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A reliable iterative method for solving the epidemic model and the prey and predator problems
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In the present article, we implement the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763] to solve two problems; the first one is the problem of spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of the prey and predator. The results demonstrate that the method has many merits such as being derivative-free, overcome the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition Method (ADM), does not require to calculate Lagrange multiplier as in Variational Iteration Method (VIM) and no needs to construct a homotopy as in Homotopy Perturbation Method (HPM). The results obtained are compared with the results by existing methods and prove that the presented method is very effective, simple and does not require any restrictive assumptions for nonlinear terms. The software used for the numerical calculations in this study was MATHEMATICA r 8.0.

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Publication Date
Wed Jan 01 2020
Journal Name
Proceedings Of The 2020 2nd International Conference On Sustainable Manufacturing, Materials And Technologies
The food web prey-predator model with toxin
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Publication Date
Sun Jan 01 2023
Journal Name
Communications In Mathematical Biology And Neuroscience
A reliable numerical simulation technique for solving COVID-19 model
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Publication Date
Sun Dec 07 2014
Journal Name
Baghdad Science Journal
New Iterative Method for Solving Nonlinear Equations
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The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

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Publication Date
Fri Jan 01 2016
Journal Name
Results In Physics
An efficient iterative method for solving the Fokker–Planck equation
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Publication Date
Sat Dec 01 2018
Journal Name
Ain Shams Engineering Journal
A semi-analytical iterative method for solving differential algebraic equations
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Publication Date
Mon Dec 30 2024
Journal Name
Iraqi Journal Of Science
The Impact of Fear and Anti-Predator Behavior on the Dynamics of Stage-Structure Prey–Predator Model With a Harvesting
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In this paper, an ecological model with stage-structure in prey population, fear, anti-predator and harvesting are suggested. Lotka-Volterra and Holling type II functional responses have been assumed to describe the feeding processes . The local and global stability of steady points of this model are established. Finally, the global dynamics are studied numerically to investigate the influence of the parameters on the solutions of the system, especially the effect of fear and anti-predation.

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Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
The Dynamics and Analysis of Stage-Structured Predator-Prey Model Involving Disease and Refuge in Prey Population
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Abstract<p>Start your abstract here the objective of this paper is to study the dynamical behaviour of an eco-epidemiological system. A prey-predator model involving infectious disease with refuge for prey population only, the (SI_) infectious disease is transmitted directly, within the prey species from external sources of the environment as well as, through direct contact between susceptible and infected individuals. Linear type of incidence rate is used to describe the transmission of infectious disease. While Holling type II of functional responses are adopted to describe the predation process of the susceptible and infected predator respectively. This model is represented mathematically by </p> ... Show More
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Publication Date
Tue Mar 26 2019
Journal Name
International Journal Of Mathematics And Mathematical Sciences
Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting
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In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.

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Publication Date
Wed Jun 03 2020
Journal Name
Journal Of Applied Mathematics
Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting
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In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect

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Publication Date
Tue Jan 10 2012
Journal Name
Iraqi Journal Of Science
THE IMPACT OF DISEASE AND HARVESTING ON THE DYNAMICAL BEHAVIOR OF PREY PREDATOR MODEL
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In this paper, a harvested prey-predator model involving infectious disease in prey is considered. The existence, uniqueness and boundedness of the solution are discussed. The stability analysis of all possible equilibrium points are carried out. The persistence conditions of the system are established. The behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that the existence of disease and harvesting can give rise to multiple attractors, including chaos, with variations in critical parameters.

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