Infectious Disease SIR Model
Simulate epidemic spread using the SIR mathematical model
SIR Model Parameters
Population (Initial Values)
Total number of people in the population
Percentages will be normalized to 100%
Disease Parameters
Average number of secondary infections
Rate per day (1/infectious period)
Transmission rate per contact per day
Simulation Settings
Duration of epidemic simulation
Simulate lockdown, vaccination, or other interventions
Simulation Results
Timeline Metrics
Final Population State
🦠 Epidemic Analysis
Classification: Major Epidemic (Critical Severity)
High transmission with significant population impact
- R₀ = 2.5: Epidemic will spread
- Peak occurs around day 46 with 24% infected
- 90% of population will be infected overall
- Herd immunity threshold: 60% of population
Epidemic Curve (Simplified)
🦠 Disease R₀ Examples
*R₀ values are representative estimates and may vary by population and conditions
📊 R₀ Interpretation
🛡️ Intervention Strategies
Most effective: can reduce R₀ below 1
Reduces contact rate, lowers effective R₀
Removes infected from susceptible population
Limits geographic spread of infection
Understanding the SIR Model in Epidemiology
What is the SIR Model?
The SIR (Susceptible-Infected-Recovered) model is a mathematical framework used to predict the spread of infectious diseases through populations. It divides the population into three compartments and models the flow between them using differential equations.
Model Components:
- •S(t): Susceptible individuals who can contract the disease
- •I(t): Infected individuals who can transmit the disease
- •R(t): Recovered/removed individuals (immune or deceased)
- •R₀: Basic reproduction number (average secondary infections)
Mathematical Framework
The SIR model uses the following differential equations to describe the rate of change in each population compartment:
Parameters:
- β: Transmission rate (contacts × infection probability)
- γ: Recovery rate (1/infectious period)
- R₀: β/γ (basic reproduction number)
- N: Total population size
SIR Model Applications and Limitations
Applications
Outbreak Prediction
Forecast epidemic peak, duration, and total cases
Intervention Planning
Model effects of vaccination, social distancing
Public Health Policy
Guide resource allocation and response strategies
Herd Immunity
Calculate vaccination thresholds for protection
Model Assumptions
Homogeneous Mixing
All individuals have equal contact probability
Constant Parameters
R₀ and recovery rates remain fixed
Lifelong Immunity
Recovered individuals cannot be reinfected
No Demographics
Ignores births, deaths, and age structure
Limitations
Population Structure
Doesn't account for age, geography, or social networks
Behavioral Changes
Cannot model adaptive behaviors during epidemics
Disease Variants
Assumes single pathogen with fixed characteristics
Short-term Focus
Most accurate for initial epidemic phases
Related Epidemiology Calculators
🦠 Important Epidemiological Model Disclaimer
FOR EDUCATIONAL AND RESEARCH PURPOSES ONLY: This SIR model calculator provides theoretical epidemic simulations based on simplified mathematical assumptions. Real-world disease spread is influenced by countless factors including population heterogeneity, behavioral changes, spatial distribution, interventions, and pathogen evolution that are not captured in this basic model. Results should not be used for public health decision-making, policy formation, or personal medical decisions. The model assumes homogeneous mixing, constant parameters, and lifelong immunity, which may not reflect reality. Predictions become less accurate over longer time periods and during dynamic epidemic phases. Always consult qualified epidemiologists, public health professionals, and official health authorities for guidance on disease outbreaks, prevention strategies, and public health responses.