包虫病传播模型的最优控制分析

Optimal Control Analysis of an Echinococcosis Transmission Model

摘要: 包虫病是一种人畜共患病，主要在最终宿主、中间宿主和最终宿主之间进行循环。例如羊作为中间宿主，由于摄入被寄生虫卵污染过的食物和水而被感染，而狗作为最终宿主可能在吃了有寄生虫幼虫的羊的内脏后被感染。本文提出了一个具有标准发病率的包虫病传播模型，得到了模型的基本再生数，研究了疾病的灭绝性与持续性。考虑屠宰场卫生检测、给狗驱虫、给绵羊接种疫苗和环境消毒等各种控制，建立控制系统并证明了最优解的存在性、刻画。

Abstract: Echinococcosis is a zoonotic disease that mainly circulates among definitive hosts, intermediate hosts and definitive hosts. For example, sheep, as intermediate hosts, are infected by ingesting food and water contaminated with parasite eggs, while dogs, as definitive hosts, may be infected after consuming the internal organs of sheep with parasitic larvae. In this paper, we propose an echinococcosis transmission model with a standard incidence rate. We obtain the basic reproduction number of the model, and study the extinction and persistence of the disease. Considering various control measures such as hygiene inspection in slaughterhouses, deworming of dogs, vaccination of sheep and environmental disinfection, a control system is established, and the existence and characterization of the optimal solution are shown.