Predicting the Effectiveness of Endemic Infectious Disease Control Interventions: The Impact of Mass Action versus Network Model Structure

Background: Analyses of the effectiveness of infectious disease control interventions often rely on dynamic transmission models to simulate intervention effects. We aim to understand how the choice of network or compartmental model can influence estimates of intervention effectiveness in the short and long term for an endemic disease with susceptible and infected states in which infection, once contracted, is lifelong. Methods: We consider 4 disease models with different permutations of socially connected network versus unstructured contact (mass-action mixing) model and heterogeneous versus homogeneous disease risk. The models have susceptible and infected populations calibrated to the same long-term equilibrium disease prevalence. We consider a simple intervention with varying levels of coverage and efficacy that reduces transmission probabilities. We measure the rate of prevalence decline over the first 365 d after the intervention, long-term equilibrium prevalence, and long-term effective reproduction ratio at equilibrium. Results: Prevalence declined up to 10% faster in homogeneous risk models than heterogeneous risk models. When the disease was not eradicated, the long-term equilibrium disease prevalence was higher in mass-action mixing models than in network models by 40% or more. This difference in long-term equilibrium prevalence between network versus mass-action mixing models was greater than that of heterogeneous versus homogeneous risk models (less than 30%); network models tended to have higher effective reproduction ratios than mass-action mixing models for given combinations of intervention coverage and efficacy. Conclusions: For interventions with high efficacy and coverage, mass-action mixing models could provide a sufficient estimate of effectiveness, whereas for interventions with low efficacy and coverage, or interventions in which outcomes are measured over short time horizons, predictions from network and mass-action models diverge, highlighting the importance of sensitivity analyses on model structure. Highlights: • We calibrate 4 models—socially connected network versus unstructured contact (mass-action mixing) model and heterogeneous versus homogeneous disease risk—to 10% preintervention disease prevalence. • We measure the short- and long-term intervention effectiveness of all models using the rate of prevalence decline, long-term equilibrium disease prevalence, and effective reproduction ratio. • Generally, in the short term, prevalence declined faster in the homogeneous risk models than in the heterogeneous risk models. • Generally, in the long term, equilibrium disease prevalence was higher in the mass-action mixing models than in the network models, and the effective reproduction ratio was higher in network models than in the mass-action mixing models.