Self-consistent Estimation of Ordinary Differential Equation Parameters Describing Dynamical Systems: A Case Study of COVID-19 in Germany

Abstract

Nowadays, the estimation of parameters for ordinary differential equations (ODEs) from historical data (time series) in optimization problems presents various challenges. These challenges include convergence to local minima when applying traditional optimization methods, inaccurate integration methods of ODEs during the optimization process, and inaccurate cost functions. To address these issues, we propose a novel methodology for estimating the parameters of ODEs that describe dynamic systems in fields such as biological populations, disease spread (e.g., COVID-19). Our methodology is based on the integration of trajectory simulation, optimization of a cost function using noisy data, and heuristic search algorithms such as genetic algorithms for minimization. We demonstrate the effectiveness of this methodology through one use case in this work: the evolution of the COVID-19 disease in German society during the first wave. The results show a highly accurate methodology capable of reproducing real-world curves with high precision.