SIR Model and its Applications

Abstract

The Susceptible-Infected-Recovered (SIR) model, first introduced by Kermack and McKendrick in 1927, represents a fundamental framework for understanding epidemic dynamics and has evolved into one of the most influential mathematical models in epidemiology. This article examines the foundations of the SIR model, including its mathematical formulation, underlying assumptions, and parameter estimation techniques. The review also explores diverse applications of the SIR model across multiple domains, including traditional epidemiological studies, economic modeling, social network analysis, and emerging areas such as cybersecurity and marketing. Through systematic analysis of recent literature, this work demonstrates the model's adaptability and continued relevance in addressing contemporary challenges, from COVID-19 pandemic modeling to understanding information diffusion in digital networks. The findings highlight both the strengths and limitations of the SIR framework while identifying future research directions for model enhancement and application.