Xu, Xiaxia, Xiao, Yanni and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2015) Models of impulsive culling of mosquitoes to interrupt transmission of West Nile Virus to birds. Applied Mathematical Modelling, 39 (13). pp. 3549-3568. ISSN 0307-904X (doi:https://doi.org/10.1016/j.apm.2014.10.072)

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Abstract

A mathematical model describing the transmission of West Nile virus (WNV) between vector mosquitoes and birds, incorporating a control strategy of culling mosquitoes and defined by impulsive differential equations is presented and its properties investigated. First, we consider a strategy of periodic impulsive culling of the mosquitoes. Theoretical results indicate that if the threshold R 0 is greater than unity the disease uniformly persists, but, if not, the disease does not necessarily become extinct. The explicit conditions determining the backward or forward bifurcation were obtained. The culling rate has a major effect on the occurrence of backward bifurcation. Analysis shows that the disease is most sensitive to mosquito-bird contacts, mosquito-culling rate and intervals between culls. The dependence of the outcomes of the culling strategy on mosquito biting rate is discussed. When the complete elimination of disease is impossible, mosquito culls are implemented once the infected birds reach a predefined but adjustable threshold value. Numerical analysis shows that the period of mosquito culling finally stabilizes at a fixed value. In addition, variations of mean prevalence of \{WNV\} in birds and the culling period are simulated.

Item Type:	Article
Additional Information:	This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Uncontrolled Keywords:	West Nile Virus, impulsive differential equation, backward bifurcation, partial rank correlation coefficient, control measures
Subjects:	Q Science > QA Mathematics Q Science > QH Natural history
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > Natural Resources Institute
Last Modified:	20 Oct 2016 13:57
URI:	http://gala.gre.ac.uk/id/eprint/12789

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