Simulation Outputs: Interpreting Results

This vignette explains how to understand, interpret, and visualize MHASpread simulation outputs—critical for evidence-based decision-making.

Overview

MHASpread produces rich output data at multiple scales:

  • Farm-level time series: Daily compartment counts (S, E, I, R, V) per species
  • Epidemic summary metrics: Outbreak size, duration, peak prevalence
  • Spatial patterns: Which farms attacked, where outbreak concentrated
  • Control action records: Farms depopulated, animals vaccinated, movements blocked
  • Stochastic ensemble: Results across 100–1000 replicate simulations

Understanding the Output Structure

Level 1: Single Replicate Time Series

Each simulation run generates daily output:

Day | Farm_001_I_bov | Farm_001_I_swi | Farm_002_I_bov | ... | Total_I_all
----|----------------|---|---|----|----|
 1  |        0       |  0 |  0  | ... |   0
 2  |        1       |  2 |  0  | ... |   3
 3  |        3       |  5 |  1  | ... |  9
 4  |        6       | 12 |  3  | ... | 21
 5  |       12       | 25 |  8  | ... | 45
...
20  |      250       | 450| 180 | ... |  880
21  |      180       | 380| 140 | ... |  700 (control begins)
...
50  |        5       |  2 |  0  | ... |  7
60  |        0       |  0 |  0  | ... |  0 (outbreak over)

Level 2: Key Metrics Per Replicate

For each simulation run, extract:

Metric Definition Example
Final Size (farms) Total unique farms attacked 47
Final Size (animals) Total animals infected 8,350
Peak Prevalence Maximum infectious animals at any time 1,200
Outbreak Duration Days from index to last recovery 68
Attack Rate Farms attacked / total farms 47/500 = 9.4%
Farms Depopulated Number culled 23
Animals Vaccinated Total vaccinated 12,500

Level 3: Ensemble Statistics

Run 100 replicates of same scenario → distribution of outcomes:

Metric Mean Median 5th % ile 95th %ile
Final Size (farms) 58 52 15 142
Peak Prevalence 950 880 200 2,100
Duration (days) 71 68 35 120

Interpretation: Median outcome is 52 farms; but 5% of scenarios will see <15 farms (best case), and 5% will see >142 farms (worst case, unlucky transmission).

Epidemic Curves: The Visual Summary

What is an Epidemic Curve?

Plot of total infectious animals vs. time:

Infectious Animals
      |
2,500 |        ╱╲
      |       ╱  ╲
2,000 |      ╱    ╲
      |     ╱      ╲
1,500 |    ╱        ╲
      |   ╱          ╲
1,000 |  ╱            ╲
      | ╱              ╲___
  500 |╱                   ╲__
      |                       ╲__
    0 |_________________________╲_____
      0    10    20    30    40    50  (Days)
            Silent    | Control Active
            Spread    |

Interpreting the Curve

  1. Days 0–20: Exponential rise (silent spread, no control)
    • Shows how fast infection spreads unimpeded
    • Steeper curve = faster transmission (swine-heavy regions)
  2. Days 20–25: Detection & zone establishment (inflection point)
    • Curve still rising (detection lags)
    • But growth rate slowing (early control actions)
  3. Days 25–50: Plateau & decline (control effective)
    • Peak prevalence marks turning point
    • Decline indicates control > new transmission
  4. Days 50+: Tail-out (resolution)
    • Remaining infectious animals recover naturally
    • Outbreak ends when I = 0

Multi-Strategy Comparison

Plot epidemic curves for different scenarios:

Infectious Animals
      |
2,500 |   Uncontrolled ════════╗
      |                        ║
2,000 |  Conservative ─────╗   ║
      |                    │   ║
1,500 | Moderate ──╗       │   ║
      |            │       │   ║
1,000 |Aggressive─╖        │   ║
      |           ║        │   ║
  500 |           ║        │   ║
      |           ║        │   ║
    0 |___________|________|___|_____
      0    10    20    30    40    50
            
Conservative: Peak ≈1500, Duration ≈45 days
Moderate:    Peak ≈800,  Duration ≈35 days
Aggressive:  Peak ≈300,  Duration ≈25 days

Finding: Aggressive strategy shortens outbreak by ~40%, but costs 2× more. Value judgement for policymakers.

Spatial Visualization

Farm Attack Map

Plot farms on geographic map; color by infection status:

Geographic Map (latitude vs. longitude)

   North
    ↑
    │ ◉ ◉ ■ ◉                 ◉ Uninfected farm
    │ ◉ ■ ■ ◉ ◉              ■ Infected farm
    │ ◉ ◉ ■ ◉ ◉              ★ Index farm
    │ ★ ◉ ■ ◉               
    │ ◉ ◉ ■ ◉ ◉
    └─────────────→ East
    
Infected zone (3 km): Concentrated cluster around index
Buffer zone (7 km):   Secondary cluster
Surveillance zone (15 km): Scattered cases
Beyond 15 km: Few cases (spatial kernel decay)

Temporal Progression

Show infection spread over time as animation frames:

Day 0     Day 10     Day 20     Day 30
(Index)   (Silent)   (Detection)(Control)

  ◉        ◉ ■       ◉ ■ ■     ◉ ◉
  ◉ ★      ◉ ★ ■     ◉ ★ ■■    ◉ ◉
  ◉        ◉ ◉ ■     ◉ ◉ ■■    ◉ ◉
          
→ Visualization shows spatial wave moving outward
→ Control zones halt spatial progression

Compartment Breakdowns

By-Species Infection Dynamics

Track I compartment by species over time:

Infectious Animals by Species

     Cattle (blue) ───
     Swine (red) ─ ─ ─
     Sheep (green) ─·─

     │
 1500│            ╱──
     │       ╱───╱
 1000│  ╱───╱─
     │╱────╱┐
  500│     ╱ ╲
     │    ╱   ╲
     │___╱_____╲___
     0  10  20  30  40  (Days)

Interpretation:
- Swine peak first (days 8–15)
- Cattle peak later (days 10–20) after swine transmission
- Sheep remain low throughout (inefficient transmitters)

Vaccination Effectiveness

Track V compartment growth in buffer zone:

Vaccinated Cattle in Buffer Zone

     │
1000│              ╱╱╱╱╱╱╱
     │           ╱╱╱
  800│         ╱╱╱       (100% coverage achieved)
     │       ╱╱╱
  600│     ╱╱╱
     │   ╱╱╱
  400│ ╱╱╱
     │╱╱╱              (Vaccination starts: day 35)
  200│
     │
    0│_____________________
     30   35    40   45   50  (Days)

Interpretation:
- Lag period (days 30–35): No vaccinations
- Rapid uptake (days 35–45): Daily capacity determines slope
- Plateau (days 45+): All eligible cattle vaccinated
- Effect: Susceptible population in buffer zone reduced 80–95%

Comparative Analysis: Scenario Comparison Tables

Standard Comparison Across Strategies

Metric Baseline Scenario A Scenario B Scenario C
Final farms 120 65 38 18
Peak I (animals) 2,100 1,200 650 280
Duration (days) 95 68 45 32
Attack rate 24% 13% 7.6% 3.6%
Cost (€k) 0 350 600 1,200
Cost per farm prevented — €4,400 €7,700 €17,000

Reading: Scenario B offers best cost-effectiveness; Scenario C has diminishing returns.

Stochastic Uncertainty Representation

Ensemble Epidemic Curves (with Percentiles)

Plot single mean curve + shaded confidence band:

Infectious Animals (Ensemble of 100 replicates)

     │              95th percentile ········
     │                  ╱╲·················
     │                 ╱  ╲················
 1500│                ╱    ╲·······════════
     │               ╱      ╲····╱ median
 1000│              ╱        ╲·╱╱╱════════
     │             ╱          ╱╱ shaded band
  500│            ╱          ╱╱  (5th-95th %ile)
     │          ╱╱╱         ╱
     │       ╱╱╱          ╱
    0│___╱╱╱___________╱_________
     0    10    20    30    40    50

Interpretation:
- Central black line: median outcome across replicates
- Shaded region: range of outcomes (uncertainty)
- Wide shading = high uncertainty (stochasticity)
- Narrow shading = consistent outcomes

Box Plots: Distribution of Key Metrics

Visualize full distribution of outcomes:

Final Size (Farms)

Scenario A                  Scenario B
  │                           │
  │ •··· outliers              │ •
  │ ╭─╮ upper quartile         │ ╭─╮
  │ │█│ median                 │ │███│
  │ ╰─╯ lower quartile         │ ╰─╯
  │ "│" whiskers               │
  │ :                          │ :
    0        100               0        50
    
Scenario A: Median=65, Range=15–180 (high variability)
Scenario B: Median=38, Range=10–95  (lower variability)

→ Scenario B is both smaller AND more predictable

Cost-Effectiveness Outputs

Cost Curves (Incremental Analysis)

Plot total cost vs. outbreak containment:

Total Cost (€M)

1.5 │              Scenario C
    │             ╱
1.0 │            ╱  Scenario B
    │           ╱  ╱
0.5 │          ╱  ╱  Scenario A
    │         ╱  ╱
0.0 │────────╱──╱────────────
    0    50   100   150 (Farms Prevented)
    
Cost-effectiveness frontier:
- Below line: dominated (worse outcomes, higher cost)
- On line: efficient (optimal for given budget)
- Scenario B typically on frontier

Cost-Benefit Summary 

COST-BENEFIT ANALYSIS

                    Scenario: Moderate
─────────────────────────────────────────
Control Cost:              €600,000
─────────────────────────────────────────
Uncontrolled Outbreak:     200 farms infected
Controlled Outbreak:        60 farms infected
Farms Prevented:           140 farms
─────────────────────────────────────────
Cost per Farm Prevented:   €4,286
Avg. Farm Value Loss:      €50,000
Benefit per Farm:          €50,000
Net Benefit:               €7,000,000
─────────────────────────────────────────
Benefit-to-Cost Ratio:     11.7:1
─────────────────────────────────────────

Interpretation: Every €1 spent on control 
saves €11.70 in prevented losses.
Very favorable return on investment.

Sensitivity Analysis Visualization

Tornado Diagram: Parameter Sensitivity

Show which parameters most affect outcome:

OUTBREAK SIZE SENSITIVITY TO PARAMETERS

Parameter                Impact on Final Size
─────────────────────────────────────────────

Depopulation speed       ████████████████ (large effect)
Detection lag            ███████████████  (large effect)
Vaccination efficacy     ████████         (moderate effect)
Movement standstill      ███████          (moderate effect)
Diagnostic sensitivity   ███              (small effect)
Kernel decay (α)         ██               (small effect)

→ Depopulation speed & detection lag drive outcomes
→ Focus preparedness investment on these

Sensitivity Table: How Outcomes Change

Parameter Low Base High Range
Depop capacity (farms/day) 1 3 5 120→60 farms
Detection lag (days) 1 3 7 35→95 farms
Vax efficacy (%) 80 95 99 55→40 farms
Standstill duration (days) 14 30 ∞ 90→50 farms

Finding: Depopulation capacity most sensitive; invest there first.

Output File Formats

Common Export Formats

MHASpread typically outputs:

  1. CSV files: Time series, summary metrics (easy to read in Excel)
  2. RDS files: Complete R objects (for further analysis)
  3. JSON files: Summary statistics (for web visualization)
  4. Figures: Scenario plots (PNG, PDF for reports)

Working with Output in R 

# Load results from single replicate
results <- readRDS("mhaspread_outbreak_rep1.rds")

# Extract time series
I_timeseries <- results$compartments$I_all

# Plot epidemic curve
plot(I_timeseries, main="Epidemic Curve")

# Extract summary metrics
final_size <- nrow(unique(results$infected_farms))
peak_I <- max(results$compartments$I_all)
duration <- which(results$compartments$I_all == 0)[1]

Communication to Stakeholders

For Government Ministers (Executive Summary)

One-page output:

MHASPREAD SCENARIO ANALYSIS: FMD PREPAREDNESS

Scenario:              Moderate Response
_________________________________________
Estimated Outbreak:    60 ± 25 farms infected
Peak Cases:            800 infectious animals
Duration:              35–45 days
Cost of Response:      €600,000
_________________________________________
OUTCOME: Containment likely; acceptable risk.

RECOMMENDATION: Adopt Moderate scenario.
Budget allocation: €600k for surge capacity.

For Farming Community (Transparency)

Clear visuals:

  • “Our response plan will detect 95% of infected farms within 3 days”
  • “Vaccination zones will protect 80% of cattle in buffer areas”
  • “Expected quarantine period: 30 days”

Common Pitfalls in Interpretation

Pitfall 1: “Single Replicate = Reality”

Wrong: Running MHASpread once and using that result.
Right: Run 100+ replicates; report median & 95% range.

Pitfall 2: “Median = Expected”

Wrong: Assuming median outcome will occur.
Right: Prepare for worst-case (95th percentile); median is optimistic.

Pitfall 3: “Model = Perfect Prediction”

Wrong: Believing model output is exactly what will happen.
Right: Model is strategic guide; real outbreak has surprises (hidden infection, variant transmission, human behavior).

Next Steps