Gompertz model in the study of confirmed cases of COVID-19 in the city of Porto Alegre

Resumo

In the present study, the behavior of the cumulative number of confirmed cases by COVID-19 in the
city of Porto Alegre (RS) was analyzed based on official data from March 8th to July 31st

, 2020, contained in the
COVID-19 Bulletin and published daily by the City Hall. The analytical solution of the Gompertz differential
equation was deduced and its exact solution was expressed by the Gompertz sigmoidal model, P(t). Nonlinear
regression techniques were used to determine the parameters of the P(t) function. Simulations were performed,
ranging the maximum number of contaminants from 100% to 20% of the total population of Porto Alegre. The
results obtained were adequate with a Pearson correlation coefficient of at least 0.99. The models were used to
predict the data for August 7th, 2020 and the largest relative percentage deviation was approximately 13% and 21%
for August 19th, 2020. The inflection point of P(t) was calculated, which shows a change in the growth rates of the
number of accumulated cases (large at the beginning of the process and changing to a slower growth).