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
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