Which numerical integration method does the simulator use?

It uses a classic 4th-order Runge-Kutta (RK4) integration algorithm solved at a fixed step size of 0.05 days.

How are the SIR and SEIR models differentiated?

SIR transitions susceptible hosts directly to infectious status, while SEIR includes an explicit latent compartment (Exposed) parameterized by the latent period.

How does incidence fitting estimate R0 and initial cases?

It performs grid and coordinate-descent least-squares fitting over R0, reporting fraction, and I0, accompanied by a log-linear growth-rate regression.

What is calculated when supplying a WAIFW matrix?

The tool builds the next-generation matrix from age-stratified transmission rates and computes the spectral radius (R0) using power iteration.

How do vaccination and hospitalization parameters alter the compartments?

SEIR-V transfers a daily percentage of susceptible individuals to a protected compartment (V), while SEIR-H diverts infectious cases into a hospital compartment (H) governed by length of stay.

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SIR SEIR Compartmental Epidemic R0 and Intervention Modeling Coach

Run SIR / SEIR / SEIR+V / SEIR+H ODEs with RK4: R0, herd-immunity threshold, analytic peak and final-size equations, growth-rate conversion, WAIFW next-generation-matrix R0, incidence fitting and intervention simulation.

Details

What this tool helps you do

A deterministic compartmental coach for learning and teaching infectious-disease dynamics.

Models: SIR, SEIR, SEIR+V (vaccination S→V) and SEIR+H (hospitalization arm I→H→R), solved with classic RK4 at a 0.05-day step. Derived quantities: R0 = β/γ, post-intervention effective R0, herd-immunity threshold 1−1/R0, analytic SIR peak I/N = 1−(1+lnR0)/R0, final size z = 1−e^(−R0·z), and the exact growth-rate relation R0 = 1+r/γ (SIR) or (1+r/σ)(1+r/γ) (SEIR, Wallinga–Lipsitch).

Optional inputs: a "day,incidence" series triggers a grid + coordinate-descent least-squares fit of (R0, reporting fraction, I0) with a log-linear growth-rate cross-check; a WAIFW matrix (e.g. "10 2; 2 1") computes the age-stratified next-generation-matrix R0 = ρ(βij/γj) by power iteration; intervention day + beta reduction, vaccination campaign, and a hospital arm with LOS show policy trade-offs on the curve.

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SIR SEIR Compartmental Epidemic R0 and Intervention Modeling Coach

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Examples

1. SEIR Outbreak with Mid-Course Transmission Reduction

2. Fitting R0 from Early-Stage Incidence Data

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