关键词: 捕食系统, 生态流行病, 恢复率, 定性分析, 最优控制

Abstract: Firstly, we established and discussed a four-dimensional ecoepidemiological model in which both prey and predator populations were infected, and the infected population had self-recovery ability. Secondly, we established the corresponding optimal control model and  used Pontryagin’s maximum principle to calculate its optimal control strategy. Finally, we investigated the dynamic behaviors of the model and its optimal control strategy by using numerical analysis. The results show that the recovery rate of diseases has a significant impact on the dynamic behavior of the system.

Key words: predator-prey system, ecological epidemics, recovery rate, qualitative analysis, optimal control