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Network Topology Matters, But Not Always: Mobility Networks in Epidemic Forecasting

Sepehr Ilami, Qingtao Cao, Babak Heydari

TL;DR

This work clarifies when mobility network topology improves short-horizon epidemic forecasts. By constructing weekly directed mobility networks for Massachusetts towns and evaluating forecasts under regimes with and without town-level case histories, the authors show large predictive gains from network interactions when local histories are coarse, but only modest gains when granular town histories are timely; autoregressive baselines dominate in the data-rich regime. The study combines empirical forecasting, an agent-based mechanistic triangulation, and a formal decomposition to explain the conditional value of topology and to propose a practical two-mode workflow for operational forecasting. The findings offer actionable guidance for when to invest in real-time network metrics and how to interpret network signals for targeting surveillance and interventions, with ABM support reinforcing the proposed mechanism.

Abstract

Short-horizon epidemic forecasts guide near-term staffing, testing, and messaging. Mobility data are now routinely used to improve such forecasts, yet work diverges on whether the volume of mobility or the structure of mobility networks carries the most predictive signal. We study Massachusetts towns (April 2020-April 2021), build a weekly directed mobility network from anonymized smartphone traces, derive dynamic topology measures, and evaluate their out-of-sample value for one-week-ahead COVID-19 forecasts. We compare models that use only macro-level incidence, models that add mobility network features and their interactions with macro incidence, and autoregressive (AR) models that include town-level recent cases. Two results emerge. First, when granular town-level case histories are unavailable, network information (especially interactions between macro incidence and a town's network position) yields large out-of-sample gains (Predict-R2 rising from 0.60 to 0.83-0.89). Second, when town-level case histories are available, AR models capture most short-horizon predictability; adding network features provides only minimal incremental lift (about +0.5 percentage points). Gains from network information are largest during epidemic waves and rising phases, when connectivity and incidence change rapidly. Agent-based simulations reproduce these patterns under controlled dynamics, and a simple analytical decomposition clarifies why network interactions explain a large share of cross-sectional variance when only macro-level counts are available, but much less once recent town-level case histories are included. Together, the results offer a practical decision rule: compute network metrics (and interactions) when local case histories are coarse or delayed; rely primarily on AR baselines when granular cases are timely, using network signals mainly for diagnostic targeting.

Network Topology Matters, But Not Always: Mobility Networks in Epidemic Forecasting

TL;DR

This work clarifies when mobility network topology improves short-horizon epidemic forecasts. By constructing weekly directed mobility networks for Massachusetts towns and evaluating forecasts under regimes with and without town-level case histories, the authors show large predictive gains from network interactions when local histories are coarse, but only modest gains when granular town histories are timely; autoregressive baselines dominate in the data-rich regime. The study combines empirical forecasting, an agent-based mechanistic triangulation, and a formal decomposition to explain the conditional value of topology and to propose a practical two-mode workflow for operational forecasting. The findings offer actionable guidance for when to invest in real-time network metrics and how to interpret network signals for targeting surveillance and interventions, with ABM support reinforcing the proposed mechanism.

Abstract

Short-horizon epidemic forecasts guide near-term staffing, testing, and messaging. Mobility data are now routinely used to improve such forecasts, yet work diverges on whether the volume of mobility or the structure of mobility networks carries the most predictive signal. We study Massachusetts towns (April 2020-April 2021), build a weekly directed mobility network from anonymized smartphone traces, derive dynamic topology measures, and evaluate their out-of-sample value for one-week-ahead COVID-19 forecasts. We compare models that use only macro-level incidence, models that add mobility network features and their interactions with macro incidence, and autoregressive (AR) models that include town-level recent cases. Two results emerge. First, when granular town-level case histories are unavailable, network information (especially interactions between macro incidence and a town's network position) yields large out-of-sample gains (Predict-R2 rising from 0.60 to 0.83-0.89). Second, when town-level case histories are available, AR models capture most short-horizon predictability; adding network features provides only minimal incremental lift (about +0.5 percentage points). Gains from network information are largest during epidemic waves and rising phases, when connectivity and incidence change rapidly. Agent-based simulations reproduce these patterns under controlled dynamics, and a simple analytical decomposition clarifies why network interactions explain a large share of cross-sectional variance when only macro-level counts are available, but much less once recent town-level case histories are included. Together, the results offer a practical decision rule: compute network metrics (and interactions) when local case histories are coarse or delayed; rely primarily on AR baselines when granular cases are timely, using network signals mainly for diagnostic targeting.
Paper Structure (27 sections, 3 equations, 3 figures, 2 tables)

This paper contains 27 sections, 3 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Overview of the approach
  4. Key Findings
  5. Network topology substantially improves short‑horizon forecasts when local case histories are unavailable
  6. With town‑level histories, autoregression dominates; network features add minimal lift
  7. When do network features help most? Epidemic phases and timing
  8. Forecast horizon: relative advantages persist beyond one week
  9. Mechanistic triangulation with an agent‑based model (ABM)
  10. Summary
  11. Discussion
  12. Mechanism and timing.
  13. How much mobility detail is needed?
  14. External validity and horizons.
  15. Mechanistic triangulation.
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Framework Overview
  • Figure 2: Prediction Horizons. Model performance (Adjusted R²) for one-week and four-week ahead forecasts of the town-level case numbers across seven model specifications. The Basic model uses only macro-level incidence (statewide cases). The combined model uses both holistic Network (Betweenness) and local Mobility (Intra-weight) metrics. All models show performance degradation from week +1 to week +4. Models incorporating interaction terms between the mobility/network metric and the statewide cases (+Int) consistently achieve the highest R² values at both time horizons, with Combined+Int reaching 0.87 at week +1. The Basic model shows the steepest decline in predictive power over time.
  • Figure 3: Added predictive value of network metrics and their interaction with state-level information, shown as a slopegraph of out-of-sample Predict-$R^2$. Points denote model variants for both the Empirical and ABM scenarios. Each trend compares model performance for Empirical and ABM scenarios under No town data (top) and With town data (bottom). The baseline uses state-level information only. The network model adds the best-performing network metric, selected from the top holistic network (betweenness) and top local mobility (intra-weight) measures. The interaction model includes both state-level predictors and the best network metric, along with their interaction term. All models include town fixed effects. Line segments illustrate incremental gains: the blue segment shows the added value of incorporating network metrics relative to the baseline; the red segment shows the added value of including the interaction term relative to the network model. The results show that when high-resolution town-level data are available, incorporating network metrics (and their interactions) provides little to no additional predictive benefit.