A dynamic power-law sexual network model of gonorrhoea outbreaks

Abstract

Human networks of sexual contacts are dynamic by nature, with partnerships forming and breaking continuously over time. Sexual behaviours are also highly heterogeneous, so that the number of partners reported by individuals over a given period of time is typically distributed as a power-law. Both the dynamism and heterogeneity of sexual partnerships are likely to have an effect in the patterns of spread of sexually transmitted diseases. To represent these two fundamental properties of sexual networks, we developed a stochastic process of dynamic partnership formation and dissolution, which results in power-law numbers of partners over time. Model parameters can be set to produce realistic conditions in terms of the exponent of the power-law distribution, of the number of individuals without relationships and of the average duration of relationships. Using an outbreak of antibiotic resistant gonorrhoea amongst men have sex with men as a case study, we show that our realistic dynamic network exhibits different properties compared to the frequently used static networks or homogeneous mixing models. We also consider an approximation to our dynamic network model in terms of a much simpler branching process. We estimate the parameters of the generation time distribution and offspring distribution which can be used for example in the context of outbreak reconstruction based on genomic data. Finally, we investigate the impact of a range of interventions against gonorrhoea, including increased condom use, more frequent screening and immunisation, concluding that the latter shows great promise to reduce the burden of gonorrhoea, even if the vaccine was only partially effective or applied to only a random subset of the population.

Fig 1

Double logarithmic plot of degree distribution of number of partners for UK MSM A: reported over 1 year by Natsal-3 respondents. B: reported over 3 months in GRASP data from London. Inset: corresponding normalised cumulative degree distributions.

Fig 2. Double logarithmic plot of degree distributions of partners in last year generated with differing parameters γ and k₀.

The orange lines represent the desired degree distribution p(k) = ck^−γ. The proportion of individuals having no partners in the last year is shown in the title of each plot as p(k = 0). Inset: corresponding normalised cumulative degree distributions.

Fig 3

A: Illustration of gonorrhoea transmission over time through the three network structures: fully connected, static and dynamic. B: Flow diagram of transmission model with rates of transition between infection states. Uninfected individuals (U) become infected after sexual contact with contagious individuals (highlighted in orange). Infections initially pass through an incubation period (I), before either developing symptoms (S) or remaining asymptomatic (A). Symptomatic individuals seek treatment, and asymptomatic infections identified by screening are also treated (T).

Fig 4. Scatter plots with overlaid density contours and marginal histograms for the mean and variance of A: the offspring distributions, and B: the distribution of generation times, for infections contracted in the first year of the outbreak.

Simulations under the fully connected, static, and dynamic network structures are shown in blue, green and red respectively.

Fig 5

A: Proportion of infected individuals split by number of partners over one year B: Probability of an individual becoming infected in first year given their total number of partnerships. C: Mean transmission events for infected individuals with a given number of partnerships.

Fig 6

A: Proportion of outbreaks persisting for at least one year. B: Number of gonorrhoea diagnoses in first year. C: Number of clinic visits in first year.