Causal Inference in Disease Spread across a Heterogeneous Social System

Diffusion processes are governed by external triggers and internal dynamics in complex systems. Timely and cost-effective control of infectious disease spread critically relies on uncovering the underlying diffusion mechanisms, which is challenging due to invisible causality between events and their time-evolving intensity. We infer causal relationships between infections and quantify the reflexivity of a meta-population, the level of feedback on event occurrences by its internal dynamics (likelihood of a regional outbreak triggered by previous cases). These are enabled by our new proposed model, the Latent Influence Point Process (LIPP) which models disease spread by incorporating macro-level internal dynamics of meta-populations based on human mobility. We analyse 15-year dengue cases in Queensland, Australia. From our causal inference, outbreaks are more likely driven by statewide global diffusion over time, leading to complex behavior of disease spread. In terms of reflexivity, precursory growth and symmetric decline in populous regions is attributed to slow but persistent feedback on preceding outbreaks via inter-group dynamics, while abrupt growth but sharp decline in peripheral areas is led by rapid but inconstant feedback via intra-group dynamics. Our proposed model reveals probabilistic causal relationships between discrete events based on intra- and inter-group dynamics and also covers direct and indirect diffusion processes (contact-based and vector-borne disease transmissions).

💡 Research Summary

This paper introduces the Latent Influence Point Process (LIPP), a novel stochastic framework that simultaneously captures exogenous environmental risk and endogenous human‑mobility‑driven dynamics in the spread of infectious diseases. Building on the Hawkes process, LIPP augments the intensity function with three components: (1) an exogenous term λ₀ᵣ = ηᵣ ρ₀ᵣ that reflects region‑specific environmental heterogeneity (temperature, humidity, vector abundance) and the probability of infection from external sources such as international travelers; (2) an endogenous term λₖᵣ(t) = ∑_{t_i<t} ζ(k) ρₖᵣ φ(t−t_i), where ζ(k) = 1 + δ(k)·ξₖ combines a latent influence ξₖ (population density, social activity) with a vector‑presence indicator δ(k), and ρₖᵣ encodes directed human‑mobility flows between regions; (3) a temporal decay kernel φ(Δt) = exp(−ϕₖ Δt) that models how the infectious impact of past events wanes over time. The total intensity for region r is λᵣ(t) = λ₀ᵣ + ∑ₖ λₖᵣ(t), yielding a multivariate Hawkes process that can represent both self‑excitation (intra‑regional transmission) and mutual excitation (inter‑regional transmission).

Parameter inference is performed via an Expectation–Maximization (EM) algorithm. Latent indicator variables Z_i denote which preceding event triggered each observed case, allowing the E‑step to compute posterior triggering probabilities and the M‑step to update ηᵣ, ξᵣ, and ϕᵣ by maximizing the expected complete‑data log‑likelihood. Synthetic experiments demonstrate accurate recovery of these parameters across a range of settings, with low mean absolute percentage error, confirming the model’s identifiability.

The authors apply LIPP to 15 years (2002‑2016) of dengue fever case data from Queensland, Australia. Cases are geocoded to 15 Statistical Area Level 4 (SA4) regions; human‑mobility information is assembled from international visitor surveys, national visitor surveys, and geotagged Twitter data, producing a normalized mobility matrix ρₖᵣ.

Causal inference results reveal a dense network of inferred transmission links, especially in the three years with the largest outbreaks (2003, 2009, 2013). Visualizations show that metropolitan hubs (e.g., Brisbane) and tourist destinations (Cairns, Gold Coast) act as major sources, with strong outgoing edges to many other regions, confirming that mobility drives inter‑regional diffusion.

Parameter analysis yields several substantive insights:

• Reflexivity (internal feedback) varies systematically across regions. High‑population areas exhibit larger ξᵣ and smaller ϕᵣ, indicating a slow but persistent feedback loop—cases trigger further cases over an extended period, producing a symmetric rise and gradual decline of outbreaks. In contrast, peripheral, low‑population regions have smaller ξᵣ but larger ϕᵣ, leading to rapid, bursty growth followed by sharp declines, reflecting an intermittent feedback pattern.

• Temporal shift in diffusion drivers: Early in the study period, the exogenous component (ρ₀ᵣ) dominates, suggesting that imported infections from outside Queensland were the primary seed. Over time, the endogenous mobility‑driven component (ρₖᵣ) grows in relative importance, indicating that the disease becomes increasingly sustained by internal human movement, resulting in a more globally interconnected outbreak landscape.

• Policy implications: High‑reflexivity regions may benefit from sustained vector‑control and community‑engagement programs, whereas low‑reflexivity, peripheral regions may require rapid, targeted interventions during outbreak spikes (e.g., temporary travel restrictions, emergency vector control). Moreover, real‑time updating of mobility matrices could enable dynamic forecasting and resource allocation.

Overall, LIPP advances epidemiological modeling by explicitly quantifying both the strength and the temporal decay of inter‑regional transmission pathways, offering a richer description of disease dynamics than classic compartmental models. The framework is generalizable to other contagion processes—social, informational, or ecological—where external triggers and internal network‑mediated feedback coexist.