具有饱和发病率的害虫治理SI模型的动力学研究

Dynamics of an SI Model for Pest Management with Saturated Morbidity

摘要: 本文建立了一个具有饱和发生率的分段光滑SI害虫治理模型，以此刻画只有当易感害虫数量达到经济阁值时才对其进行综合害虫治理的策略。 利用Filippov系统定性分析理论，分析了模型在不同阁值全局动力学，得到地方病平衡点和伪平衡点的全局稳定性。研究表明，在不同的经济阁值范围下，增加染病害虫的投放量以及减少杀虫剂的使用量能避免害虫数量爆发，可以为害虫治理提供策略和方法。

Abstract: In this paper, a piecewise smooth SI pest control model with saturation incidence rate is established, in order to draw the management strategy of chemical control only when the number of susceptible pests reaches the economic threshold. Using the qualitative analysis theory of Filippov system, the global dynamics of the model in different thresholds and parameter ranges are analyzed, and the global stability of endemic equilibrium and pseudo equilibrium is obtained. Particularly, when the parameters and thresholds are properly selected, the two endemic equilibrium points will be bi-stable. The research shows that increasing or decreasing the dosage of pesticides can effectively control the number of pests and avoid economic losses under different economic threshold ranges.