; 西安工程大学校管课题资助项目(2007XG27)
作者(Authors): 胡新利;
参考文献(References):
- [1]Kermack W O,Mckendrick A G.A contribution to the mathematical theory of epidemic[J].Proc.RSocLond,1927,A115(575):700-721.
- [2]Hethcote H W.The mathematics of infectious disease[J].SIAM Review,2000,42(4):599-653.
- [3]马知恩,周义仓,王稳地,等.传染病动力学的数学建模与研究[M].北京:科学出版社,2004.
- [4]Mukherjee Debasis.Uniform persistence in a generalized prey-predator system with parasitic infection[J].Biosystems,1988,47:149-155.
- [5]Fan Meng,Wang Ke,Jiang Da-ing.Existence and global attractibity of positive periodicsolutions of pe-riodic nspecies Lotka-Volterra competition systems with several debiating arguments[J].MathematicalBiosciences,1999,160:47-61.
- [6]李玉昆.一类时滞微分方程周期解的存在性和全局吸引性[J].中国科学:A辑,1998,28(2):108-118.
- [7]蒋达清,魏俊杰.非自治时滞微分方程周期正解的存在性[J].数学年刊:A辑,1999,20(6):715-720.
- [8]Gaines R E,Mawhin J L.Coincidence degree and nonlinear defferential equation[M].New York:Spr-inger-verlag,1997.