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 OverView
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Time delays are an important aspect of ecological systems. Delays are accurate ways of
modelling phenomena such as maturation and gestation and can result in more complicated dynamics than in the absence of delay
Delays often appear in the model equations because of age-structure in the population. Inclusion of diffusion results in nonlocal delays. Additionally, the equations can
have delay-dependent coefficients. The equilibria of such equations usually depend on
the time delays.
We propose and analyse some mathematical models of stage-structured populations
where the individuals have two stages: immature and mature. The time from birth to
maturity can be modeled by either a discrete or a distributed time delay. We study
both ordinary differential delay equations and reaction-diffusion equations with delay,
the latter to incorporate spatial effects. The possibility of individuals not all maturing
at the same age can be modeled by using a distributed delay formulation.
We start by deriving a stage-structured reaction-diffusion model with discrete delay.
Existence and monotonicity of travelling front solutions of the resulting system are
investigated. To address the possibility of individuals maturing at different ages we then
develop a distributed delay ODE model and examine its dynamics. A reaction-diffusion
extension is then developed and attention paid to travelling front solutions.
A two-species competition system is then proposed, in which only the adults are
in competition. In the absence of competition, each species evolves according to the
distributed delay model proposed earlier. Global stability of the equilibria of the competition model is investigated. In the situation when there is no coexistence equilibrium,
travelling fronts are shown to exist connecting the two boundary equilibria. These correspond to the weaker competitor being driven to extinction by the stronger in a travelling
wave of invasion.
We then propose a general stage-structured population model with a state-dependent
time delay, in which the time delay is an increasing differentiable function of the total
population (immature plus mature). This type of equation is motivated by previous
research on whale and seal populations.
Finally, we examine a three species food chain model with delay, in which the predator
is assumed to have a stage-structure. A combination of analytical and numerical methods
are used here. Results are proved on positivity, boundedness, linear and nonlinear
stability. Existence of periodic solutions is demonstrated numerically.
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 Research Intersets:
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? Applied Mathematics: Modeling Delay Differential Equations with Discrete and Distributed Delay, Stage-Structured Population systems, Nonlinear Analysis, Traveling wave front, Hopf Bifurcation, Competing and Predator-Prey Species, Reaction Diffusion.
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 Qualifications
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Degree
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University
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Specialization
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Graduation year
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| 1 | PHD | University of Surrey | Mathematics | 2003 | | 2 | MASTER DEGREE | Yarmouk University | Mathematics | 1988 |
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 Experiences
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Academic Experience:
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 2013 -2014 :Associate Prof.,Taibah University,Saudi Arabia.
2010 -2017 :Associate Prof.,Prince Hussein bin Abdullah II Academy of Civil Protection.,Jordan.
2005 -2006 :Associate Prof.,Jordan University,Jordan.
2004 -2005 :Adjunct Professor,NYIT,Jordan.
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Administrative Experience:
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 Publications
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1- Fekete-Szego results for certain BI-univalent functions
involving q-analogues of logarithmic functions ,Results in Nonlinear Analysis, 2024,Vol. 7,no. 3.
2- Dynamics of a harvested stage-structured predator?prey
model with distributed maturation delay ,Math. Meth. Appl. Sci, 2022,Vol. 44,no. 2.
3- Persistence and global stability of a stage- structured food chain model with distributed maturation delay and harvesting ,Commun. Math. Biol. and Neurosci. 2019, 2019:9, 2019,Vol. 2019,no. 9.
4- A New Version of the Generalized Kr?tzel-Fox
Integral Operators ,Mathematics, 2018,Vol. 2018,no. 6,222.
5- Some extensions of a certain Integral transform to a quotient space of generalized function
,Open Math, 2015,Vol. 13,no. 2015.
6- A stage-structured predator?prey model with distributed
maturation delay and harvesting ,Journal of Biological Dynamics, 2015,Vol. 9,no. 2015.
7- The effect of state dependent delay and harvesting on a
stage-structured predator?prey model ,Applied Mathematics and Computation, 2015,Vol. 271,no. 2015.
8- Hartley Transform for Lp Boehmians
and Spaces of Ultradistributions ,International Mathematical Forum, 2012,Vol. 7-2012,no. 9.
9- Global stability in a structured population competition model with
distributed maturation delay and harvesting ,NonLinear Analysis : Real World Applications, 2011,Vol. 12,no. 3.
10- Extension Analysis for Fourier Transformations
of Generalized Functions ,Applied Mathematical Sciences, 2010,Vol. 4,no. 60.
11- On Fourier transforms of
ultra-distributions of slow growth and their multipliers
,Applied Mathematical Sciences, 2010,Vol. 4,no. 60.
12- Modeling of Weather Characteristics in Jordan ,International Journal of Ecological Economics & Statistics, 2009,Vol. 15,no. F09.
13- Modelling and Analysis of Stage-Structured
Population Model with State-Dependent
Maturation Delay and Harvesting ,Int. Journal of Math. Analysis, 2007,Vol. 1,no. 8.
14- Stability and Optimal Harvesting in Lotka-Volterra Competition Model for Two-species with Stage Structure ,KYUNGPOOK Math. Journal, 2007,Vol. 47,no. 2007.
15- Dynamics of a stage-structured
population model incorporating a state-dependent maturation delay
,Nonlinear Analysis: Real World Applications, 2005,Vol. 6,no. 2005.
16- A nonlocal reaction-diffusion model for a single
species with stage structure and distributed
maturation delay ,Euro Jnl of Applied Mathematics, 2005,Vol. 16,no. 2005.
17- Monotone wave-fronts in a structured population model with distributed
maturation delay ,IMA Journal of Applied Mathematics, 2004,Vol. 70,no. 2005.
18- Monotone travelling fronts in an
age-structured reaction?diffusion model of a single species
,Journal of Mathematical Biology, 2002,Vol. 45,no. 2002.
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 University Courses Taught
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1- Ordinary Differential Equations.
2- Engineering Analysis.
3- Partial Differential Equations.
4- Numerical Analysis.
5- Calculus I-II.
6- Engineering Analysis 2.
7- Advanced Engineering Mathematics (Master Students).
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 Master and Phd thesis contributions
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Thesis Supervision
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 Analysis and stability of some Biomathematical Models of Multi-Species Interaction in the Differential Equations.,Al al-Bayt University,Master Thesis,2009.
Analysis and Stability of Delay Differential Equations with its Applications, ,Al al-Bayt University,Master Thesis,2009.
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 Honors and Academics Awards
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Award Name
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Donor Name
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Award Year
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Award Country
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| 1 | Distinguished Researcher | Al-Balqa Applied Univrsity | 2017 | Jordan | | 2 | Whos Who in Science and Engineering | MARQUIS Whos Who | 2007 | United States of America |
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 Journals Editor/ Reviewer
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Editors
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SCIREA Journal of Mathematics.
American Journal of Applied Mathematics and Statistics.
Journal of Applied Mathematics and Physics.
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Review:
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- Journal of Applied Mathematics and Computations.
- Communications in Mathematical Biology and Neuroscience.
- Journal of Biological Dynamics.
- African Journal of Mathematics and Computer Science Research.
- Journal of Nonlinear Dynamics.
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