| Abstract: |
| Inverse epidemiological problems involving nonlinear ordinary differential equations are generally ill-posed. For this reason, it is necessary to determine parameters, or combinations of parameters, that can be uniquely identified from available real-world data. This talk addresses inverse problems for a time-dependent SEIRS model incorporating vaccination, hospitalization, and vital dynamics. First, a mathematical analysis is performed to establish essential biological and analytical properties of the model, including non-negativity, boundedness, and the existence and uniqueness of solutions.
The core contribution of this work lies in the formulation and solution of time-discrete inverse problems aimed at identifying unknown, time-dependent model parameters from reported epidemiological data. This inverse methodology enables reliable calibration of the model and provides insight into the time evolution of the epidemic. Numerical experiments using actual COVID-19 data from the USA, Italy, and Bulgaria demonstrate the robustness and practical applicability of the proposed approach. Furthermore, the model is used to compute key epidemiological indicators, such as time-dependent basic and effective reproduction numbers. Provided that suitable epidemiological data are available, the model and its associated simulation tools can be applied to data from any country, making the framework broadly applicable for epidemic analysis and decision support. |
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