Random vs. nonrandom mixing in network epidemic models

In this paper we compare random and nonrandom mixing patterns for network epidemic models. Several of studies have examined the impact of different mixing patterns using compartmental epidemic models. We extend the work on compartmental models to the case of network epidemic models. We define two nonrandom mixing patterns for a network epidemic model and investigate the impact that these mixing patterns have on a number of epidemic outcomes when compared to random mixing. We find that different mixing assumptions lead to small but statistically significant differences in disease prevalence, cumulative number of new infections, final population size, and network structure. Significant differences in outcomes were more likely to be observed for larger populations and longer time horizons. Sensitivity analysis revealed that greater differences in outcomes between random and nonrandom mixing were associated with a larger incremental mortality rate among infected individuals, a larger average number of partners, and a greater probability of forming new partnerships. When adjusted for the initial population size, differences between random and nonrandom mixing models were approximately constant across all population sizes considered. We also considered the impact that differences between mixing models might have on the cost effectiveness ratio for epidemic control interventions.