From SIR to SEAIRD: a novel data-driven modeling approach based on the Grey-box System Theory to predict the dynamics of COVID-19

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.