Statistical data driven approach of COVID-19 in Ecuador: R 0 and R t estimation via new method.

The growth of COVID-19 pandemic throughout more than 213 countries around the world have put a lot of pressures on governments and health services to try to stop the rapid expansion of the pandemic. During 2009, H1N1 Influenza pandemic, statistical and mathematical methods were used to track how the virus spreads around countries. Most of these models that were developed at the beginning of the XXI century are based on the classical susceptible-infected-recovered (SIR) model developed almost a hundred years ago. The evolution of this model allows us to forecast and compute basic and effective reproduction numbers (R t and R 0 ), measures that quantify the epidemic potential of a pathogen and estimates different scenarios. In this study, we present a traditional estimation technique for R 0 with statistical distributions by best fitting and a Bayesian approach based on continuous feed of prior distributions to obtain posterior distributions and computing real time R t . We use data from COVID-19 officially reported cases in Ecuador since the first confirmed case on February 29th. Because of the lack of data, in the case of R 0 we compare two methods for the estimation of these parameters below exponential growth and maximum likelihood estimation. We do not make any assumption about the evolution of cases due to limited information and we use previous methods to compare scenarios about R 0 and in the case of R t we used Bayesian inference to model uncertainty in contagious proposing a new modification to the well-known model of Bettencourt and Ribeiro based on a time window of m days to improve estimations. Ecuadorian R 0 with exponential growth criteria was 3.45 and with the maximum likelihood estimation method was 2.93. The results show that Guayas, Pichincha and Manabí were the provinces with the highest number of cases due to COVID-19. Some reasons explain the increased transmissibility in these localities: massive events, population density, cities dispersion patterns, and the delayed time of public health actions to contain pandemic. In conclusion, this is a novel approach that allow us to measure infection dynamics and outbreak distribution when not enough detailed data is available. The use of this model can be used to predict pandemic distribution and to implement data-based effective measures.