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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Discrete-time Evolution and Stable Equilibria of Multi-compartment Dengue Tracker: Nonlinear Dynamics Modulated by Controlled Stochasticity
Author(s):
M. Bhaduri and M. Predescu
Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.
E-mail: mbhaduri@bentley.edu,
mpredescu@bentley.edu
Abstract:
We discuss the dynamics of solutions of a nonlinear discrete time model that will be useful in Dengue control. The proposed model may be utilized to analyze the dynamics of three variables (mosquito population, habitats and consciousness) across different parameters. Stochasticity has been introduced in realistic ways to highlight combinations of random parameters (on education and recollection) which limits the oscillatory recurrence of habitats and awareness. We propose optimal methods for implementing potential intervention strategies and offer interactive dashboards for vizualizing varied scenarios.
Paper's Title:
A Note On The Global Behavior Of A Nonlinear System of Difference Equations
Author(s):
Norman H. Josephy, Mihaela Predescu and Samuel W. Woolford
Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.
mpredescu@bentley.edu
njosephy@bentley.edu
swoolford@bentley.edu
Abstract:
This paper deals with the global asymptotic stability character of solutions of a discrete time deterministic model proposed by Wikan and Eide in Bulletin of Mathematical Biology, 66, 2004, 1685-1704. A stochastic extension of this model is proposed and discussed. Computer simulations suggest that the dynamics of the stochastic model includes a mixture of the dynamics observed in the deterministic model.
Paper's Title:
A Study of the Effect of Density Dependence in a Matrix Population Model
Author(s):
N. Carter and M. Predescu
Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.
ncarter@bentley.edu
mpredescu@bentley.edu
Abstract:
We study the behavior of solutions of a three dimensional discrete time nonlinear matrix population model. We prove results concerning the existence of equilibrium points, boundedness, permanence of solutions, and global stability in special cases of interest. Moreover, numerical simulations are used to compare the dynamics of two main forms of the density dependence function (rational and exponential).
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