@inbook{e4428b7e71d441c7b05e683dbfbc1398,
title = "Controlling a cockroach infestation",
abstract = "The cockroach is one of the world{\textquoteright}s most prolific and resilient pests, with over 3,500 species worldwide. It is important to understand the growth and adaptive mechanisms of cockroach colonies in order to safely control these populations. We present a continuous time, age-structured population model of the Blattella germanica cockroach that includes the application of pesticides and the development of resistant subpopulations. The resulting system of differential equations is then used to optimize treatment strategies using analytical and heuristic optimization techniques. While the model shows that the roach-free equilibrium is always unstable, the strategic application of pesticides can keep populations low, even when a drug-resistant subpopulation develops.",
keywords = "Blattella germanica, Mathematical model, Optimal pesticide application",
author = "Hannah Albert and Amy Buchmann and Laurel Ohm and Ami Radunskaya and Ellen Swanson",
note = "Funding Information: Acknowledgments This paper grew out of a workshop in differential equations that was part of the EDGE 2013 summer program. We would like to thank the other members of the workshop: Jessica Poole, Kara Keller, Yeng Xiong, Karamatou Yacoubou Djima and Professor Eirini Poimenidou for their work in the early stages of the project. We also thank Professor Elzie McCord for his invaluable information on the biology of cockroaches, and the effects of pesticides. The workshop was supported by a grant from the NSF, DMS 1136857. We would also like to thank the Association for Women in Mathematics for organizing the 2015 AWM Symposium and the EDGE Foundation, with support from the NSF, for continuing support of this research project. Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.",
year = "2016",
doi = "10.1007/978-3-319-34139-2_9",
language = "English (US)",
series = "Association for Women in Mathematics Series",
publisher = "Springer",
pages = "209--224",
booktitle = "Association for Women in Mathematics Series",
}