An approximate diffusion process for environmental stochasticity in infectious disease transmission modelling

TL;DR

This paper introduces an efficient approximation method for modeling environmental stochasticity in infectious disease transmission, replacing complex data-augmentation with a diffusion process expansion, demonstrated on influenza and COVID-19 models.

Contribution

It proposes a novel approximation of the transmission potential as a diffusion process, simplifying inference in stochastic disease models.

Findings

The method reduces computational complexity in inference.

It effectively models environmental stochasticity in infectious diseases.

Demonstrated on influenza and COVID-19 models.

Abstract

Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe, mechanistically, changes in extrinsic environmental factors including public behaviour and seasonal fluctuations. An elegant approach to capturing environmental stochasticity is to model the force of infection as a stochastic process. However, inference in this context requires solving a computationally expensive ``missing data" problem, using data-augmentation techniques. We propose to model the time-varying transmission-potential as an approximate diffusion process using a path-wise series expansion of Brownian motion. This approximation replaces the ``missing data" imputation step with the inference of the expansion coefficients: a simpler and computationally cheaper task. We illustrate the merit of this approach through two examples: modelling influenza using a canonical SIR model, and the modelling of COVID-19 pandemic using a multi-type SEIR model.