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.

EFFECT OF VIRAL INFECTION ON THE GENERALIZED GAUSE MODEL OF PREDATOR-PREY SYSTEM

2003 ◽  
Vol 11 (01) ◽  
pp. 19-26 ◽  
Author(s):  
J. CHATTOPADHYAY ◽  
A. MUKHOPADHYAY ◽  
P. K. ROY
Keyword(s):  
Viral Infection ◽  
Specific Growth ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Predator Population ◽  
Predator Prey ◽  
Stability Behavior ◽  
Force Of Infection ◽  
Prey System ◽  
Infected Prey

The generalized Gause model of predator-prey system is revisited with an introduction of viral infection on prey population. Stability behavior of such modified system is carried out to observe the change of dynamical behavior of the system. To substantiate the analytical results of this generalized susceptible prey, infected prey and predator population, numerical simulations of the model with specific growth and response functions are performed. Our observations suggest that the disease on prey population has a destabilizing or stabilizing effect depending on the level of force of infection and may act as a biological control for the persistence of the species.

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.

SPATIOTEMPORAL DYNAMICS OF AN ECOEPIDEMIOLOGICAL MODEL WITH STANDARD INCIDENCE

2007 ◽  
Vol 07 (02) ◽  
pp. 175-197
Author(s):  
BANIBRATA MUKHOPADHYAY ◽  
R. BHATTACHARYYA
Keyword(s):  
Traveling Wave ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Homogeneous System ◽  
Viral Disease ◽  
Prey Population ◽  
Predator Species ◽  
Predator Prey ◽  
Prey Interaction ◽  
Bifurcation Behavior

We analyze a mathematical model of predator–prey interaction where the prey population is infected with a viral disease. Infection in the prey population is assumed to follow standard incidence. The dynamical behavior of the system is studied in terms of stability aspects. To model the gestation lag of the predator species and the spatially heterogeneous characteristics of an ecological population, we incorporate the concept of diffusionally coupled delay into the system. The bifurcation behavior of the delayed homogeneous system is studied. The existence of traveling wave solutions for the delay–diffusion model is established. Numerical simulations are performed to justify analytical findings.

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 MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN INTERACTION WITH MIXED FUNCTIONAL RESPONSE

2012 ◽  
Vol 09 ◽  
pp. 334-340 ◽  
Author(s):  
MADA SANJAYA WS ◽  
ISMAIL BIN MOHD ◽  
MUSTAFA MAMAT ◽  
ZABIDIN SALLEH
Keyword(s):  
Mathematical Model ◽  
Functional Response ◽  
Food Chain ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Bifurcation Points ◽  
Dynamical Behaviors ◽  
Practical Life ◽  
Parameter Values ◽  
Chain Interaction

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

An explicit plethora of soliton solutions for a new microtubules transmission lines model: A fractional comparison

2021 ◽  
Author(s):  
Nauman Raza ◽  
Ziyad A. Alhussain
Keyword(s):  
Nonlinear Dynamics ◽  
Transmission Lines ◽  
Fractional Derivatives ◽  
Intracellular Transport ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Governing System ◽  
Parameter Values ◽  
Fractional Parameter

This paper introduces a new fractional electrical microtubules transmission lines model in the sense of Atangana–Baleanu and beta derivatives to comprehend nonlinear dynamics of the governing system. This structure possesses one of the most important parts in cellular process biology and fractional parameter incorporates the memory effects in microtubules. Also, microtubules are extremely beneficial in cell motility, signaling and intracellular transport. The new extended direct algebraic method is a compelling and persuasive integrating scheme to extract soliton solutions. The retrieved solutions include dark, bright and singular solitons. This model executes a prominent part in exhibiting the wave transmission in nonlinear systems. The novelty and advantage of the proposed method are portrayed by applying it to this model and its dynamical behavior is depicted by 3D and 2D plots. A comparative study of two fractional derivatives at distinct fractional parameter values and graphics of sensitivity analysis is also carried out in this paper.

Dynamics and bifurcations of a discrete-time prey-predator model with Allee effect on the prey population

2021 ◽  
Vol 48 ◽  
pp. 100962
Author(s):  
Z. Eskandari ◽  
J. Alidousti ◽  
Z. Avazzadeh ◽  
J.A. Tenreiro Machado
Keyword(s):  
Discrete Time ◽  
Allee Effect ◽  
Prey Population ◽  
Predator Model

Lexical and sentential priming in competition: Implications for two-stage theories of lexical access

2001 ◽  
Vol 22 (2) ◽  
pp. 191-215 ◽  
Author(s):  
ARTURO E. HERNANDEZ ◽  
CHRISTINE FENNEMA-NOTESTINE ◽  
CARE UDELL ◽  
ELIZABETH BATES
Keyword(s):  
Lexical Access ◽  
Time Window ◽  
Early Stage ◽  
Time Windows ◽  
Unrelated Word ◽  
Two Stage ◽  
Sentential Context ◽  
Lexical Priming ◽  
Priming Word ◽  
Stage Theories

This article presents a new method that can compare lexical priming (word–word) and sentential priming (sentence–word) directly within a single paradigm. We show that it can be used to address modular theories of word comprehension, which propose that the effects of sentence context occur after lexical access has taken place. Although lexical priming and sentential priming each occur very quickly in time, there should be a brief time window in which the former is present but the latter is absent. Lexical and sentential priming of unambiguous words were evaluated together, in competing and converging combinations, using time windows designed to detect an early stage where lexical priming is observed but sentential priming is not. Related and unrelated word pairs were presented visually, in rapid succession, within auditory sentence contexts that were either compatible or incompatible with the target (the second word in each pair). In lexical decision, the additive effects of lexical priming and sentential priming were present under all temporal conditions, although the latter was always substantially larger. In cross-modal naming, sentential priming was present in all temporal conditions; lexical priming was more fragile, interacting with timing and sentential congruence. No evidence was found for a stage in which lexical priming is present but sentential priming is absent – a finding that is difficult to reconcile with two-stage models of lexical versus sentential priming. We conclude that sentential context operates very early in the process of word recognition, and that it can interact with lexical priming at the earliest time window.

scholarly journals Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Kankan Sarkar ◽  
Subhas Khajanchi ◽  
Prakash Chandra Mali ◽  
Juan J. Nieto
Keyword(s):  
Growth Rate ◽  
Hopf Bifurcation ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Uniform Persistence ◽  
Functional Responses ◽  
Normal Form Theory ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Prey System

In this study, we investigate a mathematical model that describes the interactive dynamics of a predator-prey system with different kinds of response function. The positivity, boundedness, and uniform persistence of the system are established. We investigate the biologically feasible singular points and their stability analysis. We perform a comparative study by considering different kinds of functional responses, which suggest that the dynamical behavior of the system remains unaltered, but the position of the bifurcation points altered. Our model system undergoes Hopf bifurcation with respect to the growth rate of the prey population, which indicates that a periodic solution occurs around a fixed point. Also, we observed that our predator-prey system experiences transcritical bifurcation for the prey population growth rate. By using normal form theory and center manifold theorem, we investigate the direction and stability of Hopf bifurcation. The biological implications of the analytical and numerical findings are also discussed in this study.

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