基于风险感知的SIR疾病传播动力学研究

Research on the Transmission Dynamics of SIR Disease Based on Risk Perception

摘要: 近年来传染病的暴发给全球带来巨大的负面影响，越来越多的人具有风险感知的能力并采取了一定的防护措施，从而从个人角度减少疫情的扩散。为了从理论角度研究该实际情况，本文将构建基于风险感知的SIR (Susceptible-Infected-Recovered)的疾病传播模型进行研究，同时提出相应的应对策略。具体为，首先分析影响疾病传播的因素，即风险感知因素和出生率及死亡率因素，构建基于风险感知的SIR疾病传播模型。其次对该模型进行理论分析，并求出传染病扩散动力学过程的基本再生数。最后用Matlab在生成的随机规则网络、WS小世界网络、BA无标度网络和无标度特性的社区网络上开展传染病扩散的模拟仿真。研究得出，风险感知能力提升可以有效控制基本再生数，并降低感染者的数量。同时，无标度特性网络更易于传播病的扩散。最后，提出相应的传染病防控的应对策略建议。

Abstract: In recent years, the outbreak of infectious diseases has brought huge negative impacts to the world. More and more people have the ability to perceive risks and take certain protective measures, therefore, it is common sense that we can reduce the spread of the epidemic from a personal per-spective. In order to study this situation, in this paper we will build a risk perception-based SIR (Susceptible-Infected-Recovered) disease spreading model, and propose corresponding control strategies. Specifically, we consider two additional factors, comprising risk perception, and birth and mortality, and build an SIR (Susceptible-Infected-Recovered) disease spreading model. Sec-ondly, we provide detailed theoretical analysis of the model, as well as the basic reproduction number. Finally, we conduct simulation results on four generated networks using Matlab software, considering the random regular network, WS small world network, BA scale-free network and scale-free community network. This study shows that the improvement of risk perception ability can effectively control the basic reproduction number and reduce the number of infected people. At the same time, scale-free networks more easily spread disease. Finally, we give corresponding countermeasures and suggestions for the prevention and control of infectious diseases.