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

TL;DR

This paper presents a Monte Carlo method using Gompertz functions to model COVID-19 deaths and infections across six countries, providing forecasts and analyzing the effects of interventions with quantified uncertainties.

Contribution

It introduces a novel Monte Carlo framework with Gompertz functions for modeling COVID-19 dynamics, including uncertainty propagation and multi-peak analysis.

Findings

Peak death rates vary across countries with different trends.

Model predicts total deaths with specific confidence intervals.

Infection prevalence estimates align with serological studies.

Abstract

This study describes the dynamics of COVID-19 deaths and infections via a Monte Carlo approach. The analyses include death's data from USA, Brazil, Mexico, UK, India and Russia, which comprise the four countries with the highest number of deaths/confirmed cases, as of Aug 07, 2020, according to the WHO. The Gompertz functions were fitted to the data of weekly averaged confirmed deaths per day by mapping the $\chi^2$ values. The uncertainties, variances and covariances of the model parameters were calculated by propagation. The fitted functions for the average deaths per day for USA and India have an upward trend, with the former having a higher growth rate and quite huge uncertainties. For Mexico, UK and Russia, the fits are consistent with a slope down pattern. For Brazil we found a subtle trend down, but with significant uncertainties. The USA, UK and India data shown a first peak with a higher growth rate when compared to the second one, demonstrating the benefits of non-pharmaceutical interventions of sanitary measures and social distance flattening the curve. For USA, 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-steps process for the pandemic spreading. The 95% CI for the total number of deaths ($\times 10^3$) predicted by the model for Aug 31, 2020 are 160 to 220, 110 to 130, 59 to 62, 46.6 to 47.3, 54 to 63 and 16.0 to 16.7 for USA, Brazil, Mexico, UK, India and Russia, respectively. Our estimates for the prevalences of infections are in reasonable agreement with some preliminary reports from serological studies carried out in USA and Brazil. The method represents an effective framework to estimate the line-shape of the infection curves and the uncertainties of the relevant parameters based on the actual data.