考虑防护和隔离的传染病传播建模与分析

Modeling and Analysis of Infectious Disease Transmission Considering Protection and Isolation

基于SEIR模型,引入自我防护和隔离两个仓室,提出一个更加通用的传染病传播模型.通过对模型进行定性分析,计算模型的基本再生数,通过特征值理论和Routh-Hurwitz判据,分析模型的无病平衡点和地方病平衡点的局部渐近稳定性.数值模拟和COVID-19病毒真实数据拟合结果表明,所提出的SEIQRP模型能够有效地描述传染病的动态传播过程.模型中防护率、潜伏期隔离率和感染者隔离率这三个参数对疾病的传播起着非常关键的作用.提高人们加强自我防护意识、重点排查潜伏期患者和对感染者进行隔离治疗可以有效降低传染病的传播.

Based on the SEIR model,two compartments for self-protection and isolation are introduced,and a more general infectious disease transmission model is proposed.Through qualitative analysis of the model,the basic reproduction number of the model is calculated,and the local asymptotic stability of the disease-free equilibrium point and the endemic equilibrium point of the model is analyzed through eigenvalue theory and Routh-Hurwitz criterion.The numerical simulation and fitting results of COVID-19 virus show that the proposed SEIQRP model can effectively describe the dynamic transmission process of the infectious disease.In the model,the three parameters,i.e.protection rate,incubation period isolation rate,and infected person isolation rate play a very critical role in the spread of the disease.Raising people’s awareness of self-protection,focusing on screening for patients in the incubation period,and isolating and treating infected people can effectively reduce the spread of infectious diseases.