# Solution for the Mathematical Modeling and Future Prediction of the COVID-19 Pandemic Dynamics
## 5 Conclusions  
The current research proposes three estimation mathematical models for SARS-CoV-2 virus transmission dynamics based on Romanian data collection. The parameters of the proposed dynamical models are identified using information collected by Romanian  
Figure 11: The overlapping of ARX model, ARMAX model and transfer function model estimation. Figure 10: ARMAX-model best fit transfer function. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**The Curve** & \(n_{a}\) & \(n_{b}\) & \(n_{c}\) & \(n_{k}\) \\ \hline Estimation\_1 & [4 4 4 4 4 4] & [2 2 2 2 2] & [2 2 2 2 2] & [1 1 1 1 1] \\ \hline Estimation\_2 & [4 4 4 4 4] & [1 1 1 1 1] & [1 1 1 1 1] & [1 1 1 1 1] \\ \hline Estimation\_3 & [6 6 6 6 6] & [2 2 2 2 2] & [2 2 2 2 2] & [1 1 1 1 1] \\ \hline Estimation\_4 & [8 8 8 6 6] & [1 1 1 2 2] & [1 1 1 1 1] & [1 1 1 1 1] \\ \hline Estimation\_5 & [6 6 6 4 4] & [2 2 2 2 2] & [2 2 2 2] & [1 1 1 1 1] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The centralizer of the polynomials orders for the ARMAX model. Healthcare Institutions (such as the Infectious Diseases Hospital, The National Committee for Special Emergency Situations, Research Institutes and County Health Departments). In order to obtain the best solution, three types of mathematical models were evaluated: transfer vector model with transfer functions as elements, ARX models and ARMAX models. The best solution was determined in the fourth section of this manuscript by comparing the fit values obtained after the simulation of all the proposed models. Furthermore, a study regarding the complexity of the proposed models is presented in the current research work. In this study, the data corresponding to the first 6 months of the pandemic in Romania were considered and they were split into two sets; the first one (containing the data for the first 4 months) was used for the estimation of the proposed models' parameters and the second one (containing the data for the last 2 months), for testing the prediction capacity of the proposed models. The best fit was obtained for the transfer vector model (97.16%) and its associated simulations prove the efficiency of usage, in practice. The efficiency of the prediction horizon extension can be improved by considering a larger data set (associated with a longer period). As mentioned before, the proposed MISO model, based on using the transfer function, generates the best performances. As described in the introduction, in the literature, ARIMA models were utilized as well. In this context, in our research, we used ARMAX models (i.e., an ARIMA model with an exogenous variable). Consequently, they generate higher modelling performances. From our perspective, the main advantage of the mathematical models proposed in the presented research in comparison with the SIR model is the fact that we have used experimental identification. Thus, we have processed the real data adding a significant impact for an accurate model determination. In the case of a relatively new virus such as COVID-19, with unappropriated monitoring for long and consistent periods of time, we consider that the analytical modelling (used for example in determining the SIR model) is disadvantageous with respect to the experimental one. Obviously, AI-based techniques (for example, neural network usage) represent a consistent part of the future, in many domains, including mathematical modelling. However, in the case of dynamic systems with more input signals, the neural models have in general, a high complexity and they require, to be trained, significant computation power. Furthermore, in general, the neural nonlinear models generate better performances than the linear ones, an aspect which introduces supplementary problems in their numerical implementation. In opposition, the proposed MISO model based on transfer functions is a linear one, very simple for numerical implementation.