Spatial Optimization of 4-Poster Feeders for Tick-Borne Disease Management Público

Abstract

Amblyomma americanum, the Lone Star tick, is the predominant tick species through-
out the southeast United States. Its significance as a threat to human health was not
realized until recently. Recognized as an important disease vector, Amblyomma carry
a serious bacteria, Ehrlichia chaffeensis, that causes human monocytic ehrlichiosis.
In 1995, eleven cases of ehrlichiosis due to E. chafeensis were identified in Fairfield
Glade, a retirement golf community near Crossivlle, Tennessee. The placement of 4-
poster acaricide feeders has be demonstrated to be a highly effective control method
for eliminating Amblyomma populations. Here we formulate an economic criterion
to evaluate various feeder placement scenarios within Fairfield Glade that minimize
infected ticks and that tend toward future projects in optimization of this system.

Table of Contents

1 Introduction 1

1.1 Biological Background . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Mathematical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Original Method 5

2.1 Discrete Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Time model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Space model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.3 Cost-Effctiveness Analysis . . . . . . . . . . . . . . . . . . . . 10

2.2 Seeking a New Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Population Model 15

3.1 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Without Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 With Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Optimization 24

4.1 Temporal Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 Spatial Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5 Conclusion 40

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	BS
Submission	Honors Thesis
Language	English
Research Field	Mathematics
Palabra Clave	Population Model Optimization
Committee Chair / Thesis Advisor	Nagy, James, Emory University
Committee Members	Veneziani, Alessandro, Emory University Family, Fereydoon, Emory University

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