Compartmental models in epidemiology: bridging the gap with operations research for enhanced epidemic control

Abstract Compartmental models have gained significant attention not only in public health studies but also in fields such as Operations Research (OR), social sciences, and logistics, particularly following the COVID-19 pandemic. Their broad applicability in epidemiology and their utility in understanding, predicting, and controlling the global spread of infectious diseases have made them indispensable across various disciplines. The appeal of these models lies in their simplicity yet effectiveness in capturing the essential dynamics of disease transmission. This paper provides a comprehensive review of compartmental models, focusing on the Susceptible-Infectious-Recovered (SIR) models and the key aspects of their structure. The primary objective of this review is to enhance the ability of researchers and practitioners to understand and manage infectious disease outbreaks through a twofold approach: (1) an evaluation of the assumptions, equations, and methodologies used for estimating critical parameters in SIR models, and (2) an exploration of the relationship between SIR models and optimization models. Additionally, a systematic micro-level review has identified the most significant research gaps in the literature on compartmental models, leading to recommendations for future research. A key finding emphasizes the need to revisit various assumptions to clarify the connection between SIR models and optimization approaches, which is expected to offer valuable insights for epidemic disease modeling.