Using Mathematical Model to Analyze COVID-19 Spreading

Abstract

Since the first case of Coronavirus Disease 2019 (COVID-19) was discovered in Wuhan, Hubei, China, on December 31, 2019, the disease has spread globally at an unimaginable speed. COVID-19 has taken a huge toll on the society and the economy, and everyone is looking forward to its end. In this work, we established a mathematical model of COVID-19 epidemic development. First, we obtained a differential equation to describe the spreading of COVID-19: , in which is the total number of patients who are infected by COVID-19 at time . There are three parameters in this equation: the spreading coefficient , which is the average number of people infected by an unquarantined patient in a unit time; the average quarantine ratio , which is the number of quarantined patients divided by the total number of patients; and the incubation period , which is the time lapse between infection and exhibition of symptoms. In addition, we have written a Python program according to our equation, and have further used our program to analyze the COVID-19 epidemic development in various places around the world, including China, Western Europe, Latin America and Caribbean, Southern Asia, and the entire world. Through numerical fitting, we have obtained the values of the spreading coefficient and the isolation ratio for these places around the world, and predicted the development of the epidemic using these parameters we obtained. In order to ensure data consistency, we have used the data from COVID-19 case reports from Johns Hopkins University. We found that using the parameters we obtained, our calculated curves of fit the actually reported values very well, and we were able to accurately predict the values of in the near future. Lastly, we calculated the value (the number of infected persons per patient at the beginning of the epidemic) to be 2.94∼5.88, which is consistent with the current estimated value of . In summary, our results serve as a reliable guideline to understand the spreading of COVID-19 and to predict the future outcome of this epidemic, and can be provided as a reference for the government to formulate policies.