Strength and weakness of disease-induced herd immunity in networks.

When a fraction of a population becomes immune to an infectious disease, the population-wide infection risk decreases nonlinearly due to collective protection, known as herd immunity. Some studies based on mean-field models suggest that natural infection in a heterogeneous population may induce herd immunity more efficiently than homogeneous immunization. However, we theoretically show that this is not necessarily the case when the population is modeled as a network instead of using the mean-field approach. We identify two competing mechanisms driving disease-induced herd immunity in networks: the biased distribution of immunity toward socially active individuals enhances herd immunity, while the topological localization of immune individuals weakens it. The effect of localization is stronger in networks embedded in a low-dimensional space, which can make disease-induced immunity less effective than random immunization. Our results highlight the role of networks in shaping herd immunity and call for a careful examination of model predictions that inform public health policies.