Interactive SIR Modeling

Explore epidemic dynamics with real-time visualization of disease spread models

The SIR model is a fundamental epidemiological tool that divides a population into three compartments: Susceptible (S) individuals who can catch the disease, Infected (I) individuals who have the disease and can spread it, and Recovered (R) individuals who have recovered and are immune.

Disease Parameters

Population Size 100,000

Initial Infected 10

Transmission Rate (β) 0.50

Recovery Rate (γ) 0.10

Time Period (days) 365

Intervention Parameters

Mask Effectiveness 0%

Social Distancing Level

Hospital Capacity (beds) 1,000

Vaccination Rate (per day) 0/day

Vaccine Effectiveness 90%

Derived Metrics

Base R₀: 5.00

Effective R₀ (with interventions): 5.00

Infectious Period (days): 10.0

Hospital Capacity (% of population): 1.0%

Preset Scenarios

Simulation Results

Population Dynamics Over Time

Susceptible

Infected

Recovered

Vaccinated

Hospitalized

Deceased

Peak Infections

- on day -

Peak Hospitalizations

- capacity status

Total Vaccinated

- population vaccinated

Final Attack Rate

- of population infected

Total Deaths

- case fatality rate

Effective R₀

- with interventions

Hospital Capacity

Vaccination Progress

Age Group Breakdown

Daily New Infections

About the SIR Model

Mathematical Foundation

The SIR model is governed by these differential equations:

dS/dt = -βSI/N

dI/dt = βSI/N - γI

dR/dt = γI

Key Parameters

β: Transmission rate (contacts per day × probability of transmission)
γ: Recovery rate (1/infectious period)
R₀ = β/γ: Basic reproduction number

Model Assumptions

Homogeneous mixing of population
No births, deaths, or migration
Permanent immunity after recovery
Constant transmission and recovery rates