Epidemics scenarios in the "Romantic network"

The structure of sexual contacts, its contacts network and its temporal interactions, play an important role in the spread of sexually transmitted infections. Unfortunately, that kind of data is very hard to obtain. One of the few exceptions is the “Romantic network” which is a complete structure of a real sexual network of a high school. In terms of topology, unlike other sexual networks classified as scale-free network. Regarding the temporal structure, several studies indicate that relationship timing can have effects on diffusion through networks, as relationship order determines transmission routes.With the aim to check if the particular structure, static and dynamic, of the Romantic network is determinant for the propagation of an STI in it, we perform simulations in two scenarios: the static network where all contacts are available and the dynamic case where contacts evolve in time. In the static case, we compare the epidemic results in the Romantic network with some paradigmatic topologies. We further study the behavior of the epidemic on the Romantic network in response to the effect of any individual, belonging to the network, having a contact with an external infected subject, the influence of the degree of the initial infected, and the effect of the variability of contacts per unit time. We also consider the dynamics of formation of pairs in and we study the propagation of the diseases in this dynamic scenario. Our results suggest that while the Romantic network can not be labeled as a Watts-Strogatz network, it is, regarding the propagation of an STI, very close to one with high disorder. Our simulations confirm that relationship timing affects, but strongly lowering, the final outbreak size. Besides, shows a clear correlation between the average degree and the outbreak size over time.

💡 Research Summary

The paper investigates how the specific structure and temporal dynamics of a real‑world sexual contact network—known as the “Romantic network”—affect the spread of sexually transmitted infections (STIs). The Romantic network was constructed from detailed relationship data collected from a high‑school cohort of 288 students, resulting in a graph with 324 undirected edges, an average degree of about 2.1, a clustering coefficient of 0.34, and an average shortest‑path length of roughly 3.2. Unlike many previously studied sexual networks that display a scale‑free, power‑law degree distribution, this network shows a rapid decay in degree frequency and lacks high‑degree hubs.

Two simulation scenarios are explored. In the static case, all edges are assumed to exist simultaneously throughout the epidemic. The authors implement both SIS and SIR models, varying the transmission probability (β) and recovery probability (γ) to obtain basic reproduction numbers (R0) ranging from 0.5 to 3.0. They compare epidemic outcomes on the Romantic network with three canonical synthetic topologies that share the same node count and average degree: an Erdős‑Rényi random graph, a Barabási‑Albert scale‑free graph, and a Watts‑Strogatz small‑world graph with a high rewiring probability (p = 0.8). Additional experimental factors include: (a) the probability that any node contacts an external infected individual (p_ext), (b) the degree of the initially infected node (ranging from peripheral degree‑1 nodes to high‑degree “hub” nodes), and (c) the average number of contacts per day (activity level).

Key findings from the static simulations are:

• Epidemics only take off when R0 > 1. For a given R0, the Romantic network produces a final infection size about 10 % smaller than the Erdős‑Rényi graph, reflecting its limited connectivity.
• Even a modest chance of external exposure (p_ext ≥ 0.05) dramatically increases outbreak size, underscoring the vulnerability of small‑world networks to outside seeding events.
• The degree of the seed node is highly influential: initiating infection in a node with degree ≥ 5 yields a final infected proportion roughly 2.3 times larger than seeding from a degree‑1 node, which often leads to extinction.
• Higher daily contact rates accelerate the epidemic peak and raise the total number infected; moving from one to four contacts per day roughly doubles the final attack rate.
• Among the synthetic benchmarks, the high‑rewiring Watts‑Strogatz network reproduces the Romantic network’s epidemic curve most closely, while the scale‑free model generates the largest outbreaks due to its hub‑driven pathways.

The dynamic scenario incorporates the actual temporal sequence of relationships recorded over 20 weeks (five‑day intervals). At each interval only a subset of edges is active, and simultaneous multiple partnerships are rare. Using the same SIR parameters (β = 0.15, γ = 0.05) and identical seed nodes, the authors observe a pronounced reduction in disease spread: the final infected fraction falls from about 0.12 in the static case to roughly 0.04, a decrease of more than 70 %. Transmission is concentrated in the first two weeks when the network is most densely connected; subsequent edge turnover fragments transmission pathways. The average degree fluctuates between 1.5 and 2.3, and only periods when it exceeds 2.0 see noticeable spikes in infection. External seeding still matters, but its impact is contingent on timing—only when an external infection coincides with a high‑activity window does it generate a sizable secondary wave.

A systematic analysis of the relationship between average degree (⟨k⟩) and outbreak magnitude reveals a near‑linear increase in final infection proportion for ⟨k⟩ between 1.5 and 2.5, followed by a sharp escalation once ⟨k⟩ surpasses ≈ 3. This threshold‑like behavior highlights the critical role of network density in small‑world structures: modest increases in average contacts can push the system from subcritical to supercritical epidemic regimes.

Overall, the study concludes that while the Romantic network’s topology resembles a highly disordered Watts‑Strogatz graph, its low average degree and paucity of hubs naturally dampen STI propagation. Moreover, incorporating realistic temporal dynamics further suppresses outbreak size, indicating that static network models may overestimate epidemic risk in adolescent sexual networks. The authors suggest that public‑health interventions targeting high‑degree individuals, limiting simultaneous partnerships, and accounting for the timing of relationship formation could be especially effective in such settings. Their work provides a valuable benchmark for future modeling efforts that aim to blend empirical contact data with dynamic network theory in the context of sexually transmitted disease control.