Modeling the External, Internal, and Multi-Center Transmission of Infectious Diseases: The COVID-19 Case

We used the Bass model to investigate the transmission dynamics of COVID-19 taking the United States and China as examples. The Bass model was originated from business literature and initially modeled the process of new products getting adopted by the population with an external and internal influence term. First, we fit the cumulative number of confirmed COVID-19 cases in 8 major cities in the United States with the Bass model. The external and internal parameters of Bass were calculated and correlation analyses were performed between the parameters and the volume of traveling across different cities and within a city. The results show that the Bass model fits the epidemics data better than the logistic distribution which only has an internal influence term and the SIR model which is a classical infectious disease model. Besides, there is a significant positive correlation between the external parameter of Bass and the number of passengers at the airport as well as between the internal parameter of Bass and the number of short-distance trips in a city. Therefore, it is closer to true circumstances considering both external and internal transmission rather than assuming a region to be isolated. The external infection rate rises as the number of enplanements rises and the internal infection rate rises as the number of short-distance trips in a city rises. Second, we put forward an adapted multi-center Bass model for the multi-chain COVID-19 transmission in China and compared it with the original Bass model. The results indicated that the accuracy of the multi-center Bass model was higher than that of the original Bass model. In conclusion, the Bass model distinguishes the external and internal effects and is suitable for simulating the spread of COVID-19 and analyzing the infection rate caused by social interactions among different regions and inside a region. The adapted multi-center Bass model commendably described disease transmission when there is more than one transmission center. Our research proves the Bass model to be a useful tool for fine-level analyses on the transmission mechanism of COVID-19.