Modelling, Simulations and Analysis of the First and Second COVID-19 Epidemics in Beijing

Background

In December 2019, a novel coronavirus-induced pneumonia (COVID-19) broke out in Wuhan, China. On 19 January and on 8 June 2020, there were two wave COVID-19 epidemics happened in Beijing. Modelling, simulations and analysis for the two wave epidemics are important issues.

Methods

This study introduces a symptomatic-asymptomatic-recoverer-death differential equation model (SARDDE). It presents the conditions of the asymptotical stability on the disease-free equilibrium of the SARDDE. It proposes the necessary conditions of disease spreading for the SARDDE. Based on the reported data of the first and the second COVID-19 epidemics in Beijing and numerical simulations, it determines the parameters of the SARDDE, respectively.

Results

Numerical simulations of the SARDDE describe well the outcomes of the current symptomatic and asymptomatic individuals, the recovered symptomatic and asymptomatic individuals, and the died infected individuals, respectively. The numerical simulations obtain the following results.

• The transmission rate of the symptomatic infections caused by the symptomatic individuals in the second Beijing epidemic is about two times higher than the one in the first Beijing epidemic.

• Both the symptomatic and the asymptomatic individuals cause lesser asymptomatic spread than symptomatic spread.

• The blocking rates of 89.32% and 97.48% (reaching the infection turning points) to the symptomatic infections cannot prevent the spreads of the first and the second COVID-19 epidemics in Beijing, respectively.

• That on the day 28, the symptomatic infection blocking rates reached to 100% has made the second Beijing epidemics epidemic end on day 56.

• That on the day 98, the symptomatic infection blocking rates reached to 100% has made the the first Beijing epidemics epidemic end on day 140.

• Keeping the blocking rates, the recovery rates and the death rates reaching the infection turning points would make the numbers of current hospitalized infected individuals reach, on day 140, 208958 individuals and 25017 individuals for the two Beijing epidemics, respectively.

Conclusions

Virtual simulations suggest that the strict prevention and control strategies implemented by Beijing government are effective and necessary; using the data from the beginning to the days after about two weeks after the turning points can estimate well and approximately the following outcomes of the two COVID-19 epidemics, respectively. To avoid multiple epidemic outbreaks, a recommendation is that the authorities need to have maintained the prevention and control measures implemented, at least, 7 days after reaching the turning point until new current infection cases disappear. It is expected that the research can provide better understanding, explaining, and dominating for epidemic spreads, prevention and control measures.