带有个体自发行为变化的传染病模型的研究  

The Epidemic Model with Individual Spontaneous Behavior Change

作　　者：陈影 张沐涵 王琳[3] 

机构地区：[1]长春工业大学数学与统计学院,吉林 长春 [2]长春工业大学人文信息学院数理教研部,吉林 长春 [3]长春理工大学数学与统计学院,吉林 长春

出　　处：《理论数学》2024年第2期576-590,共15页Pure Mathematics

摘　　要：本文考虑了一类带有个体自发行为变化的SIR模型。在某些传染病流行期间,易感人群可以采取正常行为或谨慎行为(如戴口罩、保持社交距离等),个体通过比较两种行为的回报(包括感染风险和经济成本)自发地选择其中之一。这种个体行为变化可以通过进化博弈论中的模仿动力学建模。在个体行为变化的时间尺度比传染病传播的时间尺度快得多的情况下,用几何奇异摄动理论分析我们建立的带有个体自发行为变化的SIR模型。借助快–慢结构和入–出积分得到模型的奇异轨道,并进行数值模拟。In this paper, we consider a SIR model with individual spontaneous behavior change. During some epidemics, susceptibles can adopt normal or altered behaviors (such as wearing masks, social dis-tancing, etc.). Individuals spontaneously choose one or the other by comparing the payoff (including the risk of infection and the economic costs) of the two behaviors. This individual behavior changes are modeled by imitation dynamics in evolutionary game theory. Under the condition where the time scale of behavior change is much faster than the time scale of infectious disease transmission, we use the geometric singular perturbation theory to analyze the SIR model with individual spontaneous behavior change. The singular orbit of the model is obtained by slow-fast structure and entry-exit integration, and simulated numerically.

关 键 词：传染病模型 几何奇异摄动理论 模仿动力学 进化博弈论 

分 类 号：G63[文化科学—教育学]