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Publication Date


First Advisor

Gwen Spencer

Document Type

Honors Thesis

Degree Name

Bachelor of Arts


Mathematics and Statistics


Infectious diseases, Tuberculosis, Mathematical modeling, Antibiotic resistance, Genetic algorithms, Drug resistance, Communicable diseases-Mathematical models, Tuberculosis-Mathematical models


Tuberculosis (TB) is still a major public health issue: millions of individuals are infected by the causal bacillus Mycobacterium tuberculosis (Mtb). The greatest challenge to the eradication of the disease has been the emergence of antibiotic-resistant strains, especially those resistant to first line drugs, such as isoniazid (H), rifampin (R), pyrazinamide (PYZ) and ethambutol (ETB). Resistance renders the disease more difficult and expensive to treat [14]. The past few years, although several models have been developed to explain TB prevalence [13, 16, 20], none of them fully incorporate the effects of antibiotic resistance. The aim of this project is to integrate the effects of single- and multi- drug resistant strains to develop a more realistic and predictive model of TB dynamics in the US population. For this purpose, we developed a compartmental mathematical model described by differential equations. Data from the Centers of Disease Control and Prevention (CDC) on TB incidence and prevalence for the years 1993-2014 was collected. A set of 27 parameters was fitted to the data, using a genetic algorithm to minimize an error function that cannot be differentiated. Local minima were identified and multiple sensitivity analysis tests were performed to identify which parameters the model is sensitive to.




xiii, 39 pages, 20 unnumbered pages : color illustrations. Includes bibliographical references (pages 37-38)