具有种群动力和非线性传染率βI^PS/1+αI^P的流行病模型分析  

Analysis of an epidemic model with population dynamics and nonlinear incidence rate βI^PS/1+αI^P

作　　者：石磊[1,2] 魏敏[1] 游雄[1] 

机构地区：[1]南京农业大学理学院,南京210095 [2]南京师范大学数学科学学院,南京210046

出　　处：《华中师范大学学报（自然科学版）》2014年第5期632-636,共5页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11171155);南京农业大学理学院青年教师科技创新基金项目(LXYQ201300102)

摘　　要：研究一类具有非线性传染率βIPS/1+αIP的流行病模型,模型中引入了种群动力.运用微分方程定性理论讨论了模型的正不变集,分析了该系统疾病消除平衡点和地方病平衡点的存在性及稳定性,得出了全局渐近稳定的充分条件.最后对上述模型进行了生物学讨论.In this paper,a class of epidemic models with nonlinear incidence rate βI^PS/1＋αI^PP is studied,where we introduce population dynamics.The positive invariant set of the model is discussed by using qualitative theory of differential equations,and the existence and stability of the endemic steady state and the disease-free steady state are analyzed.We obtain the sufficient conditions for the global asymptotic stability of the models.Finally the biological significance is discussed.

关 键 词：种群动力学 非线性传染率 平衡点 稳定性 

分 类 号：O175.1[理学—数学]