一类带连续性捕杀效应的生态-流行病SIS模型  

An eco-epidemiological SIS model with continuous hunting effect

作　　者：韩俊杰[1] 窦霁虹[1] 李涛[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《西北大学学报（自然科学版）》2013年第3期345-350,共6页Journal of Northwest University（Natural Science Edition）

基　　金：陕西省教育厅自然科学专项基金资助项目(11JK0511)

摘　　要：研究一类捕食者有传染病、能康复、但不能永久免疫且具有HollingⅡ型功能性反应的食饵带有人工连续性捕杀效应的生态-流行病SIS模型的平衡点的稳定性。用特征根法,Hurwitz判据及Liapunov函数法等方法,给出了平衡点局部渐近稳定的充分条件和边界平衡点全局渐近稳定的充分条件。改进后的模型更符合生态学意义,研究它对维持物种间的生态平衡具有重要意义。The stabilities of the equilibria of an eco-epidemiological SIS model were studied, the predator with epi- demic and HollingII functional response and the prey with artificial continuous hunting were considered in the mod- el. The infectious predators were supposed to be able to recover, however, they can＇t immune permanently. With latent root method, Hurwitz criterion and Liapunov function method etc, the sufficient condition of locally asymptot- ical stabilities of the equilibria and the sufficient condition of the globally asymptotical stabilities of the boundary equilibria were given. The improved model is more consistent with ecological significance, the study is very impor- tant for maintaining ecological balance between species.

关 键 词：生态-流行病模型 连续性捕杀 HollingⅡ型功能性反应 渐近稳定 

分 类 号：O175.13[理学—数学] Q141[理学—基础数学]