FMD Disease Simulation — Ramanagara District

R₀ summary + derived indicators + Equilibrium auto

R₀ (results)

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

Herd immunity threshold

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HIT = 1 − 1/R₀ (if R₀>1)

Peak infected (I_total)

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Day —

Time to peak

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days from Day 0

Duration of infection

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days with I_total > 1

Time endemic starts

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first stable plateau window

Time epidemic starts

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first day I_total > 1

Time epidemic ends

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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)

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R* (Recovered cattle)

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I_C2*

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q_C*

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📊 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

Ramanagara District (built-in)

Historical FMD attack counts 2013–2024 with cattle population data.

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.

FMD Simulation — Ramanagara District

R₀ Results

Preparedness

Herd Immunity Threshold

📊 Year-wise Simulation Validation — District