Background: The outbreak and epidemic of COVID-19 has created worldwide impact and attracted global attention. Considerable effort has been devoted to the study of the transmission dynamics of COVID-19. However, there are lack of simple and straightforward expressions of the growing curves of important indicators, such as the cumulative number of confirmed cases and the cumulative number of dead cases.
Methods: We adopt two methods. The first method is based on regression analysis. We fit the available data into a curve by the method of least squares. The best curve is obtained by solving a multivariable minimization problem. The second method is based on differential equations. We establish an analytical model of transmission dynamics based on the susceptible-exposed-infectious-recovered-dead (SEIRD) process using a linear system of ordinary differential equations, which characterize the daily change in each compartment. The size of each compartment (i.e., the number of people in each stage of the SEIRD process) is readily available based on the solution to these differential equations.
Results: Both methods are applied to the COVID-19 epidemic data in the world as a case study. Furthermore, predictions of the cumulative number of confirmed cases and the cumulative number of dead cases in April 2020 using our models and methods are also provided. From a global perspective, unless powerful and effective social and medical impacts are made, by the end April of 2020, the cumulative number of confirmed cases is 23.333 and 36.068 millions respectively using regression analysis and analytical model, and the cumulative number of dead cases is 1.148 and 2.528 millions respectively using regression analysis and analytical model, based on the current situation.
Conclusions: In this paper, we make some progress towards analytical expressions of the daily growth of the cumulative number of confirmed cases and the cumulative number of dead cases, two most important and daily reported figures.