SEIR Model Calculator

Calculator Inputs

Total Population

Initial Susceptible

Initial Exposed

Initial Infectious

Initial Recovered

Transmission Rate (β)

Progression Rate (σ)

Recovery Rate (γ)

Projection Days

Time Step (days)

Tip: The four initial compartments should add up exactly to the total population.

Example Data Table

Scenario	Population	S0	E0	I0	β	σ	γ	Days
Urban baseline	100000	99960	25	15	0.42	0.20	0.14	120
Slower spread	100000	99970	20	10	0.28	0.18	0.16	120
Faster progression	100000	99940	35	25	0.46	0.33	0.17	100

Formula Used

The calculator uses the classical SEIR compartment system with discrete time stepping. The total population is assumed constant:

Population identity	N = S + E + I + R
New exposures	β × S × I / N
Exposed to infectious	σ × E
Recovered flow	γ × I
Discrete update	Next value = current value ± flow × time step
Basic reproduction number	R0 = β / γ
Mean latent period	1 / σ
Mean infectious period	1 / γ

This approach is practical for scenario comparison, planning exercises, and mathematical intuition. It is not a substitute for clinical forecasting or policy design.

How to Use This Calculator

Enter the total population for the modeled system.
Fill the starting values for susceptible, exposed, infectious, and recovered groups.
Make sure those four inputs add up to the total population.
Set the transmission rate β, progression rate σ, and recovery rate γ.
Choose the number of projection days and the time step.
Press the calculate button to show summary metrics above the form.
Review the trend chart for compartment movement over time.
Use the CSV or PDF buttons to export your scenario results.

Frequently Asked Questions

1. What does the SEIR model represent?

It splits a population into susceptible, exposed, infectious, and recovered groups. This helps describe how an outbreak progresses when infection includes a latent period before infectiousness begins.

2. Why is there an exposed compartment?

The exposed group captures people who are infected but not yet infectious. That delay changes peak timing and improves realism compared with simpler SIR-style models.

3. What is the meaning of β?

β is the transmission rate. Higher values increase the flow from susceptible to exposed, which generally raises the outbreak speed and the peak infectious population.

4. What is the meaning of σ?

σ is the progression rate from exposed to infectious. Its inverse gives the average latent period. Larger σ values move exposed cases into infectious status more quickly.

5. What is the meaning of γ?

γ is the recovery rate. Its inverse gives the average infectious period. Higher γ values reduce the time people stay infectious and can lower outbreak intensity.

6. Why must the initial compartments equal population?

The model assumes a closed population for the scenario. If the starting compartments do not sum to the total population, the conservation relationship becomes inconsistent.

7. Is this calculator suitable for real public health decisions?

It is best for education, mathematics practice, and simple scenario testing. Real planning should use validated data, calibrated parameters, uncertainty analysis, and expert review.

8. What do CSV and PDF exports include?

The CSV export contains the daily compartment series. The PDF export summarizes the scenario inputs and results so you can archive or share a clean snapshot.