Covid-19 - Forecasts

Time series research group:

Pedro Morettin, Airlane P. Alencar, Chang Chiann, Clelia Toloi – IME-USP

Francisco M. M. Rocha – UNIFESP, Kim Samejima – UFBA, Marcelo Taddeo – UFBA, Michel Montoril – UFSCar

Main Goal: Forecast the cumulative number of confirmed cases and deaths in São Paulo and in Brazil and the reproduction number using time series tecniques.

These forecasts will be updated next week, including new data.

Data source: https://covid.saude.gov.br/.

1. Model for the Reproduction Number of the COVID-19 Pandemic Outbreak

Michel H. Montoril – UFScar

Chang Chiann – IME-USP

Pedro A. Morettin – IME-USP

The following model deals with the estimation of the reproduction number,

where we consider the dynamic time varying heteroscedastic exponential model

The peak of the curve will be reach when .

Figure: Estimated Dynamic Reproduction Number in São Paulo

2. Nonlinear regression models

Francisco Marcelo M. da Rocha

Data from Mar, 1^st to July, 25^th.

The cumulative number of confirmed cases and deaths suggests a exponential growth, but we observe an exponentially decreasing growth coefficient.

This behaviour suggests that the Gompertz distribution is appropriate for the growth of the number of cases and deaths. We also present the forecasts using this distribution.

Figure 1: Cumulative number of confirmed cases and deaths

The daily number of confirmed cases and deaths may also be forecast assuming the this model is still valid in the future as shown in the next figure.

Our results concludes that this pandemic will last until the end of the year maintaining the current conditions.

Figure 3. Daily number of confirmed cases and deaths in Brazil and SP with forecasts.

Table 1: Forecasts of the cumulative mean number of cases and deaths in Brazil and São Paulo state until July 31^th.

Table 2: Daily mean number of cases and deaths in Brazil and São Paulo state until July 31^th.

3. ARIMA model

Airlane P. Alencar

ARIMA models were fitted for data from Mar, 1^st to July, 18^th and we calculated forecasts of the number of cases and deaths for the next 13 days (until July 31^th), including 95% confidence intervals. The series behave as random walks and it is better to calculate only short-term forecasts.

The models were estimated maximizing the likelihood and the models were chosen minimizing the Akaike’s criterion in order to obtain the best fit avoiding the excessive increase of the number of parameters. A residual analysis was performed to verify the validity of model assumptions. The variance of the residuals were smaller in the beginning of the considered period.

São Paulo State