S I R Model
R0=2.5, 10-day infectious period, 1 million population
Why This Health Metric Matters
Why: This calculation helps assess important health parameters for clinical and personal wellness tracking.
How: Enter your values above and the calculator will apply validated formulas to compute your results.
- ●Evidence-based calculations
- ●Used in clinical settings worldwide
- ●Regular monitoring recommended
Sample Disease Scenarios
👥 Population & Initial Conditions
🦠 Disease Parameters
🛡️ Intervention Settings
⚙️ Advanced Options
⚠️For informational purposes only — not medical advice. Consult a healthcare professional before acting on results.
🏥 Health Facts
— WHO
— CDC
🦠 What is the SIR Model?
The SIR model is a fundamental compartmental model in epidemiology used to predict the spread of infectious diseases through a population. Developed by Kermack and McKendrick in 1927, it divides the population into three compartments:
S - Susceptible
Individuals who can become infected. They have no immunity to the disease.
I - Infected
Individuals currently infected and capable of transmitting the disease.
R - Recovered
Individuals who have recovered and gained immunity (or died).
📋 How the SIR Model Works
The model uses differential equations to describe how individuals move between compartments over time. Key parameters determine the disease dynamics:
Key Parameters:
- β (Beta): Transmission rate - how quickly disease spreads
- γ (Gamma): Recovery rate = 1/infectious period
- R0: Basic reproduction number = β/γ
Model Assumptions:
- • Homogeneous mixing population
- • Closed population (no births/deaths)
- • Permanent immunity after recovery
- • No incubation period (instant infectivity)
⏰ When to Use the SIR Model
Best Applications:
- ✓ Understanding epidemic dynamics
- ✓ Estimating herd immunity thresholds
- ✓ Evaluating intervention strategies
- ✓ Predicting peak infection timing
- ✓ Planning healthcare capacity
Limitations:
- ✗ Assumes uniform mixing
- ✗ No age/spatial structure
- ✗ Simple immunity model
- ✗ No incubation period
📐 SIR Model Equations
Differential Equations:
dS/dt = -β × S × I / N
dI/dt = β × S × I / N - γ × I
dR/dt = γ × I
Key Relationships:
Basic Reproduction Number: R0 = β / γ
Herd Immunity Threshold: HIT = 1 - 1/R0
Effective R: Re = R0 × (S / N)
Final Size Equation:
R(∞) = N × (1 - exp(-R0 × R(∞) / N))
| Disease | R0 | HIT |
| Measles | 12-18 | 92-95% |
| COVID-19 (original) | 2.5-3.5 | 60-70% |
| Influenza | 1.3-1.8 | 23-44% |
| Ebola | 1.5-2.5 | 33-60% |