具有饱和发生率的生态流行病模型的定性分析及最优收获问题

Qualitative Analysis and Optimal Harvesting Problem of Eco-epidemiological Model with Saturation Incidence

研究了一类具有收获和庇护所效应的生态流行病模型,假设疾病仅在捕食种群之间传播,同时考虑了HollingⅡ型功能性反应及饱和发生率.首先运用Routh–Hurwitz判据讨论了非负平衡点的局部稳定性,然后通过构造Lyapunov函数并结合LaSalle不变集原理得到了平衡点全局渐近稳定的充分条件,最后利用Pontryagin最大值原理研究了最优收获策略.

An eco-epidemiological model with harvesting and refuge effect is studied,assuming that the disease only spread among predator populations,and the Holling type II functional response and saturated incidence rate are considered.First of all,the local stability of non-negative equilibria is discussed by using Routh-Hurwitz criteria.Then,the sufficient conditions for the global asymptotical stability of the equilibria are obtained by constructing Lyapunov functions and combining with LaSalle’s invariance principle.Finally,the optimal harvesting strategy is investigated by using Pontryagin’s maximum principle.