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The abrupt outbreak and transmission of biological diseases has always been along-time concern of humankind. For long, mathematical modeling has served as asimple and yet efficient tool to investigate, predict, and control spread ofcommunicable diseases through individuals. A myriad of works on epidemic modelsand their variants have been reported in the literature. For better predictionof the dynamics of a particular disease, it is important to adopt the mostsuitable model. In this paper, we study some of the widely-appreciateddeterministic epidemic models in which the population is divided intocompartments based on the health status of each individual. In particular, weprovide a demographic classification of such models and study each of them interms of mathematical formulation, near equilibrium point stability properties,and disease outbreak threshold conditions (basic reproduction ratio).Furthermore, we discuss the various influential factors that need to beconsidered during epidemic modeling. The main objective of this article is toprovide a basic understanding of the mathematical complexity incurred indeterministic epidemic models with the aid of graphical illustrations obtainedthrough implementation.

Deterministic Models in Epidemiology: From Modeling to Implementation