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 Dynamics of Leslie-Gower Pest-Predator Model with Disease in Pest Including Pest-Harvesting and Optimal Implementation of Pesticide

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Agus Suryanto ◽  
Isnani Darti
Keyword(s):  
Population Control ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Pest Population ◽  
Proposed Model ◽  
Natural Predator ◽  
Predator Model ◽  
Optimal Implementation

We propose a model which describes the interaction between pest and its natural predator. We assume that pest can be infected with diseases or pathogens such as bacteria, fungi, and viruses. The model is constructed by combining the Leslie-Gower model and S-I epidemic model. It is also considered the effects of pest harvesting. Harvesting in this case is intended to take a number of pests as one of the pest population control strategies. The proposed model will be analyzed dynamically to study its qualitative behaviour. The dynamical analysis includes the determination of all possible equilibrium points and their stability properties. Furthermore we also discuss the implementation of pesticide control where its optimal strategy is determined by Pontryagin’s maximum principle. To support our analytical studies, we perform some numerical simulations and their interpretation.

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 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 Dynamical Analysis of Transmission of Hepatitis B and C Viruses with External Source of disease by Mathematical Model

2021 ◽  
Author(s):  
Ahmed Mohsen ◽  
Khalid Hattaf ◽  
Hassan AL-Husseiny
Keyword(s):  
Mathematical Model ◽  
Hepatitis B ◽  
Hepatitis Virus ◽  
Control Strategies ◽  
Equilibrium Points ◽  
External Source ◽  
Dynamical Analysis ◽  
Proposed Model ◽  
B Virus ◽  
The Government

Abstract In this paper, we develop a deterministic mathematical model of the Hepatitis B and C viruses transmission in population, which allows transmission by two way vertical such as from pregnant mother to fetus and horizontal. Also, by two way through direct contact and due to the external source of infective such as blood transfusion or other. In reality, we know that there is a vaccination against the hepatitis B virus but so far, there is no vaccine against the hepatitis C virus this is why it is considered more dangerous than hepatitis B. Furthermore, we study the vaccination effect with the failure in the vaccine. We propose an SVIBICR model using a system of ordinary differential equations. First the major basic analysis, like the uniqueness, boundedness and positivity of the solution for the proposed model. Second the existence of all biological equilibrium points, basic reproduction number and stability analysis of all equilibrium points. The numerical simulation indicated to confirm the analytic results and the government must apply all control strategies in combating hepatitis virus at short periods of time.

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 The Dynamics of A Square Root Prey-Predator Model with Fear

2020 ◽  
pp. 139-146
Author(s):  
Nabaa Hassain Fakhry ◽  
Raid Kamel Naji
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Global Dynamics ◽  
Local Bifurcation ◽  
Square Root ◽  
Predator Species ◽  
Local Bifurcation Analysis ◽  
Predator Model ◽  
The Stability ◽  
Predator System

An ecological model consisting of prey-predator system involving the prey’s fear is proposed and studied. It is assumed that the predator species consumed the prey according to prey square root type of functional response. The existence, uniqueness and boundedness of the solution are examined. All the possible equilibrium points are determined. The stability analysis of these points is investigated along with the persistence of the system. The local bifurcation analysis is carried out. Finally, this paper is ended with a numerical simulation to understand the global dynamics of the system.

scholarly journals The Dynamical Behavior of Stage Structured Prey-Predator Model in the Harvesting and Toxin Presence

2019 ◽  
Vol 54 (6) ◽  
Author(s):  
Azhar Abbas Majeed ◽  
Moayad H. Ismaeel
Keyword(s):  
Mathematical Model ◽  
Functional Response ◽  
Lyapunov Functions ◽  
Numerical Models ◽  
Dynamical Behavior ◽  
Stage Structure ◽  
Suggested Model ◽  
Final Point ◽  
Predator Model ◽  
Predator System

In this study, a mathematical model that consists of a form of prey-predator system with stage structure in the presence of harvesting and toxicity has been proposed and studied by using the classic Lotka-Volterra functional response. The presence, uniqueness, and boundedness resolution of the suggested model are discussed. The steadiness enquiries of all possible stability points tare studied. The global steadiness of these stability points are accomplished by fitting Lyapunov functions. As a final point, numerical models are put through not just for conforming tthe hypothetical results attained, but also to demonstrate the influences of distinction of each factor on the suggested paradigm.

BIFURCATION AND CONTROL IN A DIFFERENTIAL-ALGEBRAIC HARVESTED PREY-PREDATOR MODEL WITH STAGE STRUCTURE FOR PREDATOR

2008 ◽  
Vol 18 (10) ◽  
pp. 3159-3168 ◽  
Author(s):  
CHAO LIU ◽  
QINGLING ZHANG ◽  
YUE ZHANG ◽  
XIAODONG DUAN
Keyword(s):  
Stage Structure ◽  
Algebraic Model ◽  
Model System ◽  
Positive Equilibrium ◽  
Proposed Model ◽  
Stability And Instability ◽  
Differential Algebraic System ◽  
Predator Model ◽  
And Control ◽  
Predator System

A differential-algebraic model system which considers a prey-predator system with stage structure for a predator and a harvest effort on the mature predator is proposed. By using the differential-algebraic system and bifurcation theories, the local stability and instability mechanism of the proposed model system are investigated. With the purpose of stabilizing the proposed model system at the positive equilibrium, a state feedback controller is designed. Finally, a numerical simulation is carried out to show the consistency with theoretical analysis and illustrate the effectiveness of the proposed controller.

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 An Impulsively Controlled Three-Species Prey-Predator Model with Stage Structure and Birth Pulse for Predator

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yanyan Hu ◽  
Mei Yan ◽  
Zhongyi Xiang
Keyword(s):  
Small Amplitude ◽  
Floquet Theory ◽  
Stage Structure ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Birth Pulse ◽  
Impulsive Equation ◽  
Predator Model ◽  
Predator System

We investigate the dynamic behaviors of a two-prey one-predator system with stage structure and birth pulse for predator. By using the Floquet theory of linear periodic impulsive equation and small amplitude perturbation method, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we study the permanence of the investigated model. Our results provide valuable strategy for biological economics management. Numerical analysis is also inserted to illustrate the results.

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