A Bayesian analysis of the total number of cases of the COVID 19 when only a few data is available. A case study in the state of Goias, Brazil

Abstract

The outbreak of COVID 19 has been provoking several problems to the health system around the world. One of the concerning is the crash of the health system due to the increasing demand suddenly. To avoid it, knowing the total number and daily new cases is crucial. In this study, we fitted curves growth models using a Bayesian approach. We extracted information obtained from some countries to build the prior distribution of the model. The total number of cases of the COVID 19 in the state of Goias was analyzed. Results from analysis indicated that the date of the outbreak peak is between 51 and 68 days after the beginning. Moreover, the total number of cases is around 3180 cases. The analysis did not take into consideration possibles changes in government control measures. We hope this study can provide some valuable information to public health management.

Universality in COVID-19 spread in view of the Gompertz function

“…1, we also show f S (x) and df S (x)/dx by blue curves. As already noticed [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and is discussed later, the asymmetry is clearly found in dN (t)/dt…”

“…The indicator K takes a value between zero and unity, is not affected by the weekly schedule of the test, and is found to decrease almost linearly as a function of time in the region 0.25 < K < 0.9 provided that there is only a single outbreak affecting the infection. In order to understand the linearly decreasing behavior of K, Nakano and Ikeda proposed the "constant damping hypothesis" in their paper [26], and Akiyama proved that the hypothesis of exponential decrease in discrete time shows the Gompertz curve in continuous time [27], independently of other works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Since the indicator K is expected to be useful to predict the date when the restrictions can be relaxed as K(t) 0.05, it would be valuable to analyze its solution, the Gompertz function, in more detail.…”

“…Recently, a double exponential function called the Gompertz function is found to catch the features of N (t) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The Gompertz function appears when the infection probability per infected people exponentially decreases as a function of time.…”

COVID-19 Forecasts for Cuba Using Logistic Regression and Gompertz Curves

“…[24] Dattoli used a three-parameter logistic model and the Gompertz model to make estimates for Italy. [25] Bauckhage used the logistic and Gompertz models to obtain predictions for Germany for mid-April 2020, [26] while Rodrigues-Silva used these models to obtain predictions for the state of Goias in Brazil [27] and Dutra used them to estimate the number of persons affected by COVID-19 for various US states and the whole country. [28] Attanyake fi tted logistic, Gompertz and other exponential models to data corresponding to the impact of COVID-19 in Sri Lanka, Italy and Hubei, a province in central China.…”

A Markov Chain Model for COVID19 in Mexico City

“…General stochastic processes are widely used in epidemic analysis, bayesian models also have been used in the study of COVID19, for example [Allen, 2017, Arumugam and Rajathi, 2020, Bertozzi et al, 2020, Britton, 2010, Catak and Duran, 2020, Kharroubi, 2020, Mbuvha and Marwala, 2020, Silva et al, 2020, Şenel et al, 2020, Zhang and Du, 2020.…”