Dynamics of a predator-prey model with nonlinear incidence rate, Crowley-Martin type functional response and disease in prey population

2019 ◽  
Vol 10 ◽  
pp. 100035 ◽  
Author(s):  
Sk Golam Mortoja ◽  
Prabir Panja ◽  
Shyamal Kumar Mondal
Keyword(s):  
Incidence Rate ◽  
Functional Response ◽  
Prey Population ◽  
Nonlinear Incidence Rate ◽  
Predator Prey ◽  
Nonlinear Incidence ◽  
Predator Prey Model ◽  
Prey Model ◽  
Disease In Prey

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 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.

scholarly journals Dynamic Analysis of an Impulsive Predator-Prey Model with Disease in Prey and Ivlev-Type Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yuanfu Shao ◽  
Peiluan Li ◽  
Guoqiang Tang
Keyword(s):  
Functional Response ◽  
Small Amplitude ◽  
Floquet Theory ◽  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pest Eradication ◽  
Disease In Prey

A predator-prey model with disease in prey, Ivlev-type functional response, and impulsive effects is proposed. By using Floquet theory and small amplitude perturbation skill, sufficient conditions of the existence and global stability of susceptible pest-eradication periodic solution are obtained. By impulsive comparison theorem, conditions ensuring the permanence of the system are established. Examples and simulation are given to show the complex dynamics for the key parameters.

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