Numerical optimization of parameters in systems of differential equations

Martínek, Josef, and Kučera, Václav. "Numerical optimization of parameters in systems of differential equations." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2023. 123-132. <http://eudml.org/doc/299020>.

@inProceedings{Martínek2023,
abstract = {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.},
author = {Martínek, Josef, Kučera, Václav},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {ordinary differential equations; parameter estimation; nonlinear least squares; mathematical epidemiology},
location = {Prague},
pages = {123-132},
publisher = {Institute of Mathematics CAS},
title = {Numerical optimization of parameters in systems of differential equations},
url = {http://eudml.org/doc/299020},
year = {2023},
}

TY - CLSWK
AU - Martínek, Josef
AU - Kučera, Václav
TI - Numerical optimization of parameters in systems of differential equations
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2023
CY - Prague
PB - Institute of Mathematics CAS
SP - 123
EP - 132
AB - 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.
KW - ordinary differential equations; parameter estimation; nonlinear least squares; mathematical epidemiology
UR - http://eudml.org/doc/299020
ER -