Mathematical Techniques for Epidemiological Formulation-A Review

Abstract Mathematical epidemiology provides a robust framework for modelling disease dynamics, analysing the progression of outbreaks, and informing public health policy. This review examines the evolution of these techniques, from foundational, knowledge-driven models to modern, data-intensive approaches. The field's roots lie in the pioneering work of Daniel Bernoulli in 1760 and the seminal compartmental models of Kermack and McKendrick, which use ordinary differential equations to describe the flow of a population between health-based groups. While these models are computationally efficient, they assume homogeneous mixing, a limitation that has driven the development of more advanced paradigms. To address these limitations, modern approaches include network models, which account for heterogeneous contact structures, and agent-based models, which simulate disease spread at the individual level. These methods offer greater realism but come with significant computational demands. The paper highlights the importance of nuanced interpretation of key metrics like the Basic Reproduction Number (R0​) and the Effective Reproduction Number (Re​), which are often misunderstood. Finally, it addresses the burgeoning role of modern computational techniques, including machine learning and artificial intelligence, which are increasingly used to process high-dimensional data and enhance predictive accuracy, often in combination with traditional models to create more robust and adaptable hybrid systems. Keywords Epidemiological models, Compartmental models, Agent-based models, Network models, Reproduction number, Machine learning.