Transmission Processes: How FMD Spreads

This vignette focuses on the mechanisms and dynamics of disease transmission—essential for understanding outbreak trajectory.

Overview

Disease transmission in MHASpread occurs through three pathways:

  1. Within-farm: Direct contact, environmental contamination
  2. Spatial: Distance-dependent between neighboring Farms
  3. Trade network: Animal shipments across large distances

Understanding each is critical for predicting outbreak severity.

Within-Farm Transmission: The Danger of Swine

The Transmission Hierarchy

A central finding from FMD research is that swine are super-spreaders:

  Transmission Efficiency Relative to Cattle Interpretation
Swine → anyone ~6.14 animals⁻¹day⁻¹ × 25 Very efficient
Cattle → anyone ~0.24 animals⁻¹day⁻¹ × 1 Baseline
Sheep → anyone ~0.05–0.10 animals⁻¹day⁻¹ × 0.2–0.4 Inefficient

Why Swine Dominate Transmission

Three biological factors:

  1. Viral shedding: Swine secrete 10–100× more virus in respiratory/fecal matter
  2. Housing density: Confinement buildings create high-density conditions
  3. Environmental contamination: Pig waste more extensively contaminates surroundings

Practical implication: A single infected swine farm can spark regional outbreaks if borders crossed.

Example: A Mixed Farm Outbreak (Day-by-Day)

Day 0: 1 infected swine introduced (via animal trade or infection breach).

Day 1–2: Swine latent; farm appears normal.

Day 3–4: Swine infectious; co-located cattle at ~20% cumulative infection risk.

Day 5: ~5–10 cattle become infectious. Spatial kernel activates.

Day 6–10: Neighboring farms at elevated risk. Movement of cattle/swine from mixed farm spreads to distant locations.

Day 15–20 (if undetected): Potentially 20–50 farm outbreak established across region.

Impact: Detection speed determines final outbreak size.

Spatial Transmission: Distance as Protection

How the Kernel Works

Spatially, FMD transmission follows exponential distance decay:

\[\text{Risk} \propto e^{-0.6 \times \text{distance}}\]

Quantitative Effects

Distance (km) Transmission Risk Relative to 0 km Expected Transmission Between Farms
0 km (adjacent) 100% Moderate (~1–5% per day if source infected)
1 km 55% ~0.5–2% per day
3 km 16% ~0.1–0.5% per day
5 km 5% ~0.05–0.1% per day
10 km 0.25% Rare (~1–2 times full outbreak)
20 km 0.0062% Essentially blocked unless animal moved
40 km ~0 Transmission assumed zero

What Drives Spatial Spread?

Primary mechanism: Environmental transmission (airborne when wind direction favorable, fomite).

Why limited range?

  • Virus survives in environment but doesn’t travel far
  • Most contact is local (neighboring farms, shared water)
  • Lack of direct animal contact across farm boundaries

Trade Networks: The Long-Distance Amplifier

Why Movements Matter

Animal trade is the dominant driver of large-scale spread. Consider two routes:

Route 1: Spatial Only (No Trade) 

Day 0: Infected farm A
    ↓ (spatial kernel, slow)
Day 10: Neighboring farms (3–10 km radius)
    ↓ (slow expansion)
Day 30: ~20–50 farm outbreak, confined to region

Route 2: With Trade (Movement) 

Day 0: Infected farm A
    ↓ (trade shipment)
Day 2: Farm B (100 km away) receives infected shipment
    ↓ (spatial + new trade hub)
Day 15: ~100–200 farm outbreak across regions

Impact: Movements can accelerate spread 10–100×.

Movement Patterns in Livestock

Three types of movements:

  1. Short-range (< 30 km): Local trading, restocking, grazing contracts
  2. Medium-range (30–200 km): Regional auctions, fattening operations
  3. Long-range (> 200 km): Interstate trade, international (if allowed)

FMD lesson: One long-range movement can jump infection across geographical barriers.

Example: Movement-Driven Cascade

Day 0: Farm A has 10 infected swine (purchased from endemic region).

Day 5: Farm A sells 50 swine to Farm B (100 km away).

  • ~5–10 of shipment likely infected (Day 5 is days 3–4 infectious for index animal)
  • ~90% transmission probability to recipient farm

Day 10: Farm B now infectious. Sells cattle to Auctions C and D.

Day 12: From Auctions, cattle shipped to Farms E, F, G, H, I (5 distant farms).

Day 15: If undetected, 5–6 farms now entering infectious phase.

Day 30: Without control, network-driven exponential growth possible.

Key: Early detection of Farm A (Day 1–2) stops cascade; late detection (Day 10+) unstoppable.

Detection & Its Critical Role

Detection Timing: The Bottleneck

Silent spread (Days 0–20): Infection spreads undetected because:

  • No visible signs on some farms (subclinical)
  • Farmers unaware of FMD presence
  • Surveillance not yet triggered

Detection Triggers

  1. Clinical observation: Farmer notices lesions, lameness, fever
  2. Active surveillance: Routine veterinary inspections
  3. Traceback: Tracing from detected case identifies prior movements

Sensitivity & Specificity

Diagnostic sensitivity ($s$) affects detection:

  • $s = 1.0$ (perfect): All infected farms detected when sampled
  • $s = 0.95$: 5% of infected farms missed (subclinical, sampling error)
  • $s = 0.80$: 20% missed

Even perfect testing only detects farms in surveillance zone (~1/3 sampled per day).

Phase 1: The Silent Spread (Days 0–20)

Uncontrolled Transmission

Pre-detection, all transmission pathways active:

  • Within-farm: Full rate
  • Spatial: Full kernel
  • Movements: No restrictions

What Happens in 20 Days?

Low-transmission scenario (cattle-only region, limited trade):

  • ~10–20 farms infected
  • Confined to ~30 km radius

High-transmission scenario (mixed cattle-swine, active trade):

  • ~50–200 farms infected
  • Spread across 100+ km (via long-distance movements)

Variability

Stochastic outcomes mean outbreaks vary dramatically:

  • Best case (lucky): ~5 farms, detection same region
  • Worst case (unlucky): ~200 farms across multiple regions

Implication: Policy must be prepared for worst-case.

Phase 2: After Detection (Control Active)

Zone-Based Transmission Reduction

Once control zones established, transmission modified:

Infected Zone (3 km)

  • Depopulation: Removes infected farms immediately
  • Effect: Cuts within-farm + spatial transmission from zone

Buffer Zone (3–7 km)

  • Vaccination: Cattle protected (cannot become infected)
  • Effect: Reduces susceptible population; slows spread

Surveillance Zone (7–15 km)

  • Enhanced detection: More frequent monitoring
  • Effect: New cases detected faster → earlier zone establishment

Movement Standstill Impact

30-day restriction on movements from infected/buffer zones:

  • Blocks network transmission pathway
  • Prevents long-distance jumps
  • Allows local spatial spread to be contained

Transmission Dynamics Under Different Scenarios

Scenario A: Fast Depopulation (5 farms/day) 

Day 20: 15 infected farms detected
Day 21–25: All depopulated (capacity sufficient)
Result: Outbreak contained, ~15 farms final size

Why works: Depopulation removes infection sources before spatial spread accelerates.

Scenario B: Slow Depopulation (1 farm/day) 

Day 20: 15 infected farms detected
Day 21–35: Only 15 depopulated (slow capacity)
Day 25–30: Uncontrolled depopulated farms still infectious
Result: Outbreak expands; ~80–100 farms final size (8× larger!)

Why fails: Logistical bottleneck allows spatial spread to dominate.

Scenario C: Vaccination-Focused 

Day 20: 15 infected farms detected
Day 35: Vaccination begins (15-day lag)
Day 35–45: Cattle herds vaccinated in buffer zone
Result: Spread contained but slower; ~40–60 farms

Trade-off: Preserves herds but slower epidemic control than depopulation.

Key Insights for Policy

1. Early Detection Saves Lives (and Money)

Reducing silent spread by 1 week can reduce final outbreak size by 50–80%.

Implication: Invest in passive + active surveillance.

2. Depopulation Speed Critical for Cattle Regions

In regions with cattle only:

  • Fast depopulation (5 farms/day) similar to vaccination
  • Slow depopulation fails

Implication: Maintain surge capacity for culling infrastructure.

3. Vaccination Crucial for Mixed Farming

In regions with cattle + swine:

  • Vaccination of cattle in buffer zone protects susceptible population
  • Reduces spatial spread risk
  • Complements depopulation

Implication: Emergency vaccine stockpiles essential in mixed regions.

4. Movement Control is Non-Negotiable

30-day standstill alone prevents 30–50% of outbreak expansion (via network).

Implication: Trade restrictions must be immediate and strict.

5. Context Matters

  • Cattle-only regions: Prioritize depopulation
  • Mixed regions: Combine depopulation + vaccination
  • Trade-intensive regions: Emphasize network surveillance
  • Dense farming areas: Spatial transmission dominates

Stochastic Variability: Why Replicates Matter

Same Inputs, Different Outcomes

Running MHASpread 100 times with identical parameters:

  • Best 10%: ~20–30 farms infected (lucky early detection)
  • Median: ~60–80 farms (typical)
  • Worst 10%: ~150–200 farms (unlucky, late detection, network amplification)

Implications

  1. Single-run simulation is misleading: Must report distribution (median ± 95% range)
  2. Probability of success varies: Control strategy X works 80% of time, but 20% of scenarios fail
  3. Planning for worst-case: Policy should account for 90th percentile outcome

Next Steps