Predicting the number of total COVID-19 cases and deaths in Brazil by the Gompertz model
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ORIGINAL PAPER
Predicting the number of total COVID-19 cases and deaths in Brazil by the Gompertz model Jemy A. Mandujano Valle
Received: 20 July 2020 / Accepted: 24 October 2020 © Springer Nature B.V. 2020
Abstract In this work, we estimate the total number of infected and deaths by COVID-19 in Brazil and two Brazilian States (Rio de Janeiro and Sao Paulo). To obtain the unknown data, we use an iterative method in the Gompertz model, whose formulation is well known in the field of biology. Based on data collected from the Ministry of Health from February 26, 2020, to July 2, 2020, we predict, from July 3 to 9 and at the end of the epidemic, the number of infected and killed for the whole country and for the Brazilian states of Sao Paulo and Rio de Janeiro. We estimate, until July 9, 2020, a total of 1,709,755 cases and 65,384 deaths in Brazil, 331,718 cases and 15,621 deaths in Sao Paulo, 134,454 cases and 11,574 deaths in Rio de Janeiro. We also estimate the basic reproduction number R0 for Brazil and its two states. The estimated values (R0 ) were 1.3, 1.3, and 1.4 for Brazil, Sao Paulo, and Rio de Janeiro, respectively. The results show a good fit between the observed data and those obtained by the Gompertz. The proposed methodology can also be applied to other countries and Brazilian states, and we provide an executable as well as the source code for a straightforward application of the method on such data. Keywords Model Gompertz · Minimal error method · Inverse problem · Covid-19 J. A. M. Valle (B) National Laboratory of Scientific Computation, Petrópolis, Rio de Janeiro, Brazil e-mail: [email protected]
1 Introduction The World Health Organization declared the coronavirus disease 2019 a pandemic on March 11, pointing to the over 118,000 cases in over 110 countries and territories around the world at that time [18]. The COVID19 pandemic in Brazil began on February 26, 2020, when a man from Sao Paulo who returned from Italy tested positive for the virus. The first case of COVID19 in Rio de Janeiro was confirmed on March 5, 2020. Nowadays, Brazil is considered the epidemic center of Latin America, occupying the second place in the total number of cases and, more recently, in the total number of deaths. Currently (July 9, 2020), Sao Paulo and Rio de Janeiro are the states with the highest number of deaths by the new coronavirus in Brazil, according to data from the Brazilian Health Ministry. In the past few months, a considerable number of studies related to the evolution of COVID-19 in the world have been submitted and published. In the following, we describe some of these works. Ahmadi et al. [1] developed mathematical models to predict the number of COVID-19 cases in Iran from April 3, 2020, to May 13, 2020. The unknown parameters in these models were estimated by running the fminsearch, a MATLAB function, which is a least-squares algorithm. Torrealba et al. [22] analyzed the modeling and prediction of COVID-19 in Mexico, from an initial approximation, and using the Gauss– Newton algorithm, the authors
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