具有复发效应的SEAIR模型及在新冠肺炎传染病中的应用

An SEAIR model with relapse effect and its application in COVID-19 transmission

建立了一类具有复发效应和无症状感染的SEAIR模型,给出了模型的基本再生数R_(0),证明了当R_(0)<1时无病平衡点全局渐近稳定,R_(0)>1时无病平衡点不稳定且疾病是一致持久的。作为模型的应用,选取湖北已报道的新冠肺炎累计病例数,利用模型拟合数据,并对疾病发展趋势进行了数值模拟。最后对参数进行敏感性分析,研究了不同的复发率对新冠肺炎的影响。结果表明,复发率越高,新冠肺炎疫情会越来越严重;研究结果建议采取严格的隔离措施和佩戴口罩来降低疾病的传染率和二次复发。

In this paper,an SEAIR epidemic model with relapse and asymptomatic infection is established,and the basic reproduction number R_(0)is given.It is proved that the disease-free equilibrium is globally asymptotically stable when R_(0)<1,the disease-free equilibrium is unstable and the disease is uniformly persistent when R_(0)>1.As an application of the model,the cumulative number of COVID-19 cases reported in Hubei province is selected in this study.The model is fitted with reported data and simulated the development trend of the disease.Finally,the sensitivity of the parameters is analyzed,and the effect of different relapse rates on the COVID-19 is studied.The results show that the higher the relapse rates,the more serious the COVID-19 will be.The findings suggest that strict quarantine measures and wearing masks are recommended to reduce the infection rates of the disease and reduce the relapse rates of the disease.