具有扩散的生态-流行病模型的稳定性分析  

Stability Analysis of an Eco-epidemiological Model with Dispersal

作　　者：王玲书[1] 陈若彤 WANG Lingshu;CHEN Ruotong(School of Mathematics and Statistics,Hebei University of Economics&Business,Shijiazhuang 050061,China)

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061

出　　处：《北华大学学报（自然科学版）》2024年第2期141-147,共7页Journal of Beihua University（Natural Science）

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

摘　　要：讨论一个食饵具有扩散和捕食者具有疾病的生态-流行病模型的稳定性,考虑了由捕食者种群的妊娠期引起的时滞对种群动力学性态的影响。首先,通过分析特征方程,运用Hurwitz判定定理,讨论了该模型无病平衡点和地方病平衡点的局部稳定性,给出了平衡点附近存在Hopf分支的充分条件;其次,通过构造适当的Lyapunov泛函,运用LaSalle不变性原理,讨论了该模型无病平衡点和地方病平衡点的全局稳定性,从而得到了该生态系统永久持续生存的充分条件。An eco-epidemiological model with prey dispersal and disease in the predator is discussed.A time delay due to the gestation of the predator is considered.By analyzing the corresponding characteristic equations,the local stability of the disease free equilibrium and the coexistence equilibrium are analyzed by using Hurwitz judging theorem,respectively.The existence of Hopf bifurcations is established.By using Lyapunov functional and LaSalle invariance principle,the sufficient conditions are obtained for the global stability of disease free equilibrium and the coexistence equilibrium,respectively.

关 键 词：生态模型 扩散 时滞 HOPF分支 稳定性 

分 类 号：O175.1[理学—数学]