Epidemiological Models

Mathematical Modeling · Axiom Academy

EXAMPLE Epidemiological Models Master compartmental disease models through worked examples: SIR, SEIR, SIS, and vaccination strategies. Excellent work! You've analyzed fundamental epidemic models. Here's what we learned: Basic Reproduction Number: determines whether an epidemic can spread. When , the disease dies out; when , it spreads. Epidemic Threshold: The fraction of susceptibles must exceed for an outbreak to occur. Model Choice: SIR for diseases with lasting immunity (measles), SIS for diseases without immunity (common cold), SEIR when incubation period matters (COVID-19). Endemic Equilibrium: SIS models predict persistent disease with infected fraction . Herd Immunity: Vaccination fraction protects the entire population, even unvaccinated individuals. These mathematical models guide real public health decisions: vaccination targets, social distancing measures, and resource allocation during outbreaks!

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