Statistical implications of relaxing the homogeneous mixing assumption in time series Susceptible-Infectious-Removed models

TL;DR

This paper investigates the statistical consequences of relaxing the homogeneous mixing assumption in TSIR models, revealing biases in parameter estimates and implications for epidemic modeling accuracy.

Contribution

It demonstrates that relaxing the homogeneous mixing assumption in TSIR models leads to interpretational issues and biased estimates, challenging their use in epidemic analysis.

Findings

TSIR models cannot be interpreted as approximate SIR models when mixing is non-homogeneous.

Simulation results show systematic bias in infection and mixing rate estimates.

Caution is advised when interpreting TSIR parameters under relaxed mixing assumptions.

Abstract

Infectious disease epidemiologists routinely fit stochastic epidemic models to time series data to elucidate infectious disease dynamics, evaluate interventions, and forecast epidemic trajectories. To improve computational tractability, many approximate stochastic models have been proposed. In this paper, we focus on one class of such approximations -- time series Susceptible-Infectious-Removed (TSIR) models. Infectious disease modeling often starts with a homogeneous mixing assumption, postulating that the rate of disease transmission is proportional to a product of the numbers of susceptible and infectious individuals. One popular way to relax this assumption proceeds by raising the number of susceptible and/or infectious individuals to some positive powers. We show that when this technique is used within the TSIR models they cannot be interpreted as approximate SIR models, which has important implications for TSIR-based statistical inference. Our simulation study shows that TSIR-based estimates of infection and mixing rates are systematically biased in the presence of non-homogeneous mixing, suggesting that caution is needed when interpreting TSIR model parameter estimates when this class of models relaxes the homogeneous mixing assumption.