Stochastic Epidemic Models

Mathematical Modeling · Axiom Academy

LESSON Stochastic Epidemic Models - Mathematical Modeling Unit 4: Probabilistic Models - Mathematical Modeling Why Stochastic Epidemic Models? While deterministic models like the classic SIR equations provide valuable insights into epidemic dynamics, they treat populations as continuous quantities and predict a single, deterministic trajectory. In reality: Individuals are discrete: You cannot have 2.7 infected people Transmission is random: Whether an encounter leads to infection is probabilistic Small populations matter: Random fluctuations can dominate in small outbreaks Early dynamics are crucial: A new pathogen may fade out or explode based on chance "In epidemics, randomness decides between extinction and explosion." Individual-Based vs Population-Based Models There are two fundamentally different approaches to modeling epidemics: Deterministic (Population-Based) Models Treat populations as continuous variables Predict a single trajectory given initial conditions Work well for large populations Cannot capture fadeout or probability of outbreak Stochastic (Individual-Based) Models Track discrete individuals and random events Use probability distributions and random processes Produce different trajectories each simulation run Capture variability and uncertainty Can model fadeout, probability of major epidemic When Does Stochasticity Matter? Consider introducing 5 infected individuals into a susceptible population of 1000:

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