Culling structured hosts to eradicate vector-borne diseases

Xinli Hu; Yansheng Liu; Jianhong Wu

doi:10.3934/mbe.2009.6.301

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2009, Volume 6, Issue 2: 301-319. Doi: 10.3934/mbe.2009.6.301

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Culling structured hosts to eradicate vector-borne diseases

1.
Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an, 710049
2.
Department of Mathematics, Shandong Normal University, Jinan, 250014
3.
Center for Disease Modeling, York University, Toronto, Ontario, M3J 1P3

Received: January 31, 2007

Revised: August 31, 2008

Published: February 2009

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Abstract

A compartmental model is developed, in the form of a nonautonomous system of delay differential equations subject to impulses at specific times, for mosquito-born disease control involving larvicides and insecticide sprays. Sufficient conditions in terms of the frequencies and rates of larvicides and insecticide sprays are derived, and numerical simulations are provided to illustrate the sharpness of these disease eradication conditions.

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Mathematics Subject Classification: Primary: 34K45, 34K25; Secondary: 92D30, 34K60.

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