SIR Epidemic Model

Mathematical Modeling · Axiom Academy

Understanding infectious disease dynamics through compartmental modeling The SIR model partitions a population of size N into three mutually exclusive compartments based on disease status: Individuals who can catch the disease but are not yet infected Individuals who have the disease and can transmit it to others Individuals who have recovered and gained immunity The basic SIR model makes several simplifying assumptions that define its scope and limitations: Closed population: No births, deaths (from other causes), immigration, or emigration Homogeneous mixing: Every individual has equal probability of contact with any other Permanent immunity: Once recovered, individuals cannot be reinfected Instantaneous infection: Susceptibles become infectious immediately upon infection Constant parameters: Transmission and recovery rates do not change over time The SIR model works well for diseases like measles, mumps, and rubella where infection confers lasting immunity. For diseases where immunity wanes (like the common cold), the SIRS model with reinfection is more appropriate. The dynamics are governed by a system of three coupled ordinary differential equations that describe the rate of change in each compartment: 4. The Parameters: Beta and Gamma The SIR model has two fundamental parameters that characterize the disease dynamics:

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