PPR Epidemic Simulation

Model Outputs & Epidemic Indicators

R₀

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Herd Immunity

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S_X

E_X

I_X

R_X

V_X

B_X

I_Y

I_Z

I_total (Baseline)

▲ Peak

◆ Endemic Start

● Epidemic Start

■ Epidemic End

What-if: Compare curves with different I_P:

Equilibrium Curve — All Phases (I_total)

I_X + I_Y + I_Z over time with phase markers: Peak, Endemic, Epidemic Start/End

Endemic Equilibrium Point (Analytical from Model Equations)

S_X*

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V_X*

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E_X*

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I_X*

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R_X*

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B_X*

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S_Y*

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I_Y*

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S_Z*

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I_Z*

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Peak I_total

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Day —

Time to Peak

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Outbreak Duration

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Endemic Start

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Epidemic Start

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Epidemic End

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📊 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 (ω) and isolation rates (θ₂) to compare scenarios. Each scenario is automatically categorized and tracked. The table shows effectiveness metrics and calculates efficacy compared to the "No Control" baseline.

📊 Year-wise Simulation Validation — District

How Hindcast Validation Works (RK4 Method):
For each historical year: (1) Year-specific small ruminant (Goat+Sheep) population is used as N_X. (2) The previous year's observed attacks seed I_X (the target year is never used as input). (3) β_X is fitted on earlier years only (dashboard β_X if there are none). (4) The full SEIVRBR ODE system is solved using Runge-Kutta 4th order (RK4) for 365 days with adaptive sub-steps. (5) Predicted = annual cumulative incidence from the RK4 run — same units as observed attacks. The first year of a series has no seed and is not scored. (6) Rule: Reported=Yes & model fires (pred ≥ max(5, 0.005% × N_X)) → YES (TP) | Not Reported & model quiet → YES (TN) | Not Reported & model fires → NO (FP) | Reported & model silent → NO (FN).

🎚️ Validation Level

District State

📂 District Historical Data

Jharkhand District (built-in — 2021 Livestock Census + PPR Attack Data)

Select a district to validate. Small ruminant (Goat+Sheep) population from 2021 Census; PPR attack data 2020–2025.

Upload Another District CSV

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

District Name:

Year From

Year To

Exclude Zero-Attack Years

📋 Detailed Year-wise Validation Table — District

Run validation to see results against historical PPR outbreaks.

⑤ Hindcast Validation: TP/TN/FP/FN breakdown; Accuracy, Sensitivity, Specificity with 95% Clopper-Pearson CI; Binomial log-likelihood AIC; McFadden R²; LR test.

🛡️ With Control — Intervention Scenario Simulator

No Control Peak

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With Control Peak

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Peak Reduction

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% fewer infected

No Ctrl Final I_total

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end-of-sim

With Ctrl Final I_total

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end-of-sim

Duration Saved

—

fewer outbreak days

Ω_MR — Movement Restriction

0 = none, 1 = full lockdown

ϑ_FA — Farmer Awareness

0 = unaware, 1 = fully aware

φ_Ve — Vaccine Efficacy

Reduces waning (0–1)

δ_OM — Outbreak Mgmt

Extra removal from I_X

η_sr — Surveillance

Detection & isolation

C_X — Culling Rate

Culling of infected

ρ_QR — Quarantine

Quarantine rate for B_X

μ1 — Biosecurity

Reduces Y/Z exposure

Show on chart: I_total — With Control I_total — Without Control

📊 With Control vs Without Control — Comparison Summary

Without Control Measures

Peak I_total

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Peak S_X

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Peak E_X

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Peak R_X

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Peak V_X

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Peak B_X

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Peak I_Y

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Peak I_Z

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Endemic Start

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Equilibrium I_total*

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With Control Measures

Peak I_total

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Peak S_X

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Peak E_X

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Peak R_X

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Peak V_X

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Peak B_X

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Peak I_Y

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Peak I_Z

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Endemic Start

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Equilibrium I_total*

—

*Equilibrium I_X = mean of the last 7 simulated days (same convergence method as the Equilibrium Curve panel above). Endemic Start uses the same 14-day flatness test.

🎲 N-Scenario Monte Carlo Comparison

Uniform-distribution sampling across Minimal / Moderate / Maximum control intensity vs. No-Control baseline

Run N: 100 draws per scenario (Minimal / Moderate / Maximum, uniformly re-sampled each run). Baseline values (I_X, S_X, E_X, R_X, V_X, B_X, I_Y, I_Z) are fetched live from the Without Control Measures card in the With vs Without Control comparison above — refreshed automatically every time you click Run.

BASELINE

No Control (all λ=0)

MINIMAL

Low-intensity control (U-sampled)

MODERATE

Mid-intensity control (U-sampled)

MAXIMUM

High-intensity control (U-sampled)

Metric	Baseline	Minimal (mean±SD)	Moderate (mean±SD)	Maximum (mean±SD)
Run the N-Scenario Monte Carlo to see results.

Primary Hosts (WITH CONTROL MEASURES)

\(\displaystyle\frac{dS_X}{dt} = b_X - \left(\beta_X\frac{I_X}{N_X}S_X * f_{env}\right)(1-\Omega_{MR})(1-\vartheta_{FA}) - \omega S_X + \alpha_1 B_X - \mu_X S_X + \epsilon V_X(1-\varphi_{Ve})\)

\(\displaystyle\frac{dE_X}{dt} = \left(\beta_X\frac{I_X}{N_X}S_X * f_{env}\right)(1-\Omega_{MR})(1-\vartheta_{FA}) - \sigma E_X + \alpha_2 B_X - \mu_X E_X\)

\(\displaystyle\frac{dI_X}{dt} = \sigma E_X - (\theta_1\gamma_1 I_X + \theta_2\gamma_2 I_X) + \alpha_3 B_X - (\mu_X+\delta_X)I_X - C_X I_X - (1+\delta_{OM})(1+\eta\_sr)\,I_X\)

\(\displaystyle\frac{dR_X}{dt} = \theta_1\gamma_1 I_X + \theta_2\gamma_2 I_X - \mu_X R_X + \lambda V_X(1+\varphi_{Ve})\)

\(\displaystyle\frac{dV_X}{dt} = \omega S_X - \mu_X V_X - \lambda V_X(1+\varphi_{Ve}) - \epsilon V_X(1-\varphi_{Ve})\)

\(\displaystyle\frac{dB_X}{dt} = \kappa_X - (\alpha_1+\alpha_2+\alpha_3)B_X\left(1-\rho_{QR}\right) + \mu_X B_X\)

Wild Small Ruminants hosts

\(\displaystyle\frac{dS_Y}{dt} = b_Y - \beta_{XY}\frac{I_X}{N_X}S_Y(1-\mu_1)(1-\Omega_{MR})(1-\vartheta_{FA}) * f_{env} - \mu_Y S_Y\)

\(\displaystyle\frac{dI_Y}{dt} = \beta_{XY}\frac{I_X}{N_X}S_Y * f_{env} - \mu_Y I_Y\)

Atypical hosts

\(\displaystyle\frac{dS_Z}{dt} = b_Z - \beta_{XZ}\frac{I_X}{N_X}S_Z(1-\mu_1)(1-\Omega_{MR})(1-\vartheta_{FA}) * f_{env} - \mu_Z S_Z\)

\(\displaystyle\frac{dI_Z}{dt} = \beta_{XZ}\frac{I_X}{N_X}S_Z * f_{env} - \mu_Z I_Z\)

\(\Omega_{MR}\) = Movement restriction

\(\vartheta_{FA}\) = Farmer Awareness

\(\varphi_{Ve}\) = vaccine efficacy

\(\delta_{OM}\) = outbreak management

\(\eta\_sr\) = sero surveillance

\(\rho_{QR}\) = Quarantine

\(C_X\) = culling

\(\mu_1\) = Biosecurity measures