Parameter Estimation in the SIR Model Using Collocation Method

In this paper, we present a methodology for estimating the parameters of a system of ordinary differential equations (ODEs) for the SIR model, a critical tool for understanding the dynamics of infectious diseases. The SIR model is essential for predicting outbreak patterns and informing public health interventions, playing a pivotal role in safety analysis. The parameters of the model are estimated from measured data while simultaneously solving the corresponding system of ODEs numerically. Our approach is based on the collocation method, where the solution is expressed as a linear combination of B-spline basis functions and fitted to the data through regression. The square Euclidean measure is used for both regression fitting and minimizing the ODE error. This problem is formulated as a multicriteria optimization task, balancing errors in the model fit and the numerical solution of the ODE system. The entire methodology is implemented in the MATLAB environment. We present numerical results and demonstrate the effectiveness of the approach for parameter estimation in epidemiological models using artificial benchmark datasets.

Keywords: SIR model, Epidemiological modeling, Parameter estimation, Collocation method, Regression, ODE.