  Common compartmental modeling for COVID-19 is based on a priori knowledge and
numerous assumptions. Additionally, they do not systematically incorporate
asymptomatic cases. Our study aimed at providing a framework for data-driven
approaches, by leveraging the strengths of the grey-box system theory or
grey-box identification, known for its robustness in problem solving under
partial, incomplete, or uncertain data. Empirical data on confirmed cases and
deaths, extracted from an open source repository were used to develop the
SEAIRD compartment model. Adjustments were made to fit current knowledge on the
COVID-19 behavior. The model was implemented and solved using an Ordinary
Differential Equation solver and an optimization tool. A cross-validation
technique was applied, and the coefficient of determination $R^2$ was computed
in order to evaluate the goodness-of-fit of the model. %to the data. Key
epidemiological parameters were finally estimated and we provided the rationale
for the construction of SEAIRD model. When applied to Brazil's cases, SEAIRD
produced an excellent agreement to the data, with an %coefficient of
determination $R^2$ $\geq 90\%$. The probability of COVID-19 transmission was
generally high ($\geq 95\%$). On the basis of a 20-day modeling data, the
incidence rate of COVID-19 was as low as 3 infected cases per 100,000 exposed
persons in Brazil and France. Within the same time frame, the fatality rate of
COVID-19 was the highest in France (16.4\%) followed by Brazil (6.9\%), and the
lowest in Russia ($\leq 1\%$). SEAIRD represents an asset for modeling
infectious diseases in their dynamical stable phase, especially for new viruses
when pathophysiology knowledge is very limited.
