Predictive methodology of the probability ranges of total deaths from Coronavirus 19 (COVID-19) in China, Turkey, and Brazil

Background: A country without strategies to limit the spread of a pandemic would likely result in a dramatic increase in the number of hospitalizations and deaths. Objective: to design a methodology based on probability theory to Predict the dynamics of total deaths due to Coronavirus 19 (COVID-19) in three countries. Methods:the total number of deaths from COVID-19 was systematized, from the day the rst report was made public until April 17th, 2020 in China, Turkey, and Brazil. Eight ranges were established, which have a maximum and minimum value to correlate with the total COVID-19 deaths in each of these three countries. Next, the frequency of occurrence of each range and its probability were calculated. Subsequently, these same steps were performed, but in sub-spaces of eight consecutive days. Results: the predictions gave probability values of 5.2E-43 for China, 4.4E-21 for Turkey and 7.9E-21 for Brazil. In orders of magnitude, China has a difference of 22 compared to the other two countries that have not reached the collapse of the health system that occurred in China. Additionally, the probability of the sub-spaces of these three countries reveals changes in the different ranges as the virus spreads. Conclusions: the probability values allow distinctions to be made between the dynamics of deaths from COVID-19 in different countries, additionally contributing to follow-up on pandemic mitigation interventions.


Introduction
One of the four genera within the Coronaviridae family is the Betacoronavirus genus, and among these viruses, SARS-CoV, MERS-CoV and SARS-CoV-2 are found as the main exponents (Li, 2016 Singhal, 2020). A public health emergency was declared due to the number of positive cases and deaths by COVID-19, on January 30, 2020 and later, the World Health Organization (WHO, 2020a; 2020b) classi ed it as a pandemic. As of April 26th, 2020, a total of 2,804,796 con rmed total cases and 193,722 deaths from COVID-19 have been reported (WHO,2020c). Among the group of 20 countries with the highest number of cases reported by COVID-19 are China, Turkey, and Brazil. On April 17th, China increased the total number of deaths because it had not counted the people who died in their homes (WHO,2020c), while keeping quarantine and social distancing measures, among others.
To explain and predict the behavior of the current pandemic, SEIR and SIR epidemiological models are being applied. For example, the compartmentalized SEIR epidemiological model allows researchers to analyze the behavior of four states: susceptible to infection, exposed or latent, infected, and recovered (Grifoni et al. 2020).
Apart from these four states, this model estimates the reproductive number Ro (Fan et al. 2020;), which estimates the new infections that an infectious person will produce during infection, in a totally susceptible population in the absence of interventions ). However, the results of the studies carried out using the SEIR and SIR models are very varied (Roda et al. 2020). One of the many causes of the variation in these results is attributed to the lack of reliable data from Wuhan before January 23 when the city was under quarantined as data con rmed in one day may have been subject to erroneous COVID-19 test results ). In addition to this, there are studies that have shown that the estimation of Ro in the analysis of other epidemics has generated misinterpretations. Probability was considered an empirical discipline before the end of the 19th century. For it to become a theory, it was necessary to develop proper axiomatization processes and their possible applications (Blanco, 2020;Koroliuk, 2015). In probability theory, the relationship between the frequency distribution of events and their probability is called probability distribution (Feynman et al. 1964  Range probability: it is the quotient between the occurrence frequency of each of the eight established rangesand the total sum of the occurrence frequencies of all the ranges, is calculated using the following equation: Where i takes the values of the ranges from 1 to 8.
Probability of the dynamics of the number of infected people in a country: it is calculated with the following equation: Where, x represents the number of days between the rst report of deaths by COVID-19 for a given country and the study cut-off date.

Population
Vales for total deaths secondary to COVID-19 were taken for China from January 11, for Turkey and Brazil from March 18 to April 17th, 2020 from the WHO website (2020c). These countries were selected, as they were in the top 20 countries with the highest number of individuals deceased by COVID-19 until April 17th.

Procedure
The dates and total deaths from COVID-19 were organized in spreadsheets. Subsequently, a comparison was made between the total deaths from COVID-19 in China and the eight ranges established in the methodology (see de nitions), that is, a relationship was made between the total deaths from COVID-19 with one of the eight ranges. In the same way, we proceeded with the other countries. In this way, the total number of deaths from COVID-19 from these countries, occupied one of these eight ranges established by the methodology (see de nitions).
Next, the number of times that a certain range appeared was quanti ed to later evaluate the probability of the frequency of occurrence of each of them with equation 1. This results in a probability distribution, which was evaluated by equation 2, allowing to quantify the dynamics of the total number of deaths from COVID-19 in each country.All the steps required to apply Equation 1 and 2 were performed again in a sub-space of eight consecutive days. These sub-spaces allowed analyzing the behavior of the temporal dynamics of the total number of deaths from COVID-19 in shorter xed time intervals.

Ethical Approval
This investigation does not require an institutional ethics committee approval given that research was developed with data made publicly available where no personal or con dential information was processed.

Results
The behavior of the number of total deaths from COVID-19 for the three countries can be seen in Figure 1. The total number of deaths from COVID-19 in China, Turkey and Brazil varied between 9 to 4642, 2 to 1890 and 1 to 2141 for Brazil. China, Turkey, and Brazil occupied the rst ve out eight ranges that were established in this methodology (table 1). Within the ve ranges occupied by the three countries, China is the country with the highest frequency of occurrence for a range, this is because, at the time of the study, China did not report more deaths due to COVID-19, clustering the cases in a single range more frequently. On the other hand, for Turkey and Brazil, the total frequency of occurrence of the rst ve ranges were equal, in the same way they had similar values for frequency and probability ranges, for example, range two achieved the same probability value for both countries. The behavior of the probability distribution of the frequency of appearance of each range for the three countries can be seen in Figure 2.
The probability evaluated with equation 2 for China yielded a value of 5.2E-43, while for Turkey a value of 4.4E21 was calculated and for Brazil a value of 7.9E-21 was obtained (see table 2). When comparing these three probability values, it can be seen that the difference in orders of magnitude between China, Turkey and Brazil is 22, which reveals that in orders of magnitude the dynamics of the total number of deaths from COVID-19 for April 17th were more loaded for China. On the other hand, for Turkey and Brazil, the values of probability in orders of magnitude are the same, but when observing the signi cant gures Brazil nds the possibility of a range change.
For the eight-day sub-spaces, the behavior of the dynamics of the total number of deaths secondary to COVID-19 for these three countries were analyzed. For China, during the rst two weeks, there were no alarming changes in the number of deaths secondary to COVID -19, however, during weeks 24 and 32, the dynamics of deaths from COVID-19, presented a considerable change in view of the fact that the dynamic went from range 3 to range 5. On the other hand, Turkey and Brazil dynamics migrated from range 1 to range 3 in the second week of reporting the total number of COVID-19 deaths. When comparing how the dynamics of deaths behaved in Turkey and Brazil with respect to China, it is revealed that the mortality grew more strongly in these two countries. The behavior of the dynamics of deaths from COVID-19 in these three countries can be seen in Figure 2.

Discussion
This is the rst work where a methodology founded on probability theory was developed to predict the behaviorof the dynamics of total deaths from COVID-19 in different countries. This study highlights that the lack of data was not inconvenient to make predictions, it was only necessary to observe these cases, in the context of fundamental physical and mathematical theories such as probability theory and nonrelativistic quantum mechanics. The probability ranges allow to easily compare the behavior of the dynamics of deaths in these three countries, which only after having taken the necessary mitigation measures, the cases of deaths signi cantly decreased China.
The methodology applied in this study was developed in the context of quantum mechanics. To establish the ranges for the eight ranges, an analogy was made between the particles that can only be at certain discrete energy levels and the number of deaths from COVID-19. Additionally, the behavior of the dynamics of deaths in these three countries was differentiated by means of the probability values, analogous to how the probability distributions can differentiate each energy level. Furthermore, the probability values of each sub-space can detect changes that are not noticeable as the pandemic spreads in each country (D'Arienzo and Coniglio, 2020).
It is worth noting that this study did not consider Ro as a starting point because it is an estimate calculated with the information that has been recorded and reported at the time of the start of a viral outbreak, as is the case SAR-CoV2. Furthermore, the variation between the estimated values for each country signi cantly limits forecasting the future behavior of this As mentioned, the studies developed to estimate the calculation of Ro for a given geographic area show that this parameter cannot be extrapolated to other geographical area different to the place it was calculated (Ridenhour et al. 2014). For example, in a study carried out by D´Arienzo et al. (2020), R0 was estimated using the SIR compartment method in nine cities in Italy, with the highest number of cases con rmed by COVID-19. The results of this study show that the R0 value calculated in a period between 02/25/2020 to 03/12/2020 for these nine cities varied between 2.43 and 3.10 (D'Arienzo and Coniglio, 2020).
The line of research applied in this study also has a scienti c track record in other settings of medicine as is cardiology (Rodríguez et al. 2019), Infectiology (Rodriguez et al. 2020) and molecular biology (Rodríguez et al. 2008). These methodologies demonstrate the favorability of designing methodologies based on probability theory to analyze the behavior of random or chaotic dynamics, since these approaches have made possible to predict and quantify complex phenomena, based on the study of their behavior.

Conclusion
A methodology was developed that allows us to understand from the dynamics of total deaths from COVID-19, the impact that this has on the pandemic in different countries from a physical and mathematical context applicable to any country.

Declarations
Con ict of interest statement: The authors declare than they have no con ict of interest

Supplementary Files
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