Monte Carlo approach to model COVID-19 deaths and infections using Gompertz functions

This study provides a phenomenological method to describe the exponential growth, saturation, and decay of coronavirus disease 2019 (COVID-19) deaths and infections via a Monte Carlo approach. The calculations connect Gompertz-type trial distributions of infected people per day with the distribution of deaths adopting two gamma distributions to account for the elapsed time that encompass the incubation and symptom onset to death periods. The analyses include death data from the USA, Brazil, Mexico, the United Kingdom (UK), India, and Russia, which comprise the four countries with the highest number of deaths and the four countries with the highest number of confirmed cases, as of August 07, 2020, according to the World Health Organization webpage. The Gompertz functions were fitted to the data of weekly averaged confirmed deaths per day by mapping the χ^{2} values. The uncertainties, variances, and covariances of the model parameters were calculated by propagation, taking into account the standard errors of the data for each epidemiological week. The fitted functions for the average deaths per day for the USA and India have an upward trend, with the former having a higher growth rate and quite huge uncertainties. For Mexico, the UK, and Russia, the fits are consistent with a downward-sloping pattern. For Brazil we found a subtle trend down but with significant uncertainties. The USA, UK, and India data showed first peaks with higher growth rates compared with the second ones (4.2, 2.2, and 3.5 times higher, respectively), demonstrating the benefits of nonpharmacological interventions of sanitary measures and social distance flattening the secondary peaks of the pandemic. For the case of the USA, however, a third peak seems quite plausible, most likely related with the recent relaxation policies. Brazil's data are satisfactorily described by two highly overlapped Gompertz functions with similar growth rates, suggesting a two-step process for the pandemic spreading. For the cases of Mexico and Russia single peaks with smoother slopes fitted the data satisfactorily. The 95% confidence intervals for the total number of deaths (×10^{3}) predicted by the model for August 31, 2020, are 160 to 220, 110 to 130, 59 to 62, 41.3 to 41.4, 54 to 63, and 16.0 to 16.7 for the USA, Brazil, Mexico, the UK, India, and Russia, respectively. Our estimates for the point prevalences of infections are compared with some preliminary data from serological studies and/or model calcu