Reducing Size Bias in Epidemic Network Modelling

TL;DR

This study compares random walk algorithms for sampling contact networks in epidemic models, showing MHRW reduces size bias and provides more accurate estimates than RW, especially in complex networks like cattle farms.

Contribution

It evaluates the effectiveness of RW and MHRW algorithms across different network types, highlighting MHRW's superior accuracy in representing network structures for epidemic modeling.

Findings

RW overestimates infected individuals by 25% in ER and SW networks.

MHRW reduces size bias and estimates align within 1% of real network values.

Neither algorithm samples SF networks representatively, showing high variability.

Abstract

Epidemiological models help policymakers mitigate disease spread by predicting transmission metrics based on disease dynamics and contact networks. Calibrating these models requires representative network sampling. We investigate the Random Walk (RW) and Metropolis-Hastings Random Walk (MHRW) algorithms for three network types: Erd\H{o}s-R\'enyi (ER), Small-world (SW), and Scale-free (SF). Disease transmission is simulated using a stochastic susceptible-infected-recovered (SIR) framework. For ER and SW networks, RW overestimates infected individuals and secondary infections by $25\%$ due to size bias, favouring highly connected nodes. MHRW, though more computationally intensive, reduces size bias and provides more representative samples. For time-to-infection, both algorithms provide representative estimates. However, neither algorithm samples SF networks representatively, exhibiting significant variability. Furthermore, removing duplicate sample nodes reduces MHRW's accuracy across three network types. We apply both algorithms to a cattle movement network of 46,512 farms combining ER, SW, and SF features. RW overestimates infected farms by about $100\%$ and secondary infections by over $900\%$, reflecting significant size bias, while MHRW estimates align within $1\%$ of the cattle network values. RW underestimates time-to-infection by about $40\%$, while MHRW overestimates it by $10\%$. Accuracy, again, deteriorates when duplicates nodes are removed. Our findings guide algorithm selection and intervention strategies based on network structure and disease severity; RW's conservative estimates suit high-mortality, fast-spreading epidemics, while MHRW enables more precise interventions for slower epidemics.