Simulations and Estimations of COVID-19 Epidemics in Beijing and Shanghai

• 1、School of Mathematics and Physics, University of Science and Technology Beijing, 100083

Abstract：The 2019 novel coronavirus (COVID-19) is a new virus that causes respiratory illness in people. This virus was first identified during an investigation into an outbreak in December 2019 Wuhan, China. To date, more than 15 millions on infected with COVID-19 have been identified worldwide. It causes more 600,000 deaths and affects more than 200 countries and regions. Establishing a mathematical model for epidemic infectious diseases has played an important role in the formulation,evaluation,and prevention of control strategies.This paper introduces such a model (INSIAR). This model improves one our previous mathematical model: susceptible-infected- asymptomatic-recoverer (NSIAR), and provides a subsidiary model (SM). SM can decribe the evolotions of cuumulative died, recovered infected and recovered asymptomatic individuals. Consequently INSIAR can provide more clear and detailed interpretations to the dynamics of COVID-19 epidemic than those done by NSIAR. The solutions of INSIAR are all positive and bounded. NSIAR has a disease-free equilibrium and a disease-persistent equilibrium. It provides criterions of local stability, and conditions of globally asymptotical stability on the disease-free equilibrium. It gives criterions of epidemic spread. As applications, utilizing the reported data of COVID-19 epidemics in Beijing and Shanghai (form the first infections discoveries to about two weeks\' after infectious peak points) , this paper determines the model parameters with different periods, simualtes and estimates the outmomes of the COVID-19 epidemics in Beijing and Shanghai, and evaluate the prevention of control strategies in Beijing and Shanghai. Simulation results are close to some repoted clinic data of the COVID-19 in Beijing and Shanghail. If Beijing would take group imunity or loose imunity measures for COVID-19 epidemics. Simulation results showed that in both cases, there were about 230000 death cases, and the end date of the loose imunity was not earlier than that of the group imunity. However, If the authority and people in Beijing keep the current strict prevention and control measures, a few outside input COVID-19 infectious cases will not generate epidemic spreading. The analysis suggest that Beijing and Shanghai have similar infecting and spreading patterns of COVID-19 epidemics. Both cites have implemented almost the same prevent and control measures. It is expected that the research results can provide new theoretical tools and ideas worthy of reference for better understanding and dominating of epidemic spreads, preventions and controls.

keywords： Epidemic and health statistics; new coronavirus; disease transmission; mathematical model; simulations of epidemics in Beijing and Shanghai group immunity, loose immunity, outside input infection.

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