Connecting mass-action models and network models for infectious diseases

Infectious disease modeling is used to forecast epidemics and assess the effectiveness of intervention strategies. Although the core assumption of mass-action models of homogeneously mixed population is often implausible, they are nevertheless routinely used in studying epidemics and provide useful insights. Network models can account for the heterogeneous mixing of populations, which is especially important for studying sexually transmitted diseases. Despite the abundance of research on mass-action and network models, the relationship between them is not well understood. Here, we attempt to bridge the gap by first identifying a spreading rule that results in an exact match between disease spreading on a fully connected network and the classic mass-action models. We then propose a method for mapping epidemic spread on arbitrary networks to a form similar to that of mass-action models. We also provide a theoretical justification for the procedure. Finally, we demonstrate the application of the proposed method in the theoretical analysis of reproduction numbers and the estimation of model parameters using synthetic data based on an empirical network. The method proves advantageous in explicitly handling both finite and infinite networks, significantly reducing the computation time required to estimate model parameters for spreading processes on networks. These findings help us understand when mass-action models and network models are expected to provide similar results and identify reasons when they do not.