FMD Disease Simulation — Ramanagara District

R₀ Results

Intervention day: 50

R₀ ⓘ

Reproduction number (R₀): average secondary cases from a single case in a fully susceptible population.

Herd Immunity Threshold ⓘ

—

The herd immunity threshold refers to the critical fraction of a population that must acquire immunity in order to interrupt disease transmission and protect susceptible individuals indirectly

Day

Preparedness

I_B I_P I_S R_C I_C2 I_C1 E_C S_C Day 0

Results

Susceptible Cattle (S_C)

1,092

Exposed Cattle (E_C)

179

Asymptomatic Infected Cattle (I_C1)

1,233

Symptomatic Infected Cattle (I_C2)

2,120

Recovered Cattle (R_C)

15,899

Infected Buffalo (I_B)

Infected Pig (I_P)

Infected Sheep (I_S)

4,584

R₀ summary + derived indicators + Equilibrium auto

R₀ (results)

—

from model equations (β, γ, μ, D, φ, F_env…)

Herd immunity threshold

—

HIT = 1 − 1/R₀ (if R₀>1)

Peak infected (I_total)

—

Day —

Time to peak

—

days from Day 0

Duration of infection

—

days with I_total > 1

Time endemic starts

—

first stable plateau window

Time epidemic starts

—

first day I_total > 1

Time epidemic ends

—

last day I_total > 1

I_total curve (scaled)

Markers: Peak (red), Endemic start (green), Epidemic start/end (blue/gray)

What-if: vary initial Symptomatic Infected Cattle (I_C20) and compare curves

Endemic equilibrium point (from equations)

S* (Susceptible cattle)

—

R* (Recovered cattle)

—

I_C2*

—

q_C*

—

📊 Year-wise Simulation Validation — District

How Hindcast Validation Works (RK4 Method):
For each historical year: (1) Year-specific cattle population is used as N. (2) Observed attacks seed I_C2 as the starting condition. (3) A year-specific β_C is back-calculated from observed incidence. (4) The full ODE system is solved using Runge-Kutta 4th order (RK4) for 365 days. (5) Predicted = Average Monthly I_C2 from the RK4 run. (6) Rule: Reported=Yes & model fires (pred > 0) → YES (TP) | Not Reported & model quiet → YES (TN) | Not Reported & model fires → NO (FP) | Reported & model silent → NO (FN).

📂 District Historical Data

Karnataka District (built-in — 20th Livestock Census 2019)

Select a district to validate. Cattle population from 2019 Census; FMD attack data 2019–2024.

Upload Another District CSV

Required columns: Year, Observed_Attacks, Cattle_Population. Optional: District

District Name:

Year From

Year To

Exclude Zero-Attack Years

Run validation to see hindcast validation against historical outbreaks.

📊 Scenario Comparison — Control Measures Summary

SCENARIO	VACC RATE (%)	ISOLATION (%)	PEAK R₀	FINAL R₀	PEAK INFECTED	PEAK DAY	FINAL INFECTED	ATTACK RATE	EFFICACY VS NO CONTROL
Run simulation with different control measures to see scenario comparison

How to use: Run simulation with different vaccination rates (α_C) and isolation rates (φ) to compare scenarios. Each scenario is automatically categorized and tracked. The table shows effectiveness metrics and calculates efficacy compared to the "No Control" baseline.

🔬 With vs Without Control Measures — Comparison

Side-by-side I_total curves showing impact of movement restriction, biosecurity, surveillance, culling & quarantine

No Control Peak

—

With Control Peak

—

Peak Reduction

—

% fewer infected

No Ctrl Final I

—

end-of-sim

With Ctrl Final I

—

end-of-sim

Duration Saved

—

fewer outbreak days

Metric	Without Control measures	With Control measures	Change
Run simulation to see control measures comparison

📐 View Control Measure Equations

Force of Infection (Cattle):
λ_C = β_C · (1 - m_restrict) · (I_C1 + I_C2 + f_env·F·(1-b_biosec)·I_B2 + f_env·F·(1-b_biosec)·I_P + f_env·F·(1-b_biosec)·I_S) / N

dI_C2/dt = σ₁·I_C1 + K₂·Q_C − [γ₃ + μ_C + φ_base·(1+λ_surv)·(1+θ_outbreak) + D_C + cull_rate]·I_C2
dQ_C/dt = Δ_QC·(1−s_efficacy) − (K₁ + K₂ + μ_C + φ_quarantine)·Q_C
dS_C/dt = Δ_C + α_C3·ε_vac·V_C1 + χ₂·V_C2 + K₁·Q_C·(1−s_efficacy) + ∅·R_C − [α_C + μ_C]·S_C − λ_C·S_C

🎛️ Parameter Zero-Impact Analysis

Shows what happens when each selected control parameter is individually set to zero — all other params stay at current values

Baseline (all controls ON): Peak = — Final I = —

No Control (all zero): Peak = — Final I = —

Parameter Set to Zero	Peak Infected Cases	Peak Day infected cases	Final Infected at end day of simulation	Outbreak Days	Impact vs With-Control	Risk Verdict
Select parameters above and click "Run Zero-Impact Analysis"

How to read: Each row shows what happens if that one control parameter is zeroed while all other controls stay at their current set values. "Impact vs With-Control" = extra infections caused by removing that parameter. Higher impact = that control is more critical.

📊 3-Scenario Control Measure Comparison

Uniform distribution Monte Carlo · Baseline + Minimal / Moderate / Maximum · Exportable charts & tables

N =

Baseline

No Control (all = 0)

Minimal

U(0.05, 0.20)

Moderate

U(0.30, 0.55)

Maximum

U(0.80, 0.95)

Metric	Baseline	Minimal (mean±SD)	Moderate (mean±SD)	Maximum (mean±SD)
Click ▶ Run to generate Monte Carlo results

📋 Uniform Distribution Parameter Ranges

Parameter	ODE Effect	Baseline	Minimal	Moderate	Maximum

💉 VACCINATION IMPACT ANALYSIS

Vaccination Coverage

—%

R₀ After Vaccination

—

Current Re

—

Required Control %

—%

⚠️ Run simulation to see analysis

📊 How Much Vaccination Is Needed to Control FMD?

X-axis = Vaccination Coverage %, Y-axis = Effective Reproduction Re. Push the blue dot below the green dashed line to eliminate FMD.

Run the simulation to see the analysis here.

📌 How to read this graph:
🔵 Blue curve: Re for YOUR simulation R₀ as vaccination % rises
🔴 Red curve: Re if a high-risk outbreak strain (R₀=4.5) hits
🟢 Green dashed line: Control threshold — anything below this means FMD will die out
🔵 Filled dot: YOUR current vaccination coverage and Re
Dashed vertical lines show the minimum vaccination % needed to cross the threshold.

FMD Simulation — Ramanagara District

📋 Uploaded Data Preview

📊 Batch Simulation Summary