scholarly journals Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge

2020 ◽  
Vol 6 (2) ◽  
pp. 123-134
Author(s):  
Adin Lazuardy Firdiansyah
Keyword(s):  
Incidence Rate ◽  
Numerical Solutions ◽  
Nonlinear Incidence Rate ◽  
Prey Refuge ◽  
Predator Prey ◽  
Nonlinear Incidence ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Future Work

A predator-prey system with nonlinear incidence rate and refuging in prey is proposed to describe behavior change of certain infected diseases on healthy prey when the number of infected prey is getting large, while predator can predate prey by accessing refuging in prey. Therefore, this paper discusses the dynamics behavior predator-prey model with the spread of infected disease that is denoted by nonlinear incidence rate and adding prey refuge. We find the existence of eight non-negative equilibrium in the model, which their local stability has been determined. Furthermore, we also observe the prey refuge properties in the model. We find that prey refuge can prevent extinction in prey populations. In the end, some numerical solutions are carried out to illustrate our analytic results. For future work, we can investigate the harvesting effect in both populations, which is disease control in the predator-prey model with the spread of infected disease.

Extinction and Permanence Analysis of Stochastic Predator-Prey Model with Disease, Ratio-Dependent Type Functional Response and Nonlinear Incidence Rate

2021 ◽  
Author(s):  
Conghui Xu ◽  
Yongguang Yu ◽  
Guojian Ren ◽  
Xudong Hai ◽  
Zhenzhen Lu
Keyword(s):  
Incidence Rate ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Nonlinear Incidence Rate ◽  
Predator Prey ◽  
Nonlinear Incidence ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent ◽  
Dependent Type

Abstract This paper is aimed to investigate a stochastic predator-prey model with disease in both species, which is also considered with ratio-dependent type functional response and nonlinear incidence rate. First, the existence and uniqueness of positive solution is discussed. Then, some sufficient conditions are established to ensure the solution is stochastically ultimate boundedness and permanent. Also, the extinction of susceptible prey, infected prey, susceptible predator and infected predator are analysed, respectively. Furthermore, the boundedness of moments and upper-growth rate estimation are investigated. Finally, numerical simulations are given to illustrate our main results.

scholarly journals Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Heping Jiang ◽  
Huiping Fang ◽  
Yongfeng Wu
Keyword(s):  
Hopf Bifurcation ◽  
Neumann Boundary ◽  
Herd Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Prey Model ◽  
Homogeneous Neumann Boundary Condition ◽  
The Stability

Abstract This paper mainly aims to consider the dynamical behaviors of a diffusive delayed predator–prey system with Smith growth and herd behavior subject to the homogeneous Neumann boundary condition. For the analysis of the predator–prey model, we have studied the existence of Hopf bifurcation by analyzing the distribution of the roots of associated characteristic equation. Then we have proved the stability of the periodic solution by calculating the normal form on the center of manifold which is associated to the Hopf bifurcation points. Some numerical simulations are also carried out in order to validate our analysis findings. The implications of our analytical and numerical findings are discussed critically.

Global analysis of a Holling type II predator–prey model with a constant prey refuge

2013 ◽  
Vol 76 (1) ◽  
pp. 635-647 ◽  
Author(s):  
Guangyao Tang ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Global Analysis ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Caifeng Du
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

scholarly journals Hopf bifurcation and stability in a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge

2019 ◽  
Vol 17 (1) ◽  
pp. 141-159 ◽  
Author(s):  
Zaowang Xiao ◽  
Zhong Li ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Bifurcation And Stability

Abstract In this paper, we consider a Beddington-DeAngelis predator-prey system with stage structure for predator and time delay incorporating prey refuge. By analyzing the characteristic equations, we study the local stability of the equilibrium of the system. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. After that, by constructing a suitable Lyapunov functional, sufficient conditions are derived for the global stability of the system. Finally, the influence of prey refuge on densities of prey species and predator species is discussed.

A Predator-Prey Model Incorporating Prey Refuge and Allee Effect

2015 ◽  
Vol 713-715 ◽  
pp. 1534-1539 ◽  
Author(s):  
Rui Ning Fan
Keyword(s):  
Time Delay ◽  
Time Lag ◽  
Functional Responses ◽  
Prey Refuge ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Prey Model ◽  
Discrete Time Delay ◽  
Prey Interaction

The effect of refuge used by prey has a stabilizing impact on population dynamics and the effect of time delay has its destabilizing influences. Little attention has been paid to the combined effects of prey refuge and time delay on the dynamic consequences of the predator-prey interaction. Here, a predator-prey model with a class of functional responses was studied by using the analytical approach. The refuge is considered as protecting a constant proportion of prey and the discrete time delay is the gestation period. We evaluated both effects with regard to the local stability of the interior equilibrium point of the considered model. The results showed that the effect of prey refuge has stronger influences than that of time delay on the considered model when the time lag is smaller than the threshold. However, if the time lag is larger than the threshold, the effect of time delay has stronger influences than that of refuge used by prey.

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