Acknowledgement: Aresh Dadlani, Richard O. Afolabi, Hyoyoung Jung, Khosrow Sohraby, Kiseon Kim, "Deterministic Models in Epidemiology: From Modeling to Implementation," Technical Report, CSNL, EECS, GIST, March 2013.
You can find the paper on arXiv (link).
The sudden outbreak and transmission of biological diseases have always been a longstanding concern for humankind. For a considerable time, mathematical modeling has served as a straightforward yet efficient tool to investigate, predict, and control the spread of communicable diseases among individuals. An array of studies on epidemic models and their variations are documented in the literature. To better anticipate the dynamics of a specific disease, selecting the most appropriate model is crucial. In this paper, we delve into some widely recognized deterministic epidemic models that categorize the population into compartments based on each individual's health status. Specifically, we offer a demographic classification of these models, examining each in terms of mathematical formulation, stability properties near equilibrium points, and conditions for disease outbreak thresholds (basic reproduction ratio). Moreover, we discuss various influential factors that necessitate consideration during epidemic modeling. The primary aim of this article is to provide a foundational grasp of the mathematical intricacies inherent in deterministic epidemic models, supported by graphical illustrations derived from implementation.