Modeling the situation of COVID-19 and effects of different containment strategies in China with dynamic differential equations and parameters estimation (Preprint)

Abstract

BACKGROUND An ongoing outbreak of a novel coronavirus (COVID-19) pneumonia has spread to many parts of the world generating concerns about the possibility of an extensive pandemic. China has adopted unprecedented mitigation policies especially strict quarantine measures since January 2020, to contain the spread of the epidemic. However, the long-term management and control has brought considerable inconvenience to the daily lives of people and also it has significant negative impacts on Chinese national and global economies. Therefore, it is important to estimate the dynamic evolution mechanism of the epidemic in mainland China, to find when the epidemic will end and how this result depends on different containment strategies. These are issues of great significance with important clinical and policy implications. OBJECTIVE This research aims to estimate the dynamic evolution mechanism of COVID-19 in mainland China, to find when the epidemic will end and how this result depends on different containment strategies. METHODS This paper proposed a quarantine-susceptible-exposed-infectious-resistant (QSEIR) model which considers the unprecedented strict quarantine measures in almost the whole China to resist the epidemic. Parameter estimation is the most critical part when using this kind of SEIR model to predict the trend of epidemic. We estimated the model parameters reversely for the QSEIR model from published information with statistical methods and stochastic simulations; from these experiments, we found the parameters that achieved the best simulation test results. The next stage involved quantitative predictions of future epidemic developments based on different containment strategies with QSEIR model, focused on the sensitivity of the outcomes to different parameter choices in mainland China. RESULTS If the strict quarantine measures are being retained, the peak value of confirmed cases would be in the range of [52,438-64,090] and the peak date would be expected in the range February 7 to February 19, 2020. During the period between March18-30, 2020 the epidemic would be controlled. The end date would be in the period from August 20, 2020 to September 1, 2020. With 80% probability, our prediction of the peak date is on February 13, 4 days ahead of the real date, the prediction error of the peak value is 0.43%, both estimates are much closer to the observed values compared with other published studies. The sensitivity analysis indicated that quarantine measures (or with vaccination) are the most effective containment strategy to control the epidemic, followed by measures to increase the cure rate (e.g., finding special medicines). The quarantine measures should not be relaxed before the end of March, 2020 in mainland China. China can fully resume production with appropriate anti-epidemic measures beginning in early April 2020. CONCLUSIONS The paper established a QSEIR model that considers the unprecedented strict quarantine measures which are more fit for the epidemic situation in mainland China. The paper illustrated the method to generate the parameter estimations and the application verified that the method is effective. The paper not only predicted the peak number and peak date of confirmed cases, but also provided estimates of the sensitivity of parameters of QSEIR, the duration of the epidemic and effects of different containment strategies at the same time. The long-term simulation result and sensitive analysis in mainland China showed that the QSEIR model is stable and can be empirically validated. It is suggested that the QSEIR model can be applied to predict the development trend of the epidemic in other regions or countries in the world.