Reducing Size Bias in Sampling for Infectious Disease Spread on Networks

Epidemiological models can aid policymakers in reducing disease spread by predicting outcomes based on disease dynamics and contact network characteristics. Calibrating these models requires representative network samples. In this connection, we investigate two sampling algorithms, Random Walk (RW), and Metropolis-Hastings Random Walk (MHRW), across three network types: Erd\H{o}s-R\'enyi (ER), Small-world (SW), and Scale-free (SF). Disease transmission is simulated using a susceptible-infected-recovered (SIR) framework. Our findings show that RW overestimates infected individuals and secondary infections by $25\%$ for ER and SW networks due to size bias, favouring highly connected nodes. MHRW, which corrects for size bias, provides estimates that are more consistent with the underlying network. Also, both methods yield estimates significantly closer to the underlying network for time-to-infection. However, sampling SF networks exhibits significant variability, for both algorithms. Removing duplicate sampled nodes reduces MHRW's accuracy across all network types. We apply both algorithms to a cattle movement network of $46,512$ farms, exhibiting ER, SW, and SF network features. RW overestimates infected farms by approximately $100\%$ and secondary infections by $>900\%$, reflecting size bias whereas MHRW estimates align closely with the cattle network dynamics. Time-to-infection estimates reveal that RW underestimates by approximately $40\%$, while MHRW slightly overestimates by $10\%$. Estimates differ greatly when duplicate nodes are removed. These findings underscore choosing algorithms based on network structure and disease severity. RW's conservative estimates suit high-mortality, fast-spreading diseases, while MHRW provides precise interventions suitable for less severe outbreaks. These insights can guide policymakers in optimizing resource allocation and disease control strategies.