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Article

Martínek, Josef ; Kučera, Václav
Numerical optimization of parameters in systems of differential equations. (English). In: Chleboun, J., Kůs, P., Papež, J., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Jablonec nad Nisou, June 19-24, 2022. Institute of Mathematics CAS, Prague, 2023. pp. 123-132
MSC: 65K10, 65L05, 92D30 | DOI: 10.21136/panm.2022.12
Keywords:
ordinary differential equations; parameter estimation; nonlinear least squares; mathematical epidemiology
Summary:
We present results on the estimation of unknown parameters in systems of ordinary differential equations in order to fit the output of models to real data. The numerical method is based on the nonlinear least squares problem along with the solution of sensitivity equations corresponding to the differential equations. We will present the performance of the method on the problem of fitting the output of basic compartmental epidemic models to data from the Covid-19 epidemic. This allows us to draw several conclusions on the natural limitations of these models and their validity.
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