Delayed introduction, contact variation, and susceptible dynamics explain spatial asynchrony during Korea's large pertussis outbreak

By integrating high-resolution surveillance data with a Bayesian transmission model, this study demonstrates that delayed introduction timing and regional variations in contact levels drove the unusual spatial asynchrony observed during South Korea's 2024–2025 pertussis outbreak, challenging classical epidemic theories that predict large-scale synchrony.

The Gist

Imagine the 2024–2025 Whooping Cough (Pertussis) outbreak in South Korea not as a single, uniform wave crashing over the whole country, but as a chaotic game of "musical chairs" where the music stopped at different times in different rooms.

Usually, when a virus spreads, it moves like a ripple in a pond: if you drop a stone in one spot, the ripples spread out smoothly and hit the shore everywhere at roughly the same time. Scientists call this synchrony. They expected the Whooping Cough outbreak in Korea to behave this way, moving smoothly from city to city.

But it didn't. Instead, the outbreak was asynchronous. While Seoul was in the middle of a massive wave, a city just 100 kilometers away might have been just starting, or already finishing. It was as if the virus was playing a different song in every neighborhood.

This paper asks: Why did the virus dance to different rhythms in different places?

The Detective Work: Two Suspects

The author, Sang Woo Park, investigated two main suspects that could explain this chaos:

1. The "Late Arrival" Suspect (Introduction Timing): Did the virus just show up later in some towns?
2. The "Crowded Room" Suspect (Contact Levels): Did some towns have people who hung out together more often, making the virus spread faster?

The Investigation: What the Data Said

1. The Virus Arrived at Different Times
The study found that the virus didn't hit every town at once. In some places, it arrived early; in others, it arrived late. Think of it like a fire starting in a forest. If the wind blows the embers to the north first, the north burns early. If the embers drift south later, the south burns later. This "delayed arrival" was a major reason why the peaks of the outbreak didn't line up across the country.

2. The "Crowded Room" Effect
Here is the most interesting part. The study looked at how fast the virus was spreading once it arrived (the "Effective Reproduction Number"). Surprisingly, the speed of spread was actually quite similar everywhere. The virus wasn't moving faster in Seoul than in Busan.

However, the intensity of social contact varied.

• High-Contact Towns: Imagine a town where everyone is constantly hugging, shaking hands, and going to crowded schools. If the virus gets in, it burns through the "susceptible" people (those who can get sick) very quickly. It creates a huge, sharp wave, burns out the fuel (the susceptible people), and then stops. Because it burned so fast, it might only have one big wave and then die down.
• Low-Contact Towns: In a town where people keep their distance, the virus spreads slower. It doesn't burn through the fuel all at once. It creates a smaller first wave, leaves enough "fuel" (susceptible people) left over, and then, when school starts again or the season changes, it can spark a second wave.

The Analogy of the Campfire:

• High Contact: You throw a match into a pile of dry leaves. Whoosh! A massive fire erupts immediately, consumes all the leaves, and leaves nothing but ash. No second fire.
• Low Contact: You throw a match into a pile of damp wood. It smolders, then flares up a bit, then dies down. But because the wood wasn't fully consumed, a gust of wind (or a new season) can make it flare up again later.

The "School Holiday" Factor

The study also found that the virus took a break during school holidays (summer and winter). When schools closed, kids stopped mixing, and the virus slowed down. When schools reopened, the virus jumped back up. This seasonal "pause button" helped shape the waves, but the timing of the waves depended on when the virus first arrived and how "crowded" the local social scene was.

The Big Conclusion

The paper concludes that you don't need a different virus or a different weather pattern to explain why some cities got hit hard and early while others got hit late or twice. You just need:

1. A delayed start (the virus arrived late).
2. Different social habits (some places are "crowded," others are "sparse").

These two simple factors, combined with the natural "burning out" of susceptible people, created a patchwork quilt of epidemic waves across Korea.

Why Does This Matter?

If you think the whole country is synchronized, you might send all your medical resources to the capital city at the same time, only to find out the crisis is actually hitting a rural town two weeks later.

This research teaches us that local details matter. To stop the next outbreak, we need to look at when the virus arrives in a specific town and how people in that town interact, rather than just treating the whole country as one big block. It's a reminder that in the world of viruses, the devil is in the local details.

Technical Summary

1. Problem Statement

Infectious disease outbreaks typically exhibit large-scale spatial synchrony due to shared environmental forcing (e.g., seasonality) and human mobility. However, the 2024–2025 pertussis (whooping cough) outbreak in South Korea presented a striking exception. Despite high vaccine coverage (91.1% of cases had a known vaccination history), the country experienced a massive resurgence (>50,000 cases) characterized by fine-scale spatial asynchrony.

• The Anomaly: Epidemic trajectories diverged significantly across 252 municipalities. Some regions experienced two distinct waves, while others experienced only one. The decline in spatial correlation with distance was far more pronounced than in previous outbreaks (e.g., measles or US pertussis), dropping below 0.25 within 100 km.
• The Question: What mechanisms drive such fine-scale spatiotemporal heterogeneity when all locations share identical seasonal forcing and high vaccination rates? Is the asynchrony driven by differences in transmission patterns (seasonality) or by initial conditions (introduction timing and susceptibility)?

2. Methodology

The study integrates high-resolution surveillance data with mathematical modeling and Bayesian inference.

• Data Sources:
  • Weekly pertussis case data (252 municipalities) from Jan 2024 to Nov 2025.
  • Population size and vaccine coverage data (specifically DTaP coverage for 3-year-olds in 2015).
• Descriptive Analysis:
  • Center of Gravity: Calculated to quantify the mean timing of epidemic waves for each municipality.
  • Spatial Synchrony: Measured pairwise correlations of logged case counts as a function of distance.
  • Effective Reproduction Number ($R(t)$): Estimated using a generalized additive model (GAM) and the method of Cori et al., to assess transmission dynamics independent of case counts.
• Mathematical Modeling:
  • Model Structure: An extended SEIR (Susceptible-Exposed-Infectious-Removed) model discretized for weekly time steps.
  • Key Assumptions:
    • A shared, time-varying transmission term ($\delta(t)$) across all regions to capture common seasonal forcing (e.g., school terms).
    • Region-specific parameters: Baseline contact levels (via $R_0$), initial infected fraction ($I(0)$), initial susceptible fraction ($S(0)$), and reporting rates ($\rho$).
  • Inference: Bayesian framework using rstan (4 chains, 2000 iterations) to fit the model to 42 municipalities with >400 cases.
  • Validation: The model was tested on the remaining 210 municipalities (<400 cases) and against an alternative hypothesis where $R_0$ was fixed and $S(0)$ varied.

3. Key Results

A. Descriptive Findings

• Asynchrony Drivers: The "center of gravity" (mean timing of cases) correlated strongly with the timing of introduction (first week cases >1/100k), suggesting delayed introductions drive the initial phase of asynchrony.
• Transmission Synchrony: Despite asynchronous case counts, the effective reproduction number ($R(t)$) was highly synchronous across regions (mean correlation $\rho = 0.71$ vs. $\rho = 0.30$ for cases).
• Drivers of $R(t)$: A regression analysis revealed that $R(t)$ fluctuations were primarily driven by:
  1. Susceptible depletion (cumulative cases).
  2. Seasonal forcing (peaks during school terms, troughs during holidays in Aug/Jan).
  • This indicates that the transmission potential was synchronized, but the epidemic outcome was not.

B. Modeling Findings

• Model Fit: The simple SEIR model, assuming a shared transmission term but varying initial conditions and contact levels, achieved a median $R^2$ of 0.86 in predicting epidemic dynamics.
• Mechanism of Asynchrony:
  1. Delayed Introduction: Variations in $I(0)$ (initial infected fraction) determined when an epidemic started in a specific municipality.
  2. Contact Variation ($R_0$): Regional differences in baseline contact levels (estimated $R_0$ ranged from 9.7 to 22.1) determined the magnitude of the first wave.
  3. Susceptible Depletion: High-$R_0$ regions experienced a massive first wave that depleted the susceptible pool, preventing a second wave. Low-$R_0$ regions had less depletion, allowing a second wave to emerge later.
• Alternative Hypothesis Rejection: A model assuming fixed $R_0$ and varying initial susceptibility ($S(0)$) provided similar statistical fits but failed to correlate with historical vaccine coverage data. The estimated susceptibility ranges were unrealistically wide, suggesting that contact variation is a more parsimonious and likely explanation than spatially varying immunity.

C. Simulation Insights

• Simulations confirmed that increasing $I(0)$ leads to earlier epidemics.
• Increasing $R_0$ leads to earlier, larger first waves that "burn out" the susceptible population, effectively suppressing the second wave. Conversely, lower $R_0$ allows the population to sustain a second wave.

4. Key Contributions

1. Decoupling Transmission from Dynamics: The study demonstrates that spatial asynchrony in epidemic trajectories can exist even when the underlying transmission potential ($R(t)$) is perfectly synchronized.
2. Mechanism Identification: It identifies heterogeneity in introduction timing and local contact levels as the primary drivers of fine-scale asynchrony, rather than differences in seasonal forcing or immunity.
3. Role of Susceptible Depletion: It highlights how local variations in transmission intensity ($R_0$) can alter the number of epidemic waves a region experiences via differential susceptible depletion.
4. Methodological Framework: Provides a Bayesian approach to disentangle shared seasonal forcing from local initial conditions in spatiotemporal epidemic data.

5. Significance

• Theoretical Impact: Challenges classical epidemic theory which often assumes spatial synchrony is the default. It shows that in re-emerging diseases with waning immunity, local stochasticity (introduction timing) and heterogeneity (contact rates) can dominate large-scale patterns.
• Public Health Implications:
  • Surveillance: Highlights the need for high-resolution, municipality-level surveillance to detect early introductions, as "hotspots" may emerge unpredictably based on local contact structures.
  • Intervention: Suggests that control strategies must be tailored to local contact patterns. A uniform national strategy may fail if local $R_0$ variations lead to different epidemic phases (e.g., some areas in a second wave while others are in a first).
  • Future Outbreaks: Offers a framework for understanding re-emerging vaccine-preventable diseases where immunity is not static, emphasizing that "synchrony" in transmission does not guarantee "synchrony" in outbreak timing or magnitude.

Limitations: The model is deterministic (ignoring stochasticity in small populations) and lacks age-structure, which is critical for pertussis. However, the authors argue the findings provide a robust quantitative foundation for understanding the observed asynchrony.