Covid19: Uma previsão dia-a-dia da extensão da crise
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Nesta seção, eu processo dia-a-dia os dados disponibilizados pelo Ministério da Saúde em https://covid.saude.gov.br/. O número total de casos acumulados no Brasil é ajustado, a cada dia, à curva logística (veja Bassanezi, R. C. e Ferreira Jr., W. C. (1988). Equações diferenciais com aplicações. Editora HARBRA Ltda., ou o exemplo 8.4 do meu livro), cuja equação é \[ P(t) = \frac{P_{\infty}} {\left[\frac{P_{\infty}}{P_0}-1 \right]e^{-\lambda t} + 1}. \] Portanto, a cada dia, um novo conjunto \((P_0, P_\infty, \lambda)\) é obtido. A curva converge para um valor máximo de casos, \(P_\infty\). No entanto, à medida que o tempo passa, a previsão do número máximo de casos (e de quando, na prática, esse número será atingido), muda.
No momento em que \(P_\infty\) se estabilizar, nós estaremos no pico (ou depois dele), e teremos uma ideia de quando o fim da crise ocorrerá.
In this section, I process data made available by Brazil's Health Ministry every day at https://covid.saude.gov.br/. The accumulated number of cases is adjusted every day to the logistic curve (see veja Bassanezi, R. C. e Ferreira Jr., W. C. (1988). Equações diferenciais com aplicações. Editora HARBRA Ltda., or Example 8.4 of my book, both in Portuguese), given by \[ P(t) = \frac{P_{\infty}} {\left[\frac{P_{\infty}}{P_0}-1 \right]e^{-\lambda t} + 1}. \] Therefore, each day a new set of parameters \((P_0, P_\infty, \lambda)\) is obtained. The curve converges to a maximum number of cases, \(P_\infty\). Note however that as new cases are recorded every day, this prediction changes accordingly, as well as the forecast for the duration of the crisis.
When \(P_\infty\) finally stabilizes, we will know that we are or past the peak, with an end in sight.
2020-07-14T08:46:59
Por incrível que pareça, o ministério da Saúde mudou mais uma vez o formato das planilhas em que disponibiliza os dados sobre a epidemia de Covid-19. Voltei por tanto a utilizar os dados obtidos em JohnsHopkins.
Unbelievable: the Brazilian Ministry of Health has once more changed their data format. I am back to using JohnsHopkins data.
2021-05-07T00:00:00
A previsão do número total de casos, \(P_{\infty}\) curvou-se claramente para cima com o recrudescimento da epidemia no Brasil. A escala de tempo dos gráficos agora é mensal, e foi estendida até o final de 2021.
The prediction for the total number of cases, \(P_{\infty}\) has clearly curved upwards with the rebound of the epidemics in Brazil. The time scale of the plots has been changed to monthly ticks, and extended to the end of 2021.
Eis aqui o ajuste das curvas ao longo do tempo (das mais recentes para as mais antigas). Here are the curve fittings, from latest to earliest.
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