scholarly journals A Study of a Diseased Prey-Predator Model with Refuge in Prey and Harvesting from Predator

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Ahmed Sami Abdulghafour ◽  
Raid Kamel Naji
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Equilibrium Points ◽  
Nonlinear Ordinary Differential Equations ◽  
First Order ◽  
Persistence Conditions ◽  
System Solution ◽  
Predator Model ◽  
Predator System ◽  
Infected Prey

In this paper, a mathematical model of a prey-predator system with infectious disease in the prey population is proposed and studied. It is assumed that there is a constant refuge in prey as a defensive property against predation and harvesting from the predator. The proposed mathematical model is consisting of three first-order nonlinear ordinary differential equations, which describe the interaction among the healthy prey, infected prey, and predator. The existence, uniqueness, and boundedness of the system’ solution are investigated. The system's equilibrium points are calculated with studying their local and global stability. The persistence conditions of the proposed system are established. Finally the obtained analytical results are justified by a numerical simulation.

scholarly journals A Mathematical Study on a Diseased Prey-Predator Model with Predator Harvesting

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Srinivasarao Thota
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Local Stability ◽  
Equilibrium Points ◽  
Mathematical Study ◽  
First Order ◽  
Predator Model ◽  
Predator System ◽  
Infected Prey ◽  
First Order Differential Equations

 In this paper, we present a mathematical model for a prey-predator system with infectious disease in the prey population. We assumed that there is harvesting from the predator and a defensive property against predation. This model is constituted by a system of nonlinear decoupled ordinary first order differential equations, which describe the interaction among the healthy prey, infected prey and predator. The existence, uniqueness and boundedness of the system solutions are investigated. Local stability of the system at equilibrium points is discussed.  

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

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 of varying the parameters. It is observed that the system has a chaotic dynamics.

scholarly journals A Prey-Predator Model with Michael Mentence Type of Predator Harvesting and Infectious Disease in Prey

2020 ◽  
pp. 1146-1163
Author(s):  
Hiba Abdullah Ibrahim ◽  
Raid Kamel Naji
Keyword(s):  
Infectious Disease ◽  
Numerical Simulations ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Analytical Results ◽  
Predator Model ◽  
Disease In Prey

A prey-predator model with Michael Mentence type of predator harvesting and infectious disease in prey is studied. The existence, uniqueness and boundedness of the solution of the model are investigated. The dynamical behavior of the system is studied locally as well as globally. The persistence conditions of the system are established. Local bifurcation near each of the equilibrium points is investigated. Finally, numerical simulations are given to show our obtained analytical results.

scholarly journals The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Raid Kamel Naji ◽  
Salam Jasim Majeed
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Stage Structure ◽  
Dynamical Analysis ◽  
Local Bifurcation ◽  
Structure Population ◽  
Global Stability Analysis ◽  
Proposed Model ◽  
Predator Model ◽  
Predator System

We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model are discussed. All the feasible equilibrium points are determined. The local and global stability analysis of them are investigated. The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork) near each of the equilibrium points is studied. Finally, numerical simulations are given to support the analytic results.

scholarly journals A prey-predator model with infection in both prey and predator

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1753-1767 ◽  
Author(s):  
S.P. Bera ◽  
A. Maiti ◽  
G.P. Samanta
Keyword(s):  
Differential Equation ◽  
Computer Simulations ◽  
Equilibrium Points ◽  
Predator Model ◽  
Predator System

This paper aims to study the dynamical behaviours of a prey-predator system where both prey and predator populations are affected by diseases. A system of four differential equation has been proposed and analyzed. Stability of the equilibrium points of the model has been investigated. Computer simulations are carried out to illustrate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.

Quasiperiodicity and Chaos in a Generalized Nosé–Hoover Oscillator

2016 ◽  
Vol 26 (10) ◽  
pp. 1650170 ◽  
Author(s):  
Paulo C. Rech
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Harmonic Oscillator ◽  
Parameter Space ◽  
Nonlinear Ordinary Differential Equations ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
First Order ◽  
Chaotic Region ◽  
Quasiperiodic Structures

This paper reports on an investigation of the two-dimensional parameter-space of a generalized Nosé–Hoover oscillator. It is a mathematical model of a thermostated harmonic oscillator, which consists of a set of three autonomous first-order nonlinear ordinary differential equations. By using Lyapunov exponents to numerically characterize the dynamics of the model at each point of this parameter-space, it is shown that dissipative quasiperiodic structures are present, embedded in a chaotic region. The same parameter-space is also used to confirm the multistability phenomenon in the investigated mathematical model.

A STUDY OF BIFURCATION OF PREY–PREDATOR MODEL WITH TIME DELAY AND HARVESTING USING FUZZY PARAMETERS

2018 ◽  
Vol 26 (02) ◽  
pp. 339-372 ◽  
Author(s):  
D. PAL ◽  
G. S. MAHAPATRA ◽  
G. P. SAMANTA
Keyword(s):  
Time Delay ◽  
Equilibrium Points ◽  
Fuzzy Model ◽  
Solution Procedure ◽  
Distance Method ◽  
Gestation Delay ◽  
Fuzzy Environment ◽  
Predator Model ◽  
The Stability ◽  
Predator System

In this work, a fuzzy prey–predator system with time delay is proposed. The model consists of two preys and one predator. The biological coefficients/parameters are considered as imprecise in nature and quantified by triangular fuzzy numbers. We have studied the effect of gestation delay on the stability of the system in fuzzy environment. The signed distance method for the defuzzification of the proposed fuzzy prey–predator system is adopted. For the underlying fuzzy model, we have provided a solution procedure to find all possible equilibrium points and studied their stabilities in the fuzzy sense. It is observed that there are stability switches, and Hopf-bifurcation occurs when the delay crosses some critical value in fuzzy sense. Numerical illustrations are provided in crisp as well as fuzzy environment with the help of graphical presentations to support our proposed approach.

scholarly journals Dynamic Prey Predator Model and multiple forms of Harvest of Infected Prey

2019 ◽  
Vol 24 (4) ◽  
pp. 87
Author(s):  
S. A. Wuhaib ◽  
M. H. Mansour
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Equilibrium Points ◽  
Nonlinear Function ◽  
Response Type ◽  
Multiple Forms ◽  
Predator Model ◽  
The Stability ◽  
The Relationship ◽  
Infected Prey

In this paper, the dynamic of prey predator model was discussed when the relationship between them is functional response type III. In addition, when prey exposure to the disease as nonlinear function. Also the infected prey exposed to harvest as a nonlinear and as linear function. The bounded and positive solutions, periodic, conditions of equilibrium points and the stability were we discussed Some results were illustrated in numerical simulations, and show we can use the linear function of harvesting to control on the dices   http://dx.doi.org/10.25130/tjps.24.2019.079

scholarly journals Theoretical Analysis of an Imprecise Prey-Predator Model with Harvesting and Optimal Control

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Anjana Das ◽  
M. Pal
Keyword(s):  
Complex Dynamics ◽  
Equilibrium Points ◽  
Uniform Boundedness ◽  
Optimal Harvesting ◽  
Model Parameters ◽  
Predator Species ◽  
Proposed Model ◽  
Existence And Stability ◽  
Predator Model ◽  
Predator System

In our present paper, we formulate and study a prey-predator system with imprecise values for the parameters. We also consider harvesting for both the prey and predator species. Then we describe the complex dynamics of the proposed model system including positivity and uniform boundedness of the system, and existence and stability criteria of various equilibrium points. Also the existence of bionomic equilibrium and optimal harvesting policy are thoroughly investigated. Some numerical simulations have been presented in support of theoretical works. Further the requirement of considering imprecise values for the set of model parameters is also highlighted.

scholarly journals Solving an Infectious Disease Model considering Its Anatomical Variables with Stochastic Numerical Procedures

2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Yolanda Guerrero Sánchez
Keyword(s):  
Infectious Disease ◽  
Disease Model ◽  
Mean Square ◽  
Artificial Neuron ◽  
Infectious Disease Model ◽  
Neuron Networks ◽  
Levenberg Marquardt ◽  
The Mean ◽  
Predator Model ◽  
Infected Prey

The aim of the current work is to perform the numerical investigation of the infectious disease based on the nonlinear fractional order prey-predator model using the Levenberg–Marquardt backpropagation (LMB) based on the artificial neuron networks (ANNs), i.e., LMBNNs. The fractional prey-predator model is classified into three categories, the densities of the susceptible, infected prey, and predator populations. The statistics proportions for solving three different variations of the infectious disease based on the fractional prey-predator model are designated for training 80% and 10% for both validation and testing. The numerical actions are performed using the LMBNNs to solve the infectious disease based on the fractional prey-predator model, and comparison is performed using the database Adams–Bashforth–Moulton approach. The infectious disease based on the fractional prey-predator model is solved using the LMBNNs to reduce the mean square error (M.S.E). In order to validate the exactness, capability, consistency, and competence of the proposed LMBNNs, the numerical procedures using the correlation, M.S.E, regression, and error histograms are drawn.

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