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

Ali  Gharouni; Lin Wang

doi:10.3934/mbe.2016025

Article Contents

2016, Volume 13, Issue 5: 969-980. Doi: 10.3934/mbe.2016025

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

Ali Gharouni^1, and
Lin Wang^1,

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

Received: August 31, 2015

Revised: February 29, 2016

Published: June 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 92B05, 34D23; Secondary: 34C12.

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