Practical Compartmental Models for Infectious Disease Dynamics in Closed Populations

Abstract

Compartmental models are key tools for understanding infectious disease dynamics. This article introduces several classical and extended compartmental models, including the Susceptible–Infected–Recovered (SIR) model, the Susceptible–Infected–Deceased–Susceptible (SIDS) model where immunity wanes, the Susceptible-Infected-Deceased-Immune (SIDM) model where immunity does not wane, and the Susceptible–Infected–Recovered-Vaccinated (SIRV) model incorporating vaccination dynamics. For each model, we present the governing differential and difference equations, simulate typical epidemic trajectories, and demonstrate how to estimate model parameters for synthetic incidence data.