Nonparametric Inference Framework for Time-dependent Epidemic Models

TL;DR

This paper develops a nonparametric inference framework for stochastic SIR epidemic models with time-varying infection rates, enabling flexible analysis of epidemic data and changes over time.

Contribution

It introduces a novel nonparametric approach for estimating time-dependent parameters in stochastic SIR models using likelihood approximation, B-spline modeling, and bootstrap confidence intervals.

Findings

Framework performs well across different epidemic scenarios.

Applied successfully to Ontario COVID-19 data across multiple waves.

Provides flexible inference for dynamic epidemic parameters.

Abstract

Compartmental models, especially the Susceptible-Infected-Removed (SIR) model, have long been used to understand the behaviour of various diseases. Allowing parameters, such as the transmission rate, to be time-dependent functions makes it possible to adjust for and make inferences about changes in the process due to mitigation strategies or evolutionary changes of the infectious agent. In this article, 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.