Description
Introduction & theoretic backgroundThe COVID-19 pandemic has shown how vulnerable our globalized world is to the threat of infectious diseases. To reduce the number of new infections many countries have implemented forms of social distancing. However, not only external interventions alter network structure. Avoidant health behavior, such as avoiding coworkers with symptoms or avoiding sexual contact because a partner has an STD, is known to af- fect pathways of infection [4]. Further, we know that health behavior is affected by individual risk perceptions making different people behave differently in similar situa- tions [1], while people like to mix with others who behave similarly [5]. Additionally, Coleman describes a dense network as primary source for social capital [3], while Burt describes the benefits of bridging structural holes in the network [2], two mechanisms to explain why our social networks are small-worlds with high clustering and low average path length [7].
These considerations ultimately result in homophilous clusters of heterogeneous health behavior in which agents deliberately distance themselves from a disease. The effect of these social dynamics in small-worlds on the disease dynamics, however, re- main unclear. We therefore ask: How does health behavior homophily shape epidemics in dynamic small-world networks?
Model & methods
For the current study we build on a previously developed model that integrates theories from sociology (network formation), health psychology (risk perception), and epidemi- ology (compartmental models) [6]. This ego-centered, utility-based model describes social networking in the context of infectious diseases as a trade-off between the bene- fits, efforts, and potential health damage a social tie creates. Thus, risk avoiding agents may break ties to infected peers, while risk seeking agents may not. Further, infections can travel between agents along social ties.
To control network clustering, we added benefits for the proportion of closed triads an agent is part of (α). To control homophily, we added a probability that 2 agents sim- ilar in risk perception have contact (ω). Consequently, for high α and high ω networks with homophilous interconnected clusters emerge, while low α and low ω result in ran- domly mixed networks with a single large cluster. Further, the optimum number of ties per agent is constant to reduce the influence of degree on disease dynamics.
An agent-based simulation served to study the theoretic model. A single simula- tion run consists of three parts: First, agents form ties until a pairwise stable network emerges (no agent benefits from breaking ties; no pair of agents benefits from creating a tie). Second, after a randomly selected agent (index case) is infected, disease dynamics are simulated without network dynamics (static networks). Third, disease states are re- set, the index case is reinfected, and disease dynamics are simulated including network dynamics (dynamic networks). That is, agents modify ties depending on benefits, risk perception, disease severity, and transmission probability. To understand the effect of model parameters on the number of infected agents (attack rate), the duration of the epidemic, and the maximum number of simultaneously infected agents (peak size) we analyzed 80, 305 simulation runs with randomized parameter settings.
Results, discussion, & conclusion
The results show that the presence of homophilous clusters (see table rows ”Clustering”, ”Homophily”), reduce attack rate, duration, and peak size of epidemics in dynamic net- works. That is because clusters of agents collectively perceiving high risks of infections are hard to be invaded by a disease for two reasons. First, there are only few bridges, thus reducing the probability for infections to enter the cluster. Second, bridging agents in the risk avoiding cluster perceive health risks to be more severe, thus cutting ties quicker than agents in risk seeking clusters. Although clusters of risk seeking agents may become fully infected, the epidemic remains limited to parts of the network.
Further, we see opposing effects for clustering on duration in dynamic and static networks. In static networks, the disease needs time to travel across bridges to reach other clusters. In contrast, few changes in dynamic networks can isolate infected clus- ters quickly resulting in lower attack rates and consequently in less time for the disease to disappear from the network.
In line with previous studies, epidemics in dynamic networks have on average lower attack rates, shorter duration, and lower epidemic peaks (Fig. 1). However, when the ef- fect of attack rate is attenuated (attack rates 90%), we see longer duration in dynamic networks. That is, although agents get infected at some point, they delay their infection by distancing themselves from the disease in the early stages of the epidemic.
A finding we cannot confirm, however, is that increases in average path length ought to reduce attack rate [7] (see table row ”Path length”). That is because agents in long path length networks need only a few changes to distance themselves from the disease, making it likely for the disease to have no more pathways to travel along.
In conclusion, we see that homophilous clusters of agents similar in risk perception significantly affect disease dynamics in dynamic small-world networks, affecting attack rate, duration, and peak size of epidemics. Additional findings (opposing or missing effects in dynamic and static networks) further illustrate the importance of considering theoretically sound network dynamics for network models in epidemiology.
References
Bish, A., Michie, S.: Demographic and attitudinal determinants of protective behaviours dur- ing a pandemic: A review. British Journal of Health Psychology 15(4), 797–824 (nov 2010)
Burt, R.S.: Structural holes: The social structure of competition. Harvard university press (2009)
Coleman, J.S.: Foundations of social theory. Harvard university press (1994)
Funk, S., Gilad, E., Watkins, C., Jansen, V.A.: The spread of awareness and its impact on epidemic outbreaks. Proceedings of the National Academy of Sciences of the United States of America 106(16), 6872–6877 (2009)
McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a Feather: Homophily in Social Net- works. Annual Review of Sociology 27(1), 415–444 (aug 2001)
Nunner, H., Buskens, V., Kretzschmar, M.E.: A model for the co-evolution of dynamic social networks and infectious disease dynamics, submitted
Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393(6684), 440 (1998)
| Period | 2 Dec 2020 |
|---|---|
| Event title | COMPLEX NETWORKS 2020: The 9th International Conference on Complex Networks and their Applications |
| Event type | Conference |
| Conference number | 9 |
| Location | Madrid, SpainShow on map |