Community structure in social networks: applications for epidemiological modelling

Abstract

During an infectious disease outbreak people will often change their behaviour to reduce their risk of infection. Furthermore, in a given population, the level of perceived risk of infection will vary greatly amongst individuals. The difference in perception could be due to a variety of factors including varying levels of information regarding the pathogen, quality of local healthcare, availability of preventative measures, etc. In this work we argue that we can split a social network, representing a population, into interacting communities with varying levels of awareness of the disease. We construct a theoretical population and study which such communities suffer most of the burden of the disease and how their awareness affects the spread of infection. We aim to gain a better understanding of the effects that community-structured networks and variations in awareness, or risk perception, have on the disease dynamics and to promote more community-resolved modelling in epidemiology.

Figure 1. Sample community structure, constructed with the parameters summarised in Table 1 .

Figure 2. Average number of infections entering a single community for varying community size and connectivity.

White areas represent parameter combinations that do not produce a community structure. Community size n represents fraction of total population size N. Replicated for three values of H.

Figure 3. The prevalence of the disease within a community, plotted as a function of J.

(a) - results of the individual based simulations, (b) - the isolated mean field approximation, (c) - mean field approximation including boundary node effects. τ = 1, N = 250 000.

Figure 4. The final size of the epidemic as a fraction of community population, plotted as a function of J.

(a) - results of the individual based simulations, (b) - the isolated mean field approximation, (c) - mean field approximation including boundary node effects. τ = 0.5, N = 250 000.

Figure 5. Percentage of transmissions by originating community.

(a) shows all transmissions, (b) shows only inter-community transmissions. Non-shaded bars correspond to the case where H = 0 across all communities, shaded bars correspond to H set to the value suggested in Table 1. τ = 0.1, N = 250 000.

Figure 6. Percentage of transmissions as a function of ??? for each community for the SIS model.

(a): Total transmissions, no awareness. (b): External transmissions only, no awareness. (c) and (d) Total and external transmissions respectively, with awareness as specified in Table 1. N = 250 000.

Figure 7. Percentage of transmissions as a function of ??? for each community for the SIR model.

(a): Total transmissions, no awareness. (b): External transmissions only, no awareness. (c) and (d) Total and external transmissions respectively, with awareness as specified in Table 1. N = 250 000.

Figure 8. Fraction of infected individuals per community over a window of 500 steps.

τ = 0.1, N = 500 000.

Figure 9. Boxplots of fraction of time spent infected for the whole population (N) and each community.

Replicated for three different J values. τ = 0.1, N = 250 000.

Figure 10. Time series of an epidemic outbreak in the five communities.

The lower figure represents the case in which the mitigation strategies, as described in the text, are in place. Light grey lines correspond to results from the separate simulation runs. τ = 0.05, N = 250 000.