A Nonparametric Framework for Time-dependent SIR Models with Application to COVID Data

Abstract

Compartmental models, especially the Susceptible-Infected-Removed (SIR) model, have long been used to understand the behaviour of various diseases. Within this context, it can be beneficial to let parameters such as the transmission rate be time dependent functions. In this thesis, we attempt to build a nonparametric inference framework for stochastic SIR models with time dependent infection rate. The framework includes three main steps: likelihood approximation, parameter estimation and confidence interval construction. The likelihood function of the stochastic SIR model, which is often intractable, can be approximated using methods such as diffusion approximation or tau leaping. The infection rate is modelled by a B-spline basis whose knot location and number of knots are determined by a fast knot placement method followed by a criterion based model selection procedure. Finally, a point wise confidence interval is built using a parametric bootstrap procedure. The performance of the framework is observed through various settings for different epidemic patterns. The model is then applied to the Ontario COVID-19 data across multiple waves.