The SARS-CoV-2 epidemic outbreak: a review of plausible scenarios of containment and mitigation for Mexico

Manuel Adrian Acuna-Zegarra; Andreu Comas-Garcia; Esteban Hernandez-Vargas; Mario Santana-Cibrian; Jorge X. Velasco-Hernandez

where r represents the growth rate of infection, K is the carrying capacity (or final epidemic size, and a is a scaling parameter. This model is an extension of the simple logistic growth model that has been recently used to predict cumulative COVID19 cases in China [15] . Parameters a, r and K must be estimated in order to properly describe the observed data and to provide accurate forecasts. We use an statistical approach through Bayesian inference. Details regarding the estimation procedure and the the results can be found on Appendix A. The growth rate r is close to 0.2 and it can range from 1.9 to 2.1 with a probability of 95%. However, the total size of the outbreak K is more difficult to estimate which is expected since Mexico is at the start of the outbreak and the current data shows that the contagion is accelerating. We estimate the final size of the outbreak to be 710,392 cases, ranging from 65,163 up to 1,258,296 with a probability of 95% provided no cotrol/contaiment/mitigation measures are applied. These are very long-term predictions and that is why there is too much variability in the interval. To estimate the parameters we used data up to March 24, 2020 . The last two available observations corresponding to March 25 and 26 can be seen in Figure 1 , and are closely predicted by the fitted model. Furthermore, we create 14 days predictions from March 25, 2020 to April 7, 2020 which can also be seen in Figure 1 . For example, at March 31, 2020, the model expects 1,103 cases, with a 95% probability interval of (401, 2353); and at April 7, 2020, a total of 4,202 cases are expected with a 95% probability interval of (1,440, 11,012). Table 1 shows the median posterior estimates for each parameter and 95% probability intervals. Figure 2 shows the marginal posterior distributions estimates for each parameter. Finaly, using the same data we estimated the basic reproduction number for the whole country. We use the package written in R, Estimation of R0 and Real-Time Reproduction Number from Epidemics (https://CRAN.R-project.org/package=R0) using the exponential CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.