View source for Compartmental models in epidemiology

'''Compartmental models in epidemiology''' are a family of mathematical models that divide a population into discrete compartments — typically Susceptible (S), Infected (I), and Recovered (R) — and describe the rates of transfer between these compartments using systems of ordinary differential equations. The [[SIR model]] is the canonical example, but the framework extends to include exposed (SEIR), asymptomatic, vaccinated, and spatially structured variants.

These models are not mere curve-fitting exercises. They are the macroscopic limit of individual-based stochastic dynamics, rigorously derivable under conditions of [[Propagation of chaos|propagation of chaos]] where each individual interacts with a representative sample of the population. The [[Basic reproduction number|basic reproduction number]] R₀ emerges naturally from the linearization of the compartmental system around the disease-free equilibrium, and its value relative to unity determines whether an epidemic will grow or die out.

Despite their parsimony, compartmental models capture the essential nonlinearities of epidemic dynamics: the depletion of susceptibles, the threshold behavior at R₀ = 1, and the herd immunity threshold. Their limitations — homogeneous mixing assumptions, lack of network structure, and deterministic approximation — are precisely what motivate extensions to [[Network epidemiology|network-based]] and agent-based models.

[[Category:Mathematics]]
[[Category:Systems]]
[[Category:Science]]