Strength and weakness of disease-induced herd immunity in networks
Abstract: 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.
- H. W. Hethcote, The mathematics of infectious diseases, SIAM Review 42, 599 (2000).
- M. E. J. Newman, Spread of epidemic disease on networks, Physical Review E 66, 016128 (2002).
- M. E. J. Newman, Mixing patterns in networks, Physical Review E 67, 026126 (2003).
- G. Burgio, B. Steinegger, and A. Arenas, Homophily impacts the success of vaccine roll-outs, Communications Physics 5, 70 (2022).
- R. Pastor-Satorras and A. Vespignani, Epidemic Spreading in Scale-Free Networks, Physical Review Letters 86, 3200 (2001).
- R. Pastor-Satorras and A. Vespignani, Immunization of complex networks, Physical Review E 65, 036104 (2002).
- M. J. Keeling and K. T. Eames, Networks and epidemic models, Journal of The Royal Society Interface 2, 295 (2005).
- T. Britton, F. Ball, and P. Trapman, A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2, Science 369, 846 (2020).
- H. Watanabe and T. Hasegawa, Impact of assortative mixing by mask-wearing on the propagation of epidemics in networks, Physica A: Statistical Mechanics and its Applications 603, 127760 (2022).
- T. Hasegawa and N. Masuda, Robustness of networks against propagating attacks under vaccination strategies, Journal of Statistical Mechanics: Theory and Experiment 2011, P09014 (2011).
- S. Bansal and L. A. Meyers, The impact of past epidemics on future disease dynamics, Journal of Theoretical Biology 309, 176 (2012).
- M. E. J. Newman, Threshold Effects for Two Pathogens Spreading on a Network, Physical Review Letters 95, 108701 (2005).
- D. J. Watts and S. H. Strogatz, Collective dynamics of ‘small-world’ networks, Nature 393, 440 (1998).
- M. E. J. Newman, I. Jensen, and R. M. Ziff, Percolation and epidemics in a two-dimensional small world, Physical Review E 65, 021904 (2002).
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