基于非线性时变SEIR模型的新型冠状病毒肺炎传播机制

Modeling of COVID-19 Transmission Mechanism Based on Nonlinear SEIR Model with Time-varying Delays

当前新冠肺炎仍在肆无忌惮地侵犯着人类,分析与调控其传播机制显得刻不容缓。为了使传统SEIR模型能更有效地处理实际问题,我们对其进行了改进,改进后的模型考虑了疫情区人员流动和感染者死亡等重要影响因素。人员流动情况用混合型高斯模型进行数学建模,可调参数以最大期望算法进行优化。另外,潜伏不变时滞被推广到时变时滞。本文所提模型是非线性的,且能够处理潜伏时滞是时变的情况,并以湖北省为例,给出了仿真例子,说明了所选方法的有效性。

At present, the COVID-19 is still unscrupulously violating human beings. It is urgent to analyze and regulate its transmission mechanism. In order to deal with practical problems more effectively, we improve the traditional SEIR model. The improved model takes into account the important factors such as the flow of people and the death of infected people in the epidemic area. The flow of personnel is modeled by Gaussian mixture model, and the adjustable parameters are optimized by maximum expectation algorithm. In addition, the latent invariant delay is extended to the time-varying delay. The proposed model is nonlinear and can deal with the time-varying latent delay. Finally, Taking Hubei Province as an example, a simulation example is given to illustrate the effectiveness of the proposed method.