# Solution for the Mathematical Modeling and Future Prediction of the COVID-19 Pandemic Dynamics
## 2 Data Processing for Model Identification  
The data containing all the necessary information needed for model identification were received both from the authorities involved in combating the pandemic spread, from the infectious diseases hospitals and from profile research institutes (The Clinical Hospital of Infectious Diseases, Alessandrescu Rusescu National Institute for Mother and Child Health). The data between 28 February 2020 and 30 September 2020 were collected each day, in every county of Romania and they were stored in a database. After implementing this database, the containing data were processed for determining the mathematical model of the pandemic dynamics on Romanian territory in the following way:  
* The data were analyzed, in order to verify to gaps possibility between the days and the information; the identified missing data from the database were later collected and, in the final form, the database was completed;
* The data were processed accordingly for each day; for example, in order to obtain the relevant data for the entire of Romania, the data from all counties were merged and processed (in the case of the temperature or humidity, the data processing refers to the computation of the arithmetic average);
* The consistent information was selected; at this stage, the inconsistencies from the database structure were filtered and eliminated; more exactly, the inconsistent information was replaced after a study with consistent information;
* The data were organized in such a manner as to be processed in the next steps; for example, groups of data from the database were extracted and arranged in vectorial or matrivial form. After processing the data were split into two categories:  
* Possible inputs by each date: number of taken tests, inside temperature (in closed spaces such as supermarkets, offices, and rooms), outside temperature (in open spaces), outside humidity, quantified values of COVID-19 measures taken by the authorities in order to slow the pandemic spread;
* Possible outputs by each date: number of new cases, number of new deaths, total number of cases, total number of deaths. In Tables 1 and 2, some examples of data groups from the database structure are presented. There, only a part of the available data types for one day, in each month, is exemplified. Obviously, these data are available for the entire considered period. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Date**} & **Inside Temperature** & **Outside Temperature** (°C)** & **Humidity (\%)** & **No. of Tests** & **Quantified Value of COVID-19** \\  & **(°C)** & **(°C)** & & & **Measures (\%)** \\ \hline
28 February 2020 & 21 \({}^{\circ}\)C & 10.714 \({}^{\circ}\)C & 72.286\% & 8 & 0\% \\ \hline
28 March 2020 & 20.5 \({}^{\circ}\)C & 16.571 \({}^{\circ}\)C & 68.857\% & 86 & 86.85\% \\ \hline
28 April 2020 & 19 \({}^{\circ}\)C & 22.857 \({}^{\circ}\)C & 71.571\% & 759 & 87\% \\ \hline
28 May 2020 & 21.8 \({}^{\circ}\)C & 28 \({}^{\circ}\)C & 71.286\% & 1271 & 73\% \\ \hline
28 June 2020 & 20.3 \({}^{\circ}\)C & 32.429 \({}^{\circ}\)C & 65.714\% & 1689 & 47.5\% \\ \hline
28 July 2020 & 18.8 \({}^{\circ}\)C & 33.571 \({}^{\circ}\)C & 61.714\% & 2374 & 49.5\% \\ \hline
28 August 2020 & 20.7 \({}^{\circ}\)C & 34 \({}^{\circ}\)C & 60\% & 3498 & 45.5\% \\ \hline
28 September 2020 & 19.9 \({}^{\circ}\)C & 25 \({}^{\circ}\)C & 64\% & 4632 & 31.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Examples of input data. In Table 1, the data associated with input signals are exemplified and, in Table 2, the data are associated with output signals. As a remark, the elaborated database contains much more data types (for example, the available drugs from the hospitals, medical available equipment from hospitals, and medical information regarding the patient). Several studies indicate that the transmission of COVID-19 is affected by temperature [34]. In this context, an inverse correlation was found between the outside temperature and the daily number of infections.