The COVID-19 infectious disease spread in the world represents, by far, one of the most significant moments in humankind’s recent history, affecting daily activities for a long period of time. The data available now allow important modelling developments for the simulation and prediction of the process of an infectious disease spread. The current work provides strong insight for estimation and prediction mathematical model development with emphasis on differentiation between three distinct methods, based on data gathering for Romanian territory. An essential aspect of the research is the quantification and filtering of the collected data. The current work identified five main categories considered as the model’s inputs: inside temperatures (°C), outside temperatures (°C), humidity (%), the number of tests and the quantified value of COVID-19 measures (%) and, as the model’s outputs: the number of new cases, the number of new deaths, the total number of cases or the total number of deaths. Three mathematical models were tested to find the optimal solution: transfer vector models using transfer functions as elements, autoregressive-exogenous (ARX) models, and autoregressive-moving-average (ARMAX) models. The optimal solution was selected by comparing the fit values obtained after the simulation of all proposed models. Moreover, the manuscript includes a study of the complexity of the proposed models. Based on the gathered information, the structure parameters of the proposed models are determined and the validity and the efficiency of the obtained models are proven through simulation.

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