JE Disease Simulation — Udupi District

Parameters

Click input name or ? to read its meaning

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⏱️ Simulation horizon (days)

Total number of days the JE dynamics will be simulated. Changes here re-run all curves & equilibrium.

Initial human compartments

Sₕ, I_Aₕ, Iₕ, Rₕ, V₁ₕ, V₂ₕ at t = 0.

Nₕ (Total number of human population)

Sₕ (Susceptible population of humans) Auto Computed

I_Aₕ (Asymptomatic Infectious population)

Iₕ (Infectious population of humans)

Rₕ (Recovered population of humans)

V₁ₕ (Vaccinated population of humans with dose series I)

V₂ₕ (Vaccinated population of humans with dose series II)

Initial pig compartments

Susceptible, infected, and bio-secured pigs at t = 0.

Nₚ (Total number of pigs population)

Sₚ (Susceptible population of Pigs) Auto Computed

Iₚ (Infectious population of pigs)

Bₚ (Bio-secured population of pigs)

Initial wading bird compartments

Wading birds as JEV reservoirs.

N_w (Total number of wading bird population) S_w (Susceptible population of wadingbird) Auto Computed I_w (Infectious population of wadingbird) B_w (Physical or Mechanical Barrier controlled population of wading birds)

Initial mosquito compartments

Vector population at t = 0.

N_m (Total number of mosquito population) S_m (Susceptible population of mosquitoes) Auto Computed I_m (Infectious population of mosquito)

Birth and natural death rates for each host and vector; logistic growth for birds and mosquitoes.

bₕ (Recruitment rate of human) bₚ (Recruitment rate of Pigs) b_w (Recruitment rate of wading birds) b_m (Recruitment rate of mosquitoes) μₕ (Natural death rate of humans) μₚ (Natural death rate of pigs) μ_w (Natural death rate of wading bird) μ_m (Natural death rate of mosquitoes) r_w (Intrinsic growth rate (difference of birth (b_m))) K_w (carrying capacity of wading bird population) r_m (Intrinsic growth rate (difference of birth (b_m))) K_m carrying capacity of mosquito population

JE Contact Rate – Village vs District (by species)

Use contact modifier

Level

Number of humans/animals in close JE-relevant contact

Total humans/animals in the village at risk

Village contact rate (close-contact / total at risk)

Current: 0.200

Transmission parameters

β terms are per-bite transmission probabilities; B and C partition mosquito bites between birds and pigs.

β_mp Disease transmission rate of mosquitoes to pigs(mosq → pig) β_pm Disease transmission rate of pigs to mosquitoes(pig → mosq) β_mh Disease transmission rate of mosquitoes to humans(mosq → human)

Human β seasonality modifier

β(t) = β₀/2 × [1 + cos(2π/T × (t − φ₀))]. Peak is fixed at φ₀ = 8 (August).

t (month number, 1–12) β₀ seasonal amplitude T season period φ₀ peak month β(t) seasonal output Effective β_mh = β_mh + β(t)

β_hm Disease transmission rate of humans to mosquitoes(human → mosq) β_mw Disease transmission rate of mosquitoes to wading birds(mosq → bird) β_wm Disease transmission rate of wading birds to mosquitoes(bird → mosq) B Average biting rate on susceptible wading birds by infected mosquitoes per day (bites on birds) C Average biting rate on susceptible pigs by infected mosquitoes per day(bites on pigs) φ (I_A → Iₕ)Disease transmission rate of asymptomatic to infectious humans σ Rate at diseased humans dies (JE death rate humans)

Vaccination & treatment

α, ρ, τ, ε terms control vaccination, waning, treatment and biosecurity.

α₁ The rate at which humans are vaccinated τ_1(vaccinated fraction) u₁ The rate at which humans are vaccinated with dose series I(dose I fraction) ρ₁(The rate at which vaccinated humans becomes susceptible humans with dose series I (V₁ → Sₕ)) ρ₂ (The rate at which vaccinated humans becomes susceptible humans with dose series II vaccine (V₂ → Sₕ)) τ₁ (The rate at which infected human becomes recovered with medicine) τ₂ (The rate at which infected human becomes recovered without medicine) η_h δ (Effectiveness of medicine on the human population) α₂ (The rate at which infected pigs go to the susceptible class of pigs by medicine)(treatment pigs → Sₚ) εₚ (The rate at which susceptible pigs enter the biosecured compartment)(bio-secure pigs) ε_w (The rate at which susceptible wading birds enter the Barrier compartment(barrier birds))

Temperature & biting rate

T (°C) T₀ (max biting temp) b(T)

Current implementation: b(T) = b₀ · exp(−0.1 · (T − T₀)²). biting rate of a vector in term of temperature

R₀ Results

Intervention day: 50

R₀

Herd Immunity Threshold

Peak infectious day

★ b(T)

temperature-driven biting rate

Preparedness

JE risk message will appear after simulation.

Herd Immunity Threshold

Minimum herd immunity required based on current R₀.

Humans Pigs Birds Mosquitoes

Sₕ (susceptible humans)

Iₕ (symptomatic humans)

I_Aₕ (asymptomatic)

Rₕ (recovered humans)

V₁ₕ (dose I)

V₂ₕ (dose II)

Sₚ (susceptible pigs)

Iₚ (infected pigs)

Bₚ (bio-secure pigs)

S_w (susceptible birds)

I_w (infected birds)

B_w (barrier birds)

S_m (susceptible mosq.)

I_m (infected mosq.)

Iₕ + I_Aₕ + I_m

I_total = Iₕ + I_Aₕ + Iₚ + I_w + I_m

R₀ summary + derived indicators + Equilibrium

R₀ (input)

Computed from parameters: -

Herd immunity threshold (HIT)

HIT = 1 − 1/R₀ (if R₀ > 1)

Peak infected (I_total)

Time to peak

days from Day 0

Duration of infection

days with I_total > 1

Time epidemic starts

first day I_total > 1

Time epidemic ends

last day I_total > 1

Time endemic starts

first stable plateau window

🔬 Endemic Equilibrium Point — JE Model

Fixed-point solution from ODE equations. Use separate inputs below to tune without changing main simulation.

Use separate endemic parameters

📐 Endemic Equilibrium Input Parameters (independent from main simulation panel)

β_mh (mosq→human) β_mp (mosq→pig) β_mw (mosq→bird) β_pm (pig→mosq) β_wm (bird→mosq) b(T) biting rate B (biting on birds) C (biting on pigs) μ_h (human death) μ_p (pig death) μ_w (bird death) μ_m (mosq death) φ (asymp→symp) σ (JE death rate) τ₁ (recovery w/ med) τ₂ (recovery w/o med) δ (med effectiveness) η_h (viremic days) α₁ (vaccination rate) u₁ (dose I fraction) ρ₁ (waning V1) ρ₂ (waning V2) α₂ (pig treatment) εₚ (pig biosecurity) ε_w (bird barrier) N_h (human pop) N_p (pig pop) b_h (human recruit) b_p (pig recruit) b_w / r_w / K_w

b_m / r_m / K_m

ℹ️ Threshold Alerts & Sensitivity

The calculated Endemic Equilibrium Points (E*) below serve as the outbreak thresholds. If the simulation's peak infectious cases exceed these equilibrium levels, an alert is triggered. The parameter with the most influence on the equilibrium state is marked with a ★.

📊 Endemic Equilibrium Values (E* — steady-state infectious counts):

S*ₕ (Susceptible humans)

—

I*_Aₕ (Asymptomatic)

—

I*ₕ (Infectious humans)

—

R*ₕ (Recovered)

—

V1*ₕ (Vaccinated dose I)

—

V2*ₕ (Vaccinated dose II)

—

I*ₚ (Infectious pigs)

—

I*_m (Infectious mosquitoes)

—

S*_w (Susceptible birds)

—

I*_w (Infectious birds)

—

Human infectious Iₕ + I_Aₕ curve

Solid coloured lines per scenario · Coloured dot marks each curve's peak day

🧪 Human endemic-equation tuners — R*ₕ = (τ₁·η_h + τ₂·δ) · I*ₕ / μ_h

edits update Iₕ curve & endemic tiles instantly

δ — Effectiveness of medicine (human) 0 = no efficacy, 1 = full efficacy τ₂ — Recovery rate without medicine ↑τ₂ → faster spontaneous recovery → R₀ ↓ τ₁ — Recovery rate with medicine Treated-arm clearance rate μ_h — Natural human mortality Sets denominator of R*ₕ

What-if: vary initial Iₕ₀ (I_h) and compare curves

🛡️ JE Control Measure Parameters

Adjust controls below then click ▶ Run Control Comparison — matched to JE ODE differential equations

💉 Human Vaccination

Vaccination rate α₁ 0.0001

Dose-I fraction u₁ 0.5

Higher α₁ → more V₁ₕ/V₂ₕ → fewer susceptibles → lower Rₑ

🦟 Vector Control

Fogging: +Δμ_m 0.000

Larviciding: K_m reduce % 0%

Fogging ↑μ_m; larviciding ↓K_m → fewer mosquitoes → less transmission

🐖 Pig Biosecurity

Biosecurity rate εₚ 0.0083

Pig treatment α₂ 0.200

εₚ → screened pens; α₂ → faster pig recovery. Both cut pig-mosquito cycle

🐦 Bird Barriers

Barrier rate ε_w 0.005

Higher ε_w → more birds behind barriers → dampened bird-mosquito reservoir cycle

💊 Human Treatment

Treatment rate τ₁ 0.067

Medicine effectiveness δ 0.667

Higher τ₁ and δ → faster Iₕ → Rₕ transition → shorter human infectious period

🛏️ Personal Protection

Biting reduction % 0%

Bed nets / repellents reduce effective b(T): b_ctrl = b₀ × (1 − red%)

📡 Surveillance & Isolation

Surveillance factor λ_surv 0.000

Surveillance enhances φ (I_Ah→Iₕ progression detection), reducing undetected spread

☑️ Baseline (No Control)

No-control run always uses: α₁=default, Δμ_m=0, K_m red=0, εₚ=default, ε_w=default, τ₁=default, δ=default, bite_red=0, λ_surv=0.

Tip: Set all controls to minimum to see baseline, then increase to see impact.

📊 Scenario Comparison — Control Measures Summary

SCENARIO	VACC α₁	BITE RED %	PEAK R₀	PEAK Rₑ	PEAK INFECTED	PEAK DAY	FINAL Iₕ	ATTACK RATE	EFFICACY VS NO CTRL
Run simulation with different control measures to see scenario comparison

How to use: Run control comparison with different parameter settings. Each run is auto-categorised (No Control / Minimal / Moderate / Maximum). Table calculates efficacy vs no-control baseline.

🔬 With vs Without Control Measures — Comparison

Side-by-side I_total curves showing impact of vaccination, vector control, biosecurity, treatment & personal protection

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	With Control	Change
Run control comparison to see results

📐 View Control Measure Equations (JE ODE)

dSₕ/dt = (1−α₁)·bₕ − β_mh·b(T)·(Iₘ/Nₕ)·Sₕ + ρ₁V₁ₕ + ρ₂V₂ₕ − μₕSₕ
dSₘ/dt = (bₘ − rₘNₘ/Kₘ) − ... − (μₘ + Δμₘ)·Sₘ [fogging]
dNₘ/dt = bₘ − (rₘ/K_m·(1−red%) + μₘ)·Nₘ [larviciding]
dBₚ/dt = εₚ·Sₚ − μₚBₚ | dB_w/dt = ε_w·S_w − μ_w·B_w
dIₕ/dt = φ·I_Ah − (τ₁·ηₕ + τ₂·δ)·Iₕ − σ·Iₕ − μₕIₕ
b(T)_ctrl = b₀·(1−bite_red%)·exp(−0.1·(T−T₀)²) [personal protection]
φ_enhanced = φ·(1 + λ_surv) [surveillance]

📊 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)

JE Epidemic Trajectories — 3-Scenario Monte Carlo Comparison

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

📊 Year-wise JE Simulation Validation — Udupi District

How Hindcast Validation Works (RK4 Method):
For each historical year: (1) Year-specific human population is used as N_h. (2) Observed JE Tests Positive seed I_h as starting condition. (3) A year-specific transmission rate β_mh is back-calculated from observed incidence. (4) The host–vector ODE system is solved using Runge-Kutta 4^th order (RK4) for 365 days. (5) Predicted = Average Monthly I_h 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 — NVBDCP 2008-2020)

Select a district to validate.

West Bengal District CSV data (default)

Default validation CSV data for West Bengal. Select Kolkata or Purba Barddhaman. You can still upload another district CSV in the next option.

Upload Another District CSV

Use this only when you want to add a district other than the built-in Karnataka and West Bengal defaults. Required columns: Year, Observed_Cases, Human_Population. Optional: District, Deaths, Dose1, Dose2.

District Name:

Year From

Year To

Exclude Zero-Case Years

YES rate (Accuracy)

—

McFadden R²

—

AIC (Full / Null)

—

LR χ² (p-value)

—

Run validation to see hindcast validation against historical JE outbreaks.

Year-by-Year Validation Table — Udupi District

Reported? = Yes if observed JE cases > 0. Predicted? = Yes if predicted I_h > 0. Final Result: Reported=Yes & Predicted=Yes → YES (TP) | Not Reported & Not Predicted → YES (TN) | Not Reported & Predicted=Yes → No (FP) | Reported & Not Predicted → NO (FN).

Year	Observed Cases	Deaths	Doses (1st+16m)	Population	β_mh (year)	Predicted (Avg Monthly I_h)	Active Months	Reported?	Predicted?	Final Result	Abs Error	% Error
Click "▶ Run Year-wise Validation" to see results

RK4 Method: For each year, β_mh is back-calculated from observed JE incidence. The host-vector ODE is then solved by Runge-Kutta 4^th order (RK4) for 365 days with dt=1. Predicted = Average Monthly I_h (mean over active months only).

5 Validation Criteria: ① Epidemic Curve Comparison ② Calibration-Validation Split: 70% training / 30% hold-out ③ Goodness-of-Fit: McFadden R² ④ Confidence Intervals: Clopper-Pearson exact 95% CI ⑤ Hindcast Validation: TP/TN/FP/FN breakdown.
West Bengal default: Kolkata and Purba Barddhaman CSV validation data are already available under the West Bengal option. Use Upload Another District CSV only for additional districts.

CSV upload: columns Year, Observed_Cases, Human_Population, optional District, Deaths, Dose1, Dose2.

📂 Load District-Level Data (Excel)

Upload the multi-district JE Excel workbook, then pick a district — all input fields fill and the simulation runs automatically.

Ready

1. Data Source

Built-in (4 districts)

Bellary, Udupi, Kolkata, Purba Barddhaman

Upload Excel workbook

.xlsx with per-district sheets

2. Upload File

Excel must contain sheets like "Bellary", "Udupi", … with Section B parameters.

3. Select District