Optimization modeling for identification of parameters and initial condition; Application to SIRU-type epidemic models

Differential equations serve as fundamental tools in modeling epidemics, requiring precise parameter estimation and initial condition calibration. Despite extensive research in this area, a universally applicable method tailored to specific models has yet to be proposed. This work introduces an innovative approach designed to predict parameters and calibrate initial conditions for first-order autonomous ordinary differential equation (ODE) problems. Notably, our methodology demonstrates success when applied to the SIRU-like epidemiological model, offering a promising avenue for optimizing epidemiological modeling. Our deterministic approach grounded on gradient descent, is characterized by its simplicity. It eliminates the need to ascertain the theoretical solution or gradients, which often pose significant challenges in optimization tasks.