Regularized Semiparametric Estimation for Ordinary Differential Equations

We propose a new regularized estimation procedure on the time-varying parameters of an ODE system so that these parameters could change with time during transitions but remain constants within stable stages. We found, through simulation studies, that the proposed method performs well and tends to have less variation in comparison to the nonregularized approach. On the theoretical front, we derive finite-sample estimation error bounds for the proposed method.

Applications of the proposed method to modeling the hare–lynx relationship and the measles incidence dynamic in Ontario, Canada lead to satisfactory and meaningful results. Supplementary materials for this article are available online.