Publication Date
8-2025
Advisor(s) - Committee Chair
Richard Schugart, Mikhail Khenner, Lukun Zheng
Degree Program
Department of Mathematics
Degree Type
Master of Science
Abstract
Tuberculosis (TB) remains a major public health challenge in Bangladesh and around the world, exacerbated by the emergence of multidrug-resistant strains (MDR-TB). This thesis develops and analyzes a compartmental mathematical model that describes the dynamics of TB transmission, including drug-sensitive and MDR-TB populations. The model consists of ten coupled differential equations and incorporates key epidemiological processes such as infection, progression, treatment, recovery, and reinfection.
The stability of the model was analyzed by identifying the basic reproduction number. The model was shown to be structurally identifiable.
To analyze with data, the model was reduced to six differential equations. The reduced model was curve fitted to TB case data from Bangladesh between 2010 and 2019. The practical identifiability of key model parameters was assessed using the Fisher Information Matrix (FIM) and a modified profile likelihood approach, providing insight into parameter sensitivity and uncertainty.
The results indicate that the reduced six-equation model fits the available data well, and that several epidemiologically relevant parameters are practically identifiable. However, some parameters remain poorly identified, highlighting the need for richer data and further methodological refinement. The model framework offers a foundation for future studies on TB dynamics, parameter identifiability, and control strategies in high-burden settings.
Disciplines
Applied Mathematics | Computer Sciences | Disease Modeling | Diseases | Infectious Disease | Medical Specialties | Medicine and Health Sciences | Numerical Analysis and Scientific Computing | Ordinary Differential Equations and Applied Dynamics | Physical Sciences and Mathematics
Recommended Citation
Tahsin, Anika, "ANALYZING THE PRACTICAL IDENTIFIABILITY OF A STRUCTURALLY IDENTIFIABLE MODEL FOR TUBERCULOSIS TRANSMISSION USING DATA FROM BANGLADESH" (2025). Masters Theses & Specialist Projects. Paper 3855.
https://digitalcommons.wku.edu/theses/3855
copyright permission
Included in
Disease Modeling Commons, Infectious Disease Commons, Numerical Analysis and Scientific Computing Commons, Ordinary Differential Equations and Applied Dynamics Commons