S I R Model
R0=2.5, 10-day infectious period, 1 million population
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Evidence-based calculations Used in clinical settings worldwide Regular monitoring recommended
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Sample Disease Scenarios
๐ฅ Population & Initial Conditions
๐ฆ Disease Parameters
๐ก๏ธ Intervention Settings
โ๏ธ Advanced Options
For informational purposes only โ not medical advice. Consult a healthcare professional before acting on results.
๐ฅ Health Facts
โ WHO
โ CDC
๐ฆ 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).
๐ 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:
- ฮฒ (Beta): Transmission rate - how quickly disease spreads
- ฮณ (Gamma): Recovery rate = 1/infectious period
- R0: Basic reproduction number = ฮฒ/ฮณ
Model Assumptions:
- โข Homogeneous mixing population
- โข Closed population (no births/deaths)
- โข Permanent immunity after recovery
- โข No incubation period (instant infectivity)
โฐ When to Use the SIR Model
Best Applications:
- โ Understanding epidemic dynamics
- โ Estimating herd immunity thresholds
- โ Evaluating intervention strategies
- โ Predicting peak infection timing
- โ Planning healthcare capacity
Limitations:
- โ Assumes uniform mixing
- โ No age/spatial structure
- โ Simple immunity model
- โ No incubation period
๐ SIR Model Equations
Differential Equations:
dS/dt = -ฮฒ ร S ร I / N
dI/dt = ฮฒ ร S ร I / N - ฮณ ร I
dR/dt = ฮณ ร I
Key Relationships:
Basic Reproduction Number: R0 = ฮฒ / ฮณ
Herd Immunity Threshold: HIT = 1 - 1/R0
Effective R: Re = R0 ร (S / N)
Final Size Equation:
R(โ) = N ร (1 - exp(-R0 ร R(โ) / 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% |
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