考虑隔离的三维禽流感 Filippov 控制模型的研究

A Study of a Three-Dimensional Filippov Control Model for Avian Influenza Considering Isolation

摘要: 本文深入探究了 3 种不同控制措施对禽流感传播的综合影响, 建立了一个以捕杀受感染的禽类、隔离 (人们受到媒体宣传的影响所进行的自主隔离) 已感染的人类以及利用医疗资源进行积极治疗作为控制措施的 SI-SIR 禽流感模型. 基于阈值策略, 我们将 SI-SIR 禽流感模型扩展到一个三维的Filippov 系统, 把感染禽类以及感染人类的总和作为是否采取控制措施的参考指标: 如果总和未超过阈值 𝐼_𝑇 , 则不采取任何措施; 然而, 一旦总和超过阈值 𝐼_𝑇 , 则需要立即采取控制措施. 依据阈值水平 𝐼_𝑇 , 模型的解最终稳定到一个地方病平衡点或者一个伪平衡点. 数值模拟表明, 一个良好的阈值策略可以有效控制禽流感的发展, 以使禽流感的发展保持在可接受或期望的水平。

Abstract: In this paper, we explore the comprehensive impact of three different control measures on the spread of avian influenza, and establish an SI-SIR avian influenza model with culling of infected birds, isolating (the autonomous isolation of people influenced by media propaganda) infected humans, and using active treatment of medical resources as control measures. Based on the threshold strategy, the SI-SIR avian influenza model is extended to a three-dimensional Filippov system. The total number of infected birds and humans is taken as the reference index of whether to take control measures: if the sum does not exceed the threshold 𝐼_𝑇 , no action will be taken; however, once the sum exceeds the threshold 𝐼_𝑇 , immediate control measures are required. According to the threshold level 𝐼_𝑇 , the solution of the model finally stabilizes at an endemic equilibrium or a pseudo-equilibrium. The numerical simulation shows that a good threshold strategy can effectively control the development of avian influenza, so as to keep the development of avian influenza in an acceptable or desired level.