The role of seasonality in the dynamics of deer tick populations |
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Authors: | T?Awerbuch-Friedlander R?Levins Email author" target="_blank">M?PredescuEmail author |
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Institution: | (1) Department of Population Science, Harvard School of Public Health, 665 Huntington Avenue, Boston, MA 02115, USA;(2) Department of Mathematics, Bentley College, 175 Forest Street, Waltham, MA 02452, USA |
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Abstract: | In this paper, we formulate a nonlinear system of difference equations that models the three-stage life cycle of the deer
tick over four seasons. We study the effect of seasonality on the stability and oscillatory behavior of the tick population
by comparing analytically the seasonal model with a non-seasonal one. The analysis of the models reveals the existence of
two equilibrium points. We discuss the necessary and sufficient conditions for local asymptotic stability of the equilibria
and analyze the boundedness and oscillatory behavior of the solutions. A main result of the mathematical analysis is that
seasonality in the life cycle of the deer tick can have a positive effect, in the sense that it increases the stability of
the system. It is also shown that for some combination of parameters within the stability region, perturbations will result
in a return to the equilibrium through transient oscillations. The models are used to explore the biological consequences
of parameter variations reflecting expected environmental changes. |
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Keywords: | |
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