Estimating the time-varying reproduction number of COVID-19 with a state-space method

After slowing down the spread of the novel coronavirus COVID-19, many countries have started to relax their confinement measures in the face of critical damage to socioeconomic structures. At this stage, it is desirable to monitor the degree to which political measures or social affairs have exerted influence on the spread of disease. Though it is difficult to trace back individual transmission of infections whose incubation periods are long and highly variable, estimating the average spreading rate is possible if a proper mathematical model can be devised to analyze daily event-occurrences. To render an accurate assessment, we have devised a state-space method for fitting a discrete-time variant of the Hawkes process to a given dataset of daily confirmed cases. The proposed method detects changes occurring in each country and assesses the impact of social events in terms of the temporally varying reproduction number, which corresponds to the average number of cases directly caused by a single infected case. Moreover, the proposed method can be used to predict the possible consequences of alternative political measures. This information can serve as a reference for behavioral guidelines that should be adopted according to the varying risk of infection.Author summary: Society and the media alternate between hope and despair in response to the temporary decrease or increase of daily new COVID-19 infections. The number of cases has been dependent on the political measures that were adopted in each country. Accordingly, there is a strong demand for quantifying the effects of individual measures. The reproduction number, defined as the average number of cases directly caused by a single infected case, is one of the indices of the current infectivity status. To capture the time-varying reproduction number correctly, it is necessary to incorporate the distribution of delays, which are widely dispersed from 2 to 14 days for the case of COVID-19. We have developed a state-space method for estimating the reproduction number solely from an available dataset of the number of daily cases. Our method automatically detects the change-points in the reproduction number. We apply our method to the real data and examine if the detected changes are consistent with the times at which political measures had been taken in each country. Furthermore, our method can be used to predict the number of new cases in the future to examine the possible consequences of alternative political measures.