A Prey–Predator Model with Pathogen Infection on Predator Population

2020 ◽  
pp. 275-297
Author(s):  
Sanchayita Pramanick ◽  
Joydeb Bhattacharyya ◽  
Samares Pal
Keyword(s):  
Predator Population ◽  
Pathogen Infection ◽  
Predator Model

EFFECT OF TIME-DELAY ON A PREY–PREDATOR MODEL WITH MICROPARASITE INFECTION IN THE PREDATOR

2011 ◽  
Vol 19 (02) ◽  
pp. 365-387 ◽  
Author(s):  
SWETA PATHAK ◽  
ALAKES MAITI ◽  
SHYAM PADA BERA
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Predator Population ◽  
Dynamical Characteristics ◽  
Dynamical Behaviors ◽  
Discrete Time Delay ◽  
Mathematical Analyses ◽  
Predator Model ◽  
Living Organisms

To increase a prey population that is attacked by a predator it is more convenient and economical to choose the living organisms to control the predator. In this paper, the dynamical behaviors of a prey–predator model with microparasitic infection in the predator have been discussed. In this epidemiological model the microparasite is horizontally transmitted and attacks the predator population only. The infected population does not recover or become immune. The dynamical characteristics of the system are studied through mathematical analyses. The role of discrete time-delay has been discussed to show that time-delay can induce instability and oscillation. Numerical simulations are carried out. Biological implications have been discussed.

scholarly journals Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Chao Liu ◽  
Qingling Zhang ◽  
Jinna Li
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Global Stability ◽  
Interaction Mechanism ◽  
Prey Population ◽  
Predator Population ◽  
Optimal Control Strategy ◽  
Global Stability Analysis ◽  
Selective Harvest ◽  
Predator Model

We propose an ecoepidemiological prey predator model, where selective harvest effort on predator population is considered. Vaccination and taxation are introduced as control instruments, which are utilized to control number of susceptible prey population and protect predator population from overexploitation, respectively. Conditions which influence nonnegativity and boundedness of solutions are studied. Global stability analysis around disease-free equilibrium is discussed based on robust Bendixson criterion, which is theoretically beneficial to studying coexistence and interaction mechanism of population within harvested ecoepidemiological system. By using Pontryagin’s maximum principle, an optimal control strategy is derived to maximize the total discounted net economic revenue to society as well as protect prey population from infectious disease. Numerical simulations are carried out to show the consistency with theoretical analysis.

scholarly journals Stability Analysis of a Harvested Prey-Predator Model with Stage Structure and Maturation Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Liu ◽  
Qingling Zhang ◽  
James Huang
Keyword(s):  
Stability Analysis ◽  
Stage Structure ◽  
Model System ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Maturation Delay ◽  
Effort Level ◽  
Selective Harvest ◽  
Proposed Model ◽  
Predator Model

A harvested prey-predator model with density-dependent maturation delay and stage structure for prey is proposed, where selective harvest effort on predator population is considered. Conditions which influence positiveness and boundedness of solutions of model system are analytically investigated. Criteria for existence of all equilibria and uniqueness of positive equilibrium are also studied. In order to discuss effects of maturation delay and harvesting on model dynamics, local stability analysis around all equilibria of the proposed model system is discussed due to variation of maturation delay and harvest effort level. Furthermore, global stability of positive equilibrium is investigated by utilizing an iterative technique. Finally, numerical simulations are carried out to show consistency with theoretical analysis.

scholarly journals Prey-predator model in drainage system with migration and harvesting

2021 ◽  
Vol 8 (1) ◽  
pp. 152-167
Author(s):  
Banani Roy ◽  
Sankar Kumar Roy
Keyword(s):  
Functional Response ◽  
Control Parameter ◽  
Drainage System ◽  
Fishing Effort ◽  
Future Research ◽  
Generalist Predator ◽  
Predator Population ◽  
Resource Rent ◽  
Dynamic Framework ◽  
Predator Model

Abstract In this paper, we consider a prey-predator model with a reserve region of predator where generalist predator cannot enter. Based on the intake capacity of food and other factors, we introduce the predator population which consumes the prey population with Holling type-II functional response; and generalist predator population consumes the predator population with Beddington-DeAngelis functional response. The density-dependent mortality rate for prey and generalist predator are considered. The equilibria of proposed system are determined. Local stability for the system are discussed. The environmental carrying capacity is considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighbourhood at an interior equilibrium point. Here the fishing effort is used as a control parameter to harvest the generalist predator population of the system. With the help of this control parameter, a dynamic framework is developed to investigate the optimal utilization of resources, sustainability properties of the stock and the resource rent. Finally, we present a numerical simulation to verify the analytical results, and the system is analyzed through graphical illustrations. The main findings with future research directions are described at last.

scholarly journals Adomian Decomposition Method for Solving Ratio-Dependent Prey-Predator System with Harvesting on Predator

2016 ◽  
Vol 15 ◽  
pp. 36-42
Author(s):  
V. Madhusudanan ◽  
P.N. Duraiswamy ◽  
S. Vijaya
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Predator Population ◽  
Traditional Methods ◽  
Adomian Decomposition ◽  
Numerical Discretization ◽  
Ratio Dependent ◽  
Predator Model ◽  
Predator System

In this article, Adomian Decomposition Method is used to find out the approximate solution of ratio-dependent prey-predator model with predator harvesting. The significance of ADM over other numerical discretization techniques is that it has the eminence to solve problems directly with no un-physical restrictive assumptions such as linearization, per-turbation, massive computation and any other transformation. ADM solves the problem and arrives at the approximate solution in the form of series with solution components that are easily computable. It requires very less work in comparison with other traditional methods. The graphical representations of prey and predator population contrasted with time are drawn to examine the performance and reliability of this technique.

scholarly journals Prey-Predator Model with Two-Stage Infection in Prey: Concerning Pest Control

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Swapan Kumar Nandi ◽  
Prasanta Kumar Mondal ◽  
Soovoojeet Jana ◽  
Palash Haldar ◽  
T. K. Kar
Keyword(s):  
Early Stage ◽  
Dynamical Behavior ◽  
Viral Disease ◽  
Prey Population ◽  
Predator Population ◽  
Two Stage ◽  
Alternative Source ◽  
Modified Model ◽  
Predator Model ◽  
Parameter Values

A prey-predator model system is developed; specifically the disease is considered into the prey population. Here the prey population is taken as pest and the predators consume the selected pest. Moreover, we assume that the prey species is infected with a viral disease forming into susceptible and two-stage infected classes, and the early stage of infected prey is more vulnerable to predation by the predator. Also, it is assumed that the later stage of infected pests is not eaten by the predator. Different equilibria of the system are investigated and their stability analysis and Hopf bifurcation of the system around the interior equilibriums are discussed. A modified model has been constructed by considering some alternative source of food for the predator population and the dynamical behavior of the modified model has been investigated. We have demonstrated the analytical results by numerical analysis by taking some simulated set of parameter values.

scholarly journals Effects of Refuge Prey on Stability of the Prey-Predator Model Subject to Immigrants: A Mathematical Modelling Approach

2021 ◽  
Vol 47 (4) ◽  
pp. 1376-1391
Author(s):  
Mussa Amos Stephano ◽  
Il Hyo Jung
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Functional Response ◽  
Volterra Model ◽  
Predator Population ◽  
Type I ◽  
Proposed Model ◽  
Predator Model ◽  
Model Subject ◽  
Type Ii Functional Response

Prey-predator system is enormously complex and nonlinear interaction between species. Such complexity regularly requires development of new approaches which involves more factors in analysis of its population dynamics. In this paper, we formulate a modified Lotka-Volterra model that incorporates factors such as refuge prey and immigrants. We investigate the effects of refuge prey and immigrants by varying the refuge factor, with and without immigrants. The results show that with Holling’s type I functional response, the proposed model is asymptotically convergent when a refuge prey factor is introduced. Moreover, with Holling’s type II functional response, the proposed mathematical model is unstable and does not converge. However, with Holling’s type III functional response in a system, the proposed mathematical model is asymptotically stable. These results point out the following remarks: The effects of refuge prey on stability of the dynamical system vary depending on the type of functional response, and when the predator population increases, the likelihood of prey extinction declines when the proportion of preys in refuge population increases. Hence, the factor of refuge prey is crucial for controlling the population of the predator and obtaining balances between prey and predator in the ecosystem. Keywords: Refuge prey, stability, prey-predator, immigrants, Mathematical modelling

scholarly journals Forecasting the Number of Tuberculosis (TBC) Using Fuzzy Prey Predator

2021 ◽  
Author(s):  
FE. Universitas Andi Djemma
Keyword(s):  
Infectious Disease ◽  
Health Problem ◽  
Prey Population ◽  
Predator Population ◽  
Major Health Problem ◽  
Major Health ◽  
Data Source ◽  
Predator Model

Tuberculosis (TB or TB) is an infectious disease caused by the bacteriumMycobacterium tuberculosis. Tuberculosis (TB) is still a major health problem in theworld, so from this it is necessary to forecast to determine the increase in the number ofTB diseases, and later can be taken in prevention. This study uses the Fuzzy preypredator method. The data source used is data on TB patients at Batumarmar HealthCenter. From the results of this study, it was found that the population of Prey andPredator was sought for stability, so that after applying the fuzzy prey predator model,convergent results were obtained. Prey population and Predator population decreasedfor one month, afterwards covergen.

scholarly journals Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis

2021 ◽  
Vol 18 (5) ◽  
pp. 6672-6699
Author(s):  
Yong Luo ◽  
Keyword(s):  
Classical Solution ◽  
Linear Instability ◽  
Instability Criterion ◽  
Predator Population ◽  
Population System ◽  
Dependent Case ◽  
Density Dependent ◽  
Existence And Stability ◽  
Dimensional Distribution ◽  
Predator Model

<abstract><p>We study the existence of global unique classical solution to a density-dependent prey-predator population system with indirect prey-taxis effect. With two Lyapunov functions appropriately constructed, we then show that the solution can asymptotically approach prey-only state or coexistence state of the system under suitable conditions. Moreover, linearized analysis on the system at these two constant steady states shows their linear instability criterion. By numerical simulation we find that some density-dependent prey-taxis and predators' diffusion may either flatten the spatial one-dimensional patterns which exist in non-density-dependent case, or break the spatial two-dimensional distribution similarity which occurs in non-density-dependent case between predators and chemoattractants (released by prey).</p></abstract>

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