Inverse Problem for an Extended Time-Dependent SEIRS Model: Validation with Real-World COVID-19 Data

This paper introduces a novel SEIRS-type differential model that incorporates significant real-world factors such as vaccination, hospitalization, and vital dynamics. The model is described by a system of nonlinear ordinary differential equations with time-dependent parameters and coefficients. First, fundamental biological properties of the model, including the existence, uniqueness, and non-negativity of its solution, are established. In addition, using official COVID-19 data from Bulgaria, a special inverse problem for the differential model is formulated and investigated through the construction of an appropriate family of time-discrete inverse problems. As a result, the model parameters are identified, and the model is validated using real-world data. The presented numerical experiments confirm that the proposed methodology performs well in real-world applications with actual data. A very good agreement between computed and officially reported data with respect to the $l_2$ and $l_{\infty }$ norms is obtained. The model and its simulation tools are adaptable and can be applied to datasets from other countries, provided suitable epidemiological data are available.