Modeling the Susceptibility of Treated Individuals to Further Tuberculosis Episodes Open Access

Herslebs, Erik (Spring 2018)

Permanent URL: https://etd.library.emory.edu/concern/etds/0v8380591?locale=en
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Abstract

The risk of relapse and reinfection among individuals treated for tuberculosis (TB) is an

important area of study. It has been found that treated individuals are four times more likely to

become infected with another episode of tuberculosis than those with no previous infection. In

order to explore possible causes for this, six different mathematical models are created to

describe different hypotheses of the post-treatment behavior of individuals in a hyperendemic

community. These hypotheses include heterogeneity in susceptibility among hosts and initially

high, but waning susceptibility to subsequent TB. It was found by fitting the models to relapse

and reinfection incidence data that host heterogeneity and waning susceptibility can both 

adequately explain trends in the data, while other, simpler models cannot.

Table of Contents

1. Introduction................................................................................................................................1

2. Materials and Methods..............................................................................................................5

2.1 Experimental Data...................................................................................................................5

2.2 Mathematical Models...............................................................................................................7

Instantaneous Transition...............................................................................................................7

Simple Treatment Variation...........................................................................................................9

Exposed Class.............................................................................................................................11

Immune Stabilization...................................................................................................................13

Waning Susceptibility..................................................................................................................16

Host Heterogeneity......................................................................................................................20

2.3 Fitting Procedure...................................................................................................................25

3. Results....................................................................................................................................27

3.1 Results from Literature.........................................................................................................27

3.2 Determining Within-Host Parameters...................................................................................28

3.3 Model Discrimination.............................................................................................................30

4. Discussion...............................................................................................................................40

References..................................................................................................................................42

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