一类食饵染病的捕食-食饵模型的定性分析及最优收获问题  

Qualitative Analysis and Optimal Harvesting Problem of a Predator-Prey Model with Disease in Prey

作　　者：林风光 雒志学[1] LIN Fengguang;LUO Zhixue(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《应用数学》2023年第1期41-48,共8页Mathematica Applicata

基　　金：国家自然科学基金(11561041)。

摘　　要：讨论一类具有收获且食饵染病的传染病模型,考虑了Holling Ⅱ类功能性反应及饱和发生率.利用Routh-Hurwitz判据研究了非负平衡点的局部稳定性,通过构造Lyapunov函数得到平衡点全局渐近稳定的充分条件.最后,利用Pont ryagin最大值原理研究最优收获策略.An epidemic model with harvesting and disease in prey is discussed,and the Holling type Ⅱ functional response and saturated incidence rate are considered.The local stability of non-negative equilibria is studied by using Routh-Hurwitz criteria,and the sufficient conditions for the global asymptotical stability of the equilibria are investigated by constructing the Lyapunov function.Finally,the optimal harvesting strategy is obtained by using Pontryagin ’s maximum principle.

关 键 词：捕食-食饵模型 饱和发生率 HollingⅡ类功能性反应 收获 

分 类 号：O175[理学—数学]