QUALITATIVE ANALYSIS OF A STOCHASTIC PREDATOR–PREY SYSTEM WITH DISEASE IN THE PREDATOR

2013 ◽  
Vol 06 (01) ◽  
pp. 1250068 ◽  
Author(s):  
SHUANG LI ◽  
XINAN ZHANG
Keyword(s):  
White Noise ◽  
Predator Population ◽  
Deterministic System ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Predator Prey ◽  
Prey System ◽  
Long Time ◽  
Global Positive Solution ◽  
Disease Free

A stochastic predator–prey system with disease in the predator population is proposed, the existence of global positive solution is derived. When the white noise is small, there is a stationary distribution. In addition, conditions of global stability for the deterministic system are also established from the above result. By Lyapunov function, the long time behavior of solution around the disease-free equilibrium of deterministic system is derived. These results mean that stochastic system has the similar property with the corresponding deterministic system. When the white noise is small, however, large environmental noise makes the result different. Finally, numerical simulations are carried out to support our findings.

ANALYSIS OF A PREDATOR–PREY MODEL WITH DISEASE IN THE PREY

2013 ◽  
Vol 06 (03) ◽  
pp. 1350012 ◽  
Author(s):  
CHUNYAN JI ◽  
DAQING JIANG
Keyword(s):  
White Noise ◽  
Stochastic System ◽  
Stochastic Perturbation ◽  
Deterministic System ◽  
Time Behavior ◽  
Large White ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Long Time

In this paper, we discuss the behavior of a predator–prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analyzing stabilities of its four equilibria. Then, we consider the asymptotic behavior of the stochastic system. By Lyapunov analysis methods, we show the stochastic stability and its long time behavior around the equilibrium of the deterministic system. We obtain there are similar properties between the stochastic system and its corresponding deterministic system, when white noise is small. But large white noise can make a unstable deterministic system to be stable.

Dynamic Analysis of a Stochastic Predator–Prey Model With Crowley–Martin Functional Response, Disease in Predator, and Saturation Incidence

2020 ◽  
Vol 15 (7) ◽  
Author(s):  
Conghui Xu ◽  
Yongguang Yu ◽  
Guojian Ren
Keyword(s):  
Functional Response ◽  
Existence And Uniqueness ◽  
Global Attractivity ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Disease In Predator ◽  
Long Time

Abstract This work aims to study some dynamical properties of a stochastic predator–prey model, which is considered under the combination of Crowley–Martin functional response, disease in predator, and saturation incidence. First, we discuss the existence and uniqueness of positive solution of the concerned stochastic model. Second, we prove that the solution is stochastically ultimate bounded. Then, we investigate the extinction and the long-time behavior of the solution. Furthermore, we establish some conditions for the global attractivity of the model. Finally, we propose some numerical simulations to illustrate our main results.

CONTROL OF DISEASE IN PREY POPULATION BY SUPPLYING ALTERNATIVE FOOD TO PREDATOR

2014 ◽  
Vol 22 (04) ◽  
pp. 677-690 ◽  
Author(s):  
SUDIP SAMANTA ◽  
AKSHYAY K. MANDAL ◽  
KUSUMIKA KUNDU ◽  
J. CHATTOPADHYAY
Keyword(s):  
Alternative Food ◽  
Prey Population ◽  
Predator Population ◽  
Free System ◽  
Predator Prey ◽  
System Disease ◽  
Prey System ◽  
Free Enrichment ◽  
Disease Free ◽  
Disease In Prey

A simple predator–prey system with disease in prey population and alternative food for the predator is proposed and analyzed. The main objective of the present investigation is to observe the conditions for which the disease in prey population will be controlled. It is observed that supply of alternative food to the predator population can make the system disease free. Enrichment also plays an important role in suppressing the infected population in the presence of alternative food. However, in the absence of predator population, enrichment increases the disease prevalence instead of reducing it. We finally conclude that supply of alternative food to the predator provides a healthy disease free system.

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