Spatial Optimization of 4-Poster Feeders for Tick-Borne Disease Management Público
Nance, James Daniel (2011)
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
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