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Mathematical modeling is one of the widely used scientific tools which allow us to predict the evolution of the disease. At least four types of models can be used to study the evolution of infectious diseases: the compartmental mod-els (deterministic differential equations like SIR or SEIR), agent-based models (that consider people as lattice sites on a network), stochastic differential equations (differential equations which feature random variables) and data-driven model (that simply take the existing data disease's spread over a period and use machine learning methods to generate a forecast for the next short period). Each of them has advantages and limitations. A combination between the compartmental and data-driving techniques can be considered the grey modeling. Its philosophy is to use appropriate deterministic models (dynamical systems) whose coefficients are determined using data series from measurements. The purpose of the article is to apply the grey modeling in order to identify a mathematical model that fits as accurately as possible the statistical data on the spread of COVID 19 in Romania. The study considers two categories of population (infected, respectively vaccinated people) about which daily statistical data are available. We try to point out a correlation between them, using the grey Lotka-Volterra model. Short time predictions are also presented and discussed. [ABSTRACT FROM AUTHOR]