What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases?

Summary Background The COVID-19 epidemic, which started in late December 2019 and rapidly spread throughout the world, was accompanied by an unprecedented release of reported case data. Our objective is to propose a fresh look at this data by coupling a phenomenological description to the epidemiological dynamics. Methods We use a phenomenological model to describe and regularize the data. This model can be matched by a single mathematical model reproducing the epidemiological dynamics with a time-dependent transmission rate. We provide a method to compute this transmission rate and reconstruct the changes in the social interactions between people as well as changes in host-pathogen interactions. This method is applied to the cumulative case data of 8 different geographic areas. Findings We reconstruct the transmission rate from the data, therefore we are in position to understand the contribution of the dynamical effects of social interactions (contacts between individuals) and the contribution of the dynamics of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important in the dynamic of COVID-19. We obtain an instantaneous reproduction number that stays below 3.5 from early beginning of the epidemic. Conclusion The instantaneous reproduction number staying below 3.5 implies that it is sufficient to vaccinate 71% of the population in each state or country considered in our study. Therefore assuming the vaccines will remain efficient against the new variants, and to be more confident it is sufficient to vaccinate 75 − 80% to get rid of COVID-19 in each state or country. Funding This research was funded by the Agence Nationale de la Recherche in France (Project name: MPCUII (PM) and (QG))