ANOVA to Compare Three Methods to Track COVID-19 in Nine Countries ANOVA en la comparación de tres métodos para rastrear COVID-19 en nueve países

A new coronavirus denominated !rst 2019-nCoV and later SARS-CoV-2 was found in Wuhan, China in December of 2019. This paper compares three mathematical methods: nonlinear regression, SIR, and SEIR epidemic models, to track the covid-19 disease in nine countries a"ected by the SARS-CoV-2 virus, to help epidemiologists to know the disease trajectory, considering initial data in the pandemic, mainly 100 days from the beginning. To evaluate the results obtained with the three methods one-way ANOVA is applied. The average of predicted infected cases with SARS-CoV-2, obtained with the mentioned methods was: for United States of America 1,098,508, followed by Spain with 226,721, Italy with 202,953, France with 183,897 United Kingdom with 182,190, Germany with 159,407, Canada with 58,696, Mexico with 50,366 and Argentina with 4,860 in average. The one-way ANOVA does not show a signi!cant di"erence among the results of the projected infected cases by SARS-CoV-2, using nonlinear regression, SIR, and SEIR epidemic methods. The above could mean that initially any method can be used to model the pandemic course.

Currently, exist mathematical models to predict or simulate an epidemic spread among them: Nonlinear regression 13 , SIR 14 , SEIR 15 . Other methods exist that use more variables, but they can be used when the pandemic has already produced enough data it means no at the beginning of the pandemic outbreak. The nonlinear method was employed as a irst statistics approximation and the SIR and SEIR models are based on differential equations solutions taken in account the infected, recovery, susceptible, and dead people.

MATERIALS AND METHODS
Tree mathematical models are applied to simulate COVID-19 disease: Nonlinear regression, SIR, and SEIR. These are described below. Two programs were used from GitHub of MathWorks.

Nonlinear regression model
The nonlinear regression method to obtain the A, B, and C to solve the equation 1 , was modeled with Coronavirus Tracker-Country Modeling, available at https://rb.gy/pbwexu.

SIR Model
The SIR model also called Kermack and McKendrick's model was evaluated using the function itVirus-CV19v3 COVID-19 SIR Model from the MathWorks webpage at https://rb.gy/qblldl. This method has three variables or parameters: susceptible S , infected I , and recovered R 14 . N is the variable that represents the number of total populations in the S t , I t , and R t functions. This model can be solved by ordinary differential equations solutions with the initial conditions S 0 = S0>0, I 0 = I0>0, R 0 = R0>0. Figure 1 shows the epidemic flow diagram and the equations of the model in 2 , 3 , 4 .

SEIR Model
The SEIR method was modeled with the Epidemic Calculator program obtained from https://rb.gy/4qguan.
The SEIR model can analyse infectious diseases where the people have an exposed period to the virus and can transmit the infection to the rest of the population. The epidemic SEIR model diagram is shown in Figure 2 and its equations in 6 , 7 , 8 , 9 . infected, I t , and recovery, R t , people respectively with exposed E t in the function of time.
The exposed people E t into the SEIR model is constituted by two classes, the irst one is related to people that do not have the infection yet, and the second is the persons that change to recovered status. The new population number is:

RESULTS AND DISCUSSION
The nine countries were chosen as a representation To study the propagation of the disease in the countries, one irst statistics approximation to predict the maximum of infected cases of COVID-19 disease was realized with the coronavirus tracker, country model-

c) France, d) Germany, e) Italy, f) Mexico, g) Spain, h) the UK and i) the US.
The data obtained for , and Ro with the SIR model were used in the simulator of SEIR epidemic model in http://gabgoh.github.io/COVID/index.html to obtain the graphs of Figure 6 to predict the projected infected cases in Argentina, Canada, France, Germany, Italy, Mexico, Spain, UK, and the US. Table 4 shows the data of the variables obtained with the SEIR epidemic model to make the predictions. Table 4 shows values of the contact rate , the mean exposed period 1/ , the rate at a recovery of disease   Table 5 shows the results predicted using the three models: the nonlinear regression, the SIR and SEIR epidemic model, and the average of the total projected con irmed cases of COVID-19 in the nine studied countries. One-way ANOVA study is showed in Table 6. As can be seen from the data the three methods mean are not signi icantly different. Other studies have modeled SARS-COV 2, applying different models including nonlinear regression, SIR, and SEIR epidemic models 7 11 12 13 14 15 18 19 20 , but they have no compared the results obtained among them as it is done in this paper. ations, since there is no effect to take into account "for this virus" with the asymptomatic people who were exposed, E t , since they do not generate signi icant variations for the model. Then the two models present similar results, which is what is being obtained in the one-way ANOVA. Therefore, it could be said from this comparison, that the SIR model is suf icient to predict the rest of the pandemic. Additionally, it is possible to see that for the SEIR model, there is a little effect when asymptomatic exposed people to this virus are taken into account, it can be assumed that there is no effect because they are only infecting the others, and since they do not present symptoms, the SEIR model considers them healthy until they are already part of the group of infected, I t , so the results are similar.
On the other hand, the linear regression model is only making an adjustment with the real data and only allows predicting the maximum value of possible cases of infected people, but the SIR model can predict the daily cases and their decrease per day and predict how long the infection period can last.

CONCLUSIONS
The nine countries studied concerning the projected infected cases by SARS-CoV-2 using nonlinear regression method, SIR and SEIR epidemic model simulation, do no show equal predicted values, but those are not statistically different. It is con irmed by one-way ANOVA analysis. The above could mean that initially any method can be used to model the pandemic course.
These methods can be a irst approximation and could help health professionals, not only the epidemiologist, to make decisions with a general point of view of a pandemic evolution.