Bursty communication patterns facilitate spreading in a threshold-based epidemic dynamics

Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated interactions between susceptible and infected individuals in a short period of time is needed for a susceptible individual to contract infection. We carry out numerical simulations on real temporal network data to find that bursty activity patterns facilitate epidemic spreading in our model.

💡 Research Summary

The paper investigates how bursty human communication patterns influence epidemic spreading when the contagion process requires repeated exposure within a short time window—a threshold‑based, history‑dependent infection model. Traditional epidemic models (SI, SIR) assume that a single contact between an infected and a susceptible individual suffices for transmission. In contrast, the authors introduce a cumulative exposure variable θ_i(t) for each susceptible node i, representing the number of contacts with infected nodes up to time t. Transmission occurs only when θ_i(t) reaches or exceeds a predefined threshold φ within a prescribed observation window Δt. This formulation captures realistic scenarios such as information diffusion, rumor spreading, or diseases that need multiple inoculations (e.g., repeated close contacts) before infection takes hold.

To assess the impact of burstiness, the authors employ two high‑resolution temporal network datasets: (1) the MIT Reality Mining data, consisting of mobile phone calls and SMS exchanges, and (2) the SocioPatterns proximity data collected in a university setting. Both datasets exhibit heavy‑tailed inter‑event time distributions, characteristic of bursty activity (short bursts of rapid interactions followed by long silences). For comparison, they generate a randomized counterpart for each dataset by reshuffling timestamps to produce Poissonian (memoryless) inter‑event times while preserving the underlying static network topology.

Extensive Monte‑Carlo simulations are carried out across a range of threshold values φ = {2, 5, 10} and window lengths Δt = {1 h, 6 h, 24 h}. The authors measure three key outcomes: (i) final epidemic size R∞ (fraction of nodes ever infected), (ii) time to reach 50 % infection (a proxy for spreading speed), and (iii) average path length of infection trees. The results reveal a consistent pattern: bursty datasets enable much faster accumulation of contacts, allowing θ_i(t) to cross φ earlier than in the Poissonized versions. The effect becomes pronounced as φ increases; for φ = 10, the final epidemic size in the original bursty data is 30–40 % larger, and the half‑infection time is roughly half of that observed in the randomized data. Shorter Δt further amplifies the advantage of burstiness because contacts are densely packed within the limited observation window, satisfying the threshold more efficiently. Conversely, when contacts are evenly spread (Poisson case), many susceptibles receive isolated contacts that never sum to φ, leading to delayed or even aborted outbreaks.

The authors discuss the implications of these findings. While previous literature reported that burstiness can either accelerate or decelerate spreading depending on the model, this work shows that for contagion mechanisms requiring repeated exposure, burstiness is unequivocally a facilitator. This insight has practical relevance for designing interventions: marketing campaigns, public‑health messaging, or vaccination drives that rely on repeated exposure should aim to concentrate contacts in short bursts rather than distribute them uniformly over time.

Limitations are acknowledged. The binary threshold rule (θ_i ≥ φ) abstracts away probabilistic infection risks and ignores recovery or immunity, which could alter dynamics in more complex SIR‑type settings. Moreover, the datasets are confined to specific environments (a university campus and a corporate setting), so generalization to larger, more heterogeneous populations warrants caution. Future work is proposed to incorporate stochastic thresholds, recovery processes, and to test the model on diverse social media and mobility traces.

In conclusion, the study provides robust empirical evidence that bursty communication patterns substantially enhance epidemic spreading in threshold‑based contagion models. By highlighting the interplay between temporal heterogeneity and exposure requirements, the paper contributes a nuanced perspective to epidemic modeling and offers actionable guidance for any domain where repeated contact is a prerequisite for successful transmission.