一个捕食者染病、食饵具有阶段结构的生态-流行病模型的稳定性  

Stability of an Eco-epidemiological Model with Disease in the Predators and Stage-structure for the Prey

作　　者：张梅[1] 王玲书[1] 贾美枝[1] ZHANG Mei;WANG Lingshu;JIA Meizhi(School of Mathematics and Statistics,Hebei University of Economics&Business,Shijiazhuang 050061)

机构地区：[1]河北经贸大学数学与统计学学院,石家庄050061

出　　处：《工程数学学报》2022年第2期224-236,共13页Chinese Journal of Engineering Mathematics

基　　金：河北省自然科学基金(A2019207070);河北经贸大学基金(2021ZD07).

摘　　要：研究了一个捕食者染病且食饵具有阶段结构的生态-流行病模型的稳定性,考虑了捕食者对食饵的Holling-Ⅱ型功能性反应函数,并讨论了由捕食者的妊娠期引起的时滞对模型稳定性的影响。通过计算特征方程的特征值,运用Hurwitz判定定理,得到了该模型的在平凡平衡点、捕食者灭绝平衡点、无病平衡点和正平衡点的局部稳定性,得到了正平衡点处存在Hopf分支的充分条件。通过构造Lyapunov泛函,运用LaSall不变集原理得到了该模型的平凡平衡点、捕食者灭绝平衡点、无病平衡点和正平衡点全局稳定的充分条件。An eco-epidemiological model with disease in the predator and stage-structure for the prey is analyzed.The Holling type-II functional response and a time delay due to the gestation of the predator are considered in this model.By analyzing the corresponding characteristic equations,the local stability of the trivial equilibrium,the predator-extinction equilibrium,the disease free equilibrium and the positive equilibrium are discussed,respectively.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the trivial equilibrium,the predator-extinction equilibrium,the disease free equilibrium and the positive equilibrium,respectively.

关 键 词：生态-流行病模型 稳定性 阶段结构 时滞 

分 类 号：O175.1[理学—数学]