Analysis of a nonlinear system for community intervention inmosquito control

M. Predescu; R. Levins; T. Awerbuch-Friedlander

doi:10.3934/dcdsb.2006.6.605

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2006, Volume 6, Issue 3: 605-622. Doi: 10.3934/dcdsb.2006.6.605

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Analysis of a nonlinear system for community intervention in mosquito control

1.
Department of Mathematics, Bentley College, 175 Forest Street, Waltham, MA 02452
2.
Department of Population and International Health, Harvard School of Public Health, 665 Huntington Avenue, Boston, MA 02115

Received: March 2005

Revised: December 2005

Published: May 2007

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Abstract

Non-linear difference equation models are employed in biology to describe the dynamics of certain populations and their interaction with the environment. In this paper we analyze a non-linear system describing community intervention in mosquito control through management of their habitats. The system takes the general form:

$x_{n+1}= a x_{n}h(p y_{n})+b h(q y_{n})$ n=0,1,...
$y_{n+1}= c x_{n}+d y_{n}$

where the function $h\in C^{1}$ ( [ $0,\infty$) $\to $ [$0,1$] ) satisfying certain properties, will denote either $h(t)=h_{1}(t)=e^{-t}$ and/or $h(t)=h_{2}(t)=1/(1+t).$ We give conditions in terms of parameters for boundedness and stability. This enables us to explore the dynamics of prevalence/community-activity systems as affected by the range of parameters.

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Mathematics Subject Classification: 39A11; Secondary: 92D40.

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