IJCVInternational Journal of Coronaviruses2692-1537Open Access PubUnited States10.14302/issn.2692-1537.ijcv-20-3453IJCV-20-3453research-articleA quick Look at the Registered Cases of Covid-19 Throughout the WorldRaulIsea1*KarlE Lonngren2Fundación Instituto de Estudios Avanzados IDEA, Hoyo de la Puerta, Baruta, VenezuelaDepartment of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USACorresponding authorSashoStoleski1Institute of Occupational Health of R. Macedonia, WHO CC and Ga2len CC, Macedonia.
Raul Isea, Fundación Instituto de EstudiosAvanzados IDEA, Hoyo de la Puerta, Baruta, Venezuela, Email: raul.isea@gmail.com
The authors have declared that no competing interests exist.
The present work analyzes the registered cases of Covid-19 throughout the world according the data registered at Johns Hopkins University. We selected 15 countries to analyze their data. In alphabetical order the countries are: Argentina, Australia, Brazil, Chile, China, Colombia, Germany, India, Italy, Mexico, Peru, Portugal, Spain, United States and Venezuela. With this information, three different studies were carried out. First, the data was validated using Benford's Law which is based on forensic techniques that allow us to guarantee the integrity of the information. Later, we calculated the value of the basic reproduction number (R_{0}), ie., the number of secondary host infections caused by one primary host infection that helps us to determine if a country has an outbreak of Covid-19. Finally, we show that the best representation for the change in the number of cases in the time is to calculate the mantissa value, ie., the floating number obtained from the logarithm of the data.
The World Health Organization (WHO) decreed on March 11, 2020 that a new pandemic caused by a new virus first detected in the Wuhan market in China the was caused by a new coronavirus (Covid-19), which was named according to the International Committee of Taxonomy of Virus as Severe Acute Respiratory Syndrome (SARS-CoV-2).
Until June 3, more than six million cases have been registered throughout the world that is distributed in more than 190 countries and causing more than 380,000 recorded deaths according to the records John Hopkins University records. As a result of all this data, it has been possible to determine, for example, the credibility of the information according to a recent paper published by Isea 1 where he analyzed 23 countries using the Benford Law. It is interesting to comment that approximately a third of the countries do not satisfy this validation procedure criterion. It is necessary to wait until the end of the epidemic in order to confirm these results 1.
On the other hand, a large number of mathematical models have appeared in the scientific literature that could explain the transmission dynamics of the Covid-19 virus but they depend on a large number of variables which must be continuously adjusted according to the new data 23456. Therefore, it is necessary to use another type of methodology that allows us to know in real time if a certain country has an epidemic outbreak. To do that, it is necessary to calculate the Basic Reproduction Number (R_{0}) that mean the number of new infections that can be generated from one infected person. If the value of R_{0}> 1 implies that this country has an epidemic and a value of R_{0}<1 implies that the country has overcome the crisis due to this disease.
Finally, it is necessary to makea new graphic to see the changes of Covid-19’s infection in each country. To do that, we calculate the mantissa values of the register of cases according to details provided in the following section Therefore, the goal of this paper is to determine: (1) the veracity of the data based on Benford’s Law in the following countries in alphabetical order: Argentina, Australia, Brazil, Chile, China, Colombia, Germany, India, Italy, Mexico, Peru, Portugal, Spain, United States and Venezuela. (2) Calculate the value of R_{0} to determine whether an epidemic outbreak is occurring in a country, and (3)Present the values of the mantissa values for the various countries, ie., China, Italy, Portugal, Spain, United States, Venezuela and World.
Methodology
On June 3, 2020, all cases of Covid-19 infections were obtained from the Johns Hopkins University database in the listed countries. Subsequently, the validity of the data was determined using two digital data analysis techniques based on Benford's Law, according to the procedure recently published by Isea 1 which specifies a new critical parameter based on the p-value, which said that is p-value must be greater than 0.05, then the information has received no manipulation or alteration.
The next step was to determine the value of the Basic Reproduction Number (R_{0}) according to the works published by Isea and Lonngren 78 which is based on the methodology developed by Wallinga and Lipsitch 9. It is necessary to calculate a function called the generation time (mGT) which is the lag time between infection in a primary case and a secondary case. This function before forwards n can only be logarithmic, gamma and weibull, and these definitions are explained in 10.
Finally, the mantissa value is obtained according to the following expression:
where log_{10} is the logarithm in base 10 of each cases obtained up to Jun 3, 2020, and “Int” is the whole part of this number.
Results and Discussions
(Table 1) shows the results obtained after validating the results using Benford's Law. Remember that the values of χ^{2} and L^{2} should be close to zero in order to guarantee the integrity of the data and the calculated values of the p-value must be greater than 0.05. From the results shown in Table 1, Australia and China are the countries that best satisfy Benford's Law and therefore, these two countries appear to not manipulate the provided information. Brazil, Colombia, India, Peru, Portugal and Venezuela satisfy two of the tests proposed in this paper and therefore do not alter the data. It is interesting to note that Colombia passes both tests but the value of χ^{2} is higher than the other countries.
Number of Covid-19 case records in 15 countries that have been analyzed in this paper. The others parameters indicated in this table has been explained in the reference 1.
Country
χ^{2}
p-value (χ^{2})
p-value (arcmantissa)
L^{2}
China
2,3991
0,9663
0,4131
0,0063
Australia
6,2668
0,6174
0,0669
0,0289
Venezuela
8,5768
0,3792
0,4845
0,0110
Colombia
13,2410
0,1038
0,1052
0,0265
Brasil
7,2605
0,5088
0,1637
0,0203
Peru
10,1920
0,2518
0,0810
0,0292
Chile
36,2620
10-5
0,0015
0,0711
Mexico
13,7910
0,0874
0,0304
0,0397
USA
67,1250
10-4
10-10
0,1976
Spain
14,5880
0,0677
0,0109
0,0481
Portugal
6,6784
0,5717
0,3982
0,0101
Italy
18,7460
0,0163
0,0006
0,0717
Germany
11,9940
0,1515
0,0334
0,0347
India
10,2410
0,2485
0,1532
0,0204
Argentina
21,9220
0,0051
0,0002
0,1017
On the other hand, Germany, Mexico and Spain meet one of the two tests so these countries do not appear to have manipulated their data either. However, Argentina, Chile, Italy and the United States appear to not pass these tests and therefore, there is no guarantee of the validity of the information. However, it is necessary to wait until the end of the pandemic to confirm these preliminary results.
The next step is to calculate the value of R_{0}, it means, the number of new infections that can be generated from one infected person, obtained with the methodology proposed by Isea and Lonngren 78, where values greater than 1 indicate that this country is undergoing an epidemic. These results using these criteria are shown in Table 2. Australia and China are the countries with the lowest R_{0} value. Therefore, there does not appear to be an epidemic outbreak in these two countries while Germany, Italy and Spain have values just below 1 which theoretically implies that there is no emergency for enduring this disease, but it is necessary checking these results to known when these countries can generated an outbreaks. The remaining countries are presently undergoing Covid-19 epidemics (R_{0}> 1).
Calculated values of R0 according to of number of dates, and the rest of parameters are explained in the reference 10.
Country
No dates
Function
Median
SD
R_{
0
}
Chin
156
Lognormal
0,1946
5,2571
0,9365±0,1666
Australia
97
Lognormal
0,1237
0,3108
0,9675±0,0739
Venezuela
81
Weibull
0,2196
0,2750
1,0829±0,1276
Colombia
85
Gamma
0,2420
0,2711
1,0713±0,0792
Brasil
91
Gamma
0,1944
0,2821
1,0888±0,0994
Peru
87
Gamma
0,2308
0,3322
1,0778±0,0864
Chile
91
Gamma
0,2183
0,3024
1,0882±0,0905
Mexico
88
Gamma
0,2842
0,3800
1,0780±0,0758
USA
104
Gamma
0,3774
0,5184
1,0295±0,0406
Spain
92
Gamma
0,2706
0,3224
0,9902±0,0455
Portugal
92
Weilbull
0,2414
0,2282
1,0012±0,0483
Italy
95
Weibull
0,3448
0,3087
0,9897±0,0341
Germany
98
Gamma
0,2977
0,3416
0,9895±0,0402
India
93
Gamma
0,2533
0,3840
1,0877±0,0838
Argentina
89
Gamma
0,2612
0,2963
1,0692±0,0725
Finally, in the Figure 1 shows the results of the mantissa values in the following countries: China, Italy, Portugal, United States, Venezuela and World. When the country does not present an outbreak, the mantissa values are constant in time (see China results). However, the results obtained in the United States and Venezuela show that they have not reached the maximum of cases of Covid-19, while Italy is almost free of this pandemic. Finally, the results obtained in the World shows that has not reached the equilibrium during this time. These results are according to the R_{o}’s values obtained in the previous step.
The results of the mantissa values in the following countries: China, Italy, Portugal, United States, Venezuela and World.Conclusions
This paper analyzes the data recorded for Covid-19 throughout the world. With this information, it is possible to verify which countries are currently experiencing a new coronavirus (Covid-19) epidemic according to the R_{0} value, and also the known countries which countries do not manipulate the data. Finally, it was possible to know if a country presents an outbreak according to the mantissa result, but it is necessary to do more investigations in the future.
IseaRHow valid are the reported cases of people infected with Covid-19 in the worlds?International2020IseaRLa dinámica de transmisión del Covid-2019 desde una perspectiva matemática. Revista Observador del2020YangCWangJA mathematical model for the novel coronavirus epidemic in Wuhan2020LiQGuanXWuPWangXZhouLTongYEarly transmission dynamics in Wuhan, China of novel coronavirus-infected pneumonia,N Engl J Med.2020:2020TangBWangXLiQNL BragazziTangSXiauYWuJianhongEstimation of the transmission risk of the 2019-nCoV and its implication for publichealting intervantions2020ZhaoSLinQRanJSYangGWangWLouYPreliminary estimation of the basis reproduction number of novel coronavirus (2019-nCoV) in China from(2019 to 2020).A data-driven analysis in the early phase of the outbreak2020IseaRLonngrenK EToward an early warning system for Dengue, Malaria and Zika in Venezuela2018IseaRLonngrenK EProposal for an early warning system against an AH1N1 Influenza pandemic in America2017WallingaJ y LipsithMHow generation intervals shape the relationship between growth rates and reproductive2007ObadiaRHaneelRBoëlleP YThe R0package: a toolbox to estimateproduction numbers for epidemic outbreaks. BMC Medical Informatics and Decision Making.12:2012147