New S.I.R. model used in the projection of COVID 19 cases in Brazil

Abstract

In this work, we proposed a variant of the SIR model, taking as based on models used to describe the epidemic outbreak in South Korea and Portugal, to study the COVID-19epidemic curve in Brazil. The model presented here describes with reasonable agreement the number of COVID-19 cases registered in Brazil between February 26 and May 18, 2020 based on the hypothesis that there a large number no notified cases (11 to 1) and variation in contagion rate according to social isolation measures and greater or lesser exposure to the virus (highest rate in beginning from epidemic). To this end, we introduced an exposure factor, called β 1 /β 2 , which allows us to describe the influence of factors such as social isolation on dispersal from disease. The results also corroborate a phenomenon observed in countries that registered a high growth in cases in short period of time, to example of Italy, Spain and USA: if isolation measures are imposed late, the total number of cases explodes when the epidemic is approaching from peak, which implies a higher exposure rate in the first days of case registration.From the data collected, we made the linear adjustment of the infected curve according to the time between the 41st and 74th days since the official notification of the first case and we obtained a high infection rate in the period, close to 4.0. The result indicates that the relaxation of social exclusion measures contributed to the high increase in cases in the period. This result reinforces the adoption of the model that differentiates unexposed susceptible from those that are most exposed to contagion. The model also predicts that the peak epidemic outbreak in Brazil, based on the number of cases, will occur around in late May and early June.

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