Stochastic dynamics of an SEIR epidemic model on heterogeneous networks: A case of COVID-19

In this paper, a stochastic SEIR epidemic model on heterogeneous networks is established, and the law of large numbers and the central limit theorem of the epidemic process are obtained. By using the random time transformation, the mean behavior of the epidemic process is analyzed, that is, the solution of the deterministic model is given. Further, the asymptotic distribution of the final size is provided. Then, the network-based stochastic epidemic model is applied to a COVID-19 infection at a construction site in Qingpu District of Shanghai, and the parameters of the model are estimated by fitting the data of confirmed cases. Based on the estimated parameter values, the intervention measure implemented at the site is assessed by numerical simulations, and we find that the intervention does not effectively curb the development of the disease. In addition, simulation results show that the asymptotic approximation for the final size is good. The impact of the detecting or symptomatic rate on the final size is also analyzed by numerical studies. The results indicate that as the rate increases, the mean of the final size decreases and the variance increases, which is more conducive to controlling the spread of the disease.