Parameter estimation for networked SIR models with stochastic perturbations using JEKF: a study using COVID-19 daily data from Indian states

Abstract

By using graph Laplacian diffusion, the susceptible-infected-removed (SIR) epidemic model is expanded to include a weighted network that exhibits randomness in the transmission rate parameter, representing population mobility between network nodes. Our goal is to estimate critical parameters, transmission rate (β), and recovery rate (γ), using the Joint Extended Kalman Filter (JEKF). This sophisticated estimation algorithm iteratively predicts and refines the state based on current estimates, combining model predictions with observed data to enhance accuracy, making it effective for estimating critical parameters in dynamic systems. Finally, we visually illustrate our algorithms through experiments conducted on a small-world Watts-Strogatz graph and a simple tree network. The conclusive results identify the best-fit parameters for effective COVID-19 management in India.

Keywords

• Graph Laplacian diffusion
• epidemic model
• joint extended Kalman filter
• stochastic perturbations
• Euler-Maruyama method