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Analysis of a nonlinear system for community intervention in mosquito control

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  • 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.

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

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