Chapter 12 A Deterministic Compartmental Modeling Framework for Disease Transmission King James B. Villasin, Eva M. Rodriguez, and Angelyn R. Lao Abstract Mathematical models for the spread of diseases help us understand the mechanisms on how diseases spread, evaluate the possible effects of interventions, predict outcomes of epidemics, and forecast the course of outbreaks. Compartmental models are widely used in synthetic biology since they can represent a biological system as an assembly of various parts or compartments with different functions. Here we present a framework for the analysis of a compartmental model for the transmission of diseases using ordinary differential equations. We apply this method on a study about the spread of tuberculosis. Key words Epidemic, Spread of disease, Compartmental model, Stability analysis, Deterministic model, Ordinary differential equations, Tuberculosis 1 Introduction In the face of globalization, the ease of mobility and climate change, we are confronted with a greater danger of rapidly spread- ing diseases. From history, we have seen their destructive conse- quences in the lives of people, the economy, and even the security of nations. It is important therefore, to understand the dynamics of these illnesses so that we can detect them early on and reduce their impact and damage. Mathematical models can help us understand the mechanisms of how diseases spread, evaluate the possible effects of interventions, predict outcomes of epidemics, and forecast the course of outbreaks. They also provide valuable information for making public health policies to prevent and control epidemics. In this chapter, we present a framework for the analysis of a compartmental model for the spread of diseases using ordinary differential equations (ODEs). We apply this method on a study about the spread of tuberculosis. A compartmental model simulates how individuals, in different “compartments” (groupings or classes), of a population interact with each other. The model is composed of interconnected Mario Andrea Marchisio (ed.), Computational Methods in Synthetic Biology, Methods in Molecular Biology, vol. 2189, https://doi.org/10.1007/978-1-0716-0822-7_12, © Springer Science+Business Media, LLC, part of Springer Nature 2021 157