食饵具有避难所效应的生态-传染病模型的分析  

The Dynamic of the Eco-Epidemiological Model with the Prey Refuge

作　　者：康爱花[1,2] 

机构地区：[1]中北大学数学系,山西太原035000 [2]朔州师范高等专科学校数学系,山西朔州036000

出　　处：《数学的实践与认识》2015年第15期310-314,共5页Mathematics in Practice and Theory

摘　　要：建立并分析了疾病在食饵中传播、食饵考虑避难所效应的捕食与被捕食模型,捕食者不仅捕食感染食饵而且捕食易感食饵.讨论了系统的有界性和各平衡点的存在性,利用Routh-Hurwitz判据分析各平衡点的局部渐进稳定性,通过构造Lyapunov函数证明了各平衡点的全局渐进稳定性,并进行数值模拟以验证结论的正确性.In the paper, we analyze the prey-predator model with the disease in the prey, considering the prey refuge. The boundness of solutions and the existence of the equilibria are studied,and the sufficient conditions of locally asymptotically stable of the equilibria are obtained by the Routh-Hurwitz criterion. We analyze the global stability of all equilibria by using Lyapunov functions. At last, Numeric simulations are carried out to illustrate the feasibility of the main results.

关 键 词：避难所 生态-传染病模型 稳定性 

分 类 号：O175[理学—数学]