基于数据驱动的一类具有信息效应的传染病模型研究

Research on a Class of Infectious Disease Model with Information Effects Based on Data Driven

摘要: 本文我们提出了一类具有信息效应的SS_aEAIRD传染病动力学模型来揭示非药物干预措施对传染病传播的影响。首先，给出了模型的基本再生数，研究了无病平衡点的局部渐近稳定性；其次，基于我国COVID-19疫情传播的病例数据，利用bootstrap抽样、极大似然估计以及非线性最小二乘拟合对该模型的参数进行了估计；通过95%置信区间可以看出模型拟合的可靠性；最后，为了确定关键参数对疫情发展的影响，还进行了不确定性和敏感性分析。研究结果表明，加大信息宣传效应会使个人的行为发生改变，有意识的人群增多，对疾病的防护意识增强；还会降低感染者对无意识易感者的有效传染率，减少感染的人群，从而更好地控制疾病的传播。

Abstract: In this paper, we propose a class of SSaEAIRD infectious disease dynamics models with information effects to reveal the impact of non pharmacological interventions on the spread of infectious diseases. Firstly, the basic reproduction number of the model is given, and the local asymptotic stability of the disease-free equilibrium point is studied; secondly, based on the case data of COVID-19 transmission in China, the parameters of the model are estimated by using bootstrap sampling, maximum likelihood estimation, and nonlinear least squares fitting. The accuracy of model fitting can be seen through the 95% confidence interval; finally, in order to determine the influence of key parameters on the development of the disease, uncertainty and sensitivity analyses are also conducted. The research results indicate that increasing the effect of information dissemination can lead to changes in human behavior, an increase in conscious population, and an improvement in disease prevention. It will also reduce the effective transmission rate of infected individuals to unconscious susceptible individuals, reduce the number of infected individuals, and better control the spread of the disease.