# American Institute of Mathematical Sciences

2016, 13(5): 969-980. doi: 10.3934/mbe.2016025

## Modeling the spread of bed bug infestation and optimal resource allocation for disinfestation

 1 Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

Received  September 2015 Revised  March 2016 Published  July 2016

A patch-structured multigroup-like $SIS$ epidemiological model is proposed to study the spread of the common bed bug infestation. It is shown that the model exhibits global threshold dynamics with the basic reproduction number as the threshold parameter. Costs associated with the disinfestation process are incorporated into setting up the optimization problems. Procedures are proposed and simulated for finding optimal resource allocation strategies to achieve the infestation free state. Our analysis and simulations provide useful insights on how to efficiently distribute the available exterminators among the infested patches for optimal disinfestation management.
Citation: Ali Gharouni, Lin Wang. Modeling the spread of bed bug infestation and optimal resource allocation for disinfestation. Mathematical Biosciences & Engineering, 2016, 13 (5) : 969-980. doi: 10.3934/mbe.2016025
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##### References:
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