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.

Complex Dynamics of an Eco-Epidemic System with Disease in Prey Species

2021 ◽  
Vol 31 (03) ◽  
pp. 2150046
Author(s):  
Absos Ali Shaikh ◽  
Harekrishna Das ◽  
Nijamuddin Ali
Keyword(s):  
Prey Species ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Alternative Food ◽  
Predator Population ◽  
Free System ◽  
Predator Prey ◽  
Force Of Infection ◽  
Prey System ◽  
Half Saturation Constant

The objective of this study is to investigate the complex dynamics of an eco-epidemic predator–prey system where disease is transmitted in prey species and predator population is being provided with alternative food. Holling type-II functional response is taken into consideration for interaction of predator and prey species. The half saturation constant for infected prey, the growth rate of susceptible prey and force of infection play a significant role to create complex dynamics in this predator–prey system where alternative food is present. It is seen that healthy disease-free system is possible here. The system shows some important dynamics viz. stable coexistence, Hopf bifurcation, period-doubling bifurcation and chaos. The analytical results obtained from the model are justified numerically.

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 Revealing the role of predator interference in a predator–prey system with disease in prey population

2015 ◽  
Vol 21 ◽  
pp. 100-111 ◽  
Author(s):  
Subhendu Chakraborty ◽  
Bob W. Kooi ◽  
Barasha Biswas ◽  
J. Chattopadhyay
Keyword(s):  
Prey Population ◽  
Predator Prey ◽  
Prey System ◽  
Predator Interference ◽  
Disease In Prey

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.

AN ECO-EPIDEMIOLOGICAL STUDY WITH PARASITE ATTACK AND ALTERNATIVE PREY

2009 ◽  
Vol 17 (02) ◽  
pp. 269-282 ◽  
Author(s):  
A. K. MANDAL ◽  
KUSUMIKA KUNDU ◽  
P. CHATTERJEE ◽  
J. CHATTOPADHYAY
Keyword(s):  
Global Stability ◽  
Food Source ◽  
Alternative Food ◽  
Food Sources ◽  
Predator Population ◽  
Alternative Prey ◽  
Predator Prey ◽  
Prey System ◽  
Alternative Food Source ◽  
Alternative Food Sources

The present paper deals with the problem of a predator-prey system with disease in the prey population. We observe the dynamics of such a system under the influence of severe as well as unnoticeable parasite attack and also alternative food sources for predator population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Local and global stability of the system around the biological feasible equilibria are studied. The conditions for which all three species will persist are worked out. Our results indicate that in the case of severe parasite attack, the predator population will prefer the alternative food source and not the infected one. But the strategy is reversed in the case of unnoticeable parasite attack.

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.

A linear birth-and-death predator–prey process

1995 ◽  
Vol 32 (01) ◽  
pp. 274-277
Author(s):  
John Coffey
Keyword(s):  
Death Rate ◽  
Birth Rate ◽  
Prey Population ◽  
Death Process ◽  
Predator Population ◽  
Birth And Death Process ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ 1 X and death rate μ 1 X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ 2 Y and the death rate is . It is proven that and iff

scholarly journals Cooperative hunting in a discrete predator–prey system

2020 ◽  
Vol 13 (07) ◽  
pp. 2050063
Author(s):  
Yunshyong Chow ◽  
Sophia R.-J. Jang ◽  
Hua-Ming Wang
Keyword(s):  
Growth Rate ◽  
Discrete Time ◽  
Reproductive Number ◽  
Model Parameters ◽  
Predator Population ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Cooperative Hunting ◽  
Prey System ◽  
Dependent Growth

We propose and investigate a discrete-time predator–prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson–Bailey host-parasitoid system with density dependent growth rate. A sufficient condition based on the model parameters for which both populations can coexist is derived, namely that the predator’s maximal reproductive number exceeds one. We study existence of interior steady states and their stability in certain parameter regimes. It is shown that the system behaves asymptotically similar to the model with no cooperative hunting if the degree of cooperation is small. Large cooperative hunting, however, may promote persistence of the predator for which the predator would otherwise go extinct if there were no cooperation.

scholarly journals Effects of Behavioral Tactics of Predators on Dynamics of a Predator-Prey System

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hui Zhang ◽  
Zhihui Ma ◽  
Gongnan Xie ◽  
Lukun Jia
Keyword(s):  
Time Scale ◽  
Stable State ◽  
Volterra Model ◽  
Fast Time ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Interaction ◽  
Game Dynamic

A predator-prey model incorporating individual behavior is presented, where the predator-prey interaction is described by a classical Lotka-Volterra model with self-limiting prey; predators can use the behavioral tactics of rock-paper-scissors to dispute a prey when they meet. The predator behavioral change is described by replicator equations, a game dynamic model at the fast time scale, whereas predator-prey interactions are assumed acting at a relatively slow time scale. Aggregation approach is applied to combine the two time scales into a single one. The analytical results show that predators have an equal probability to adopt three strategies at the stable state of the predator-prey interaction system. The diversification tactics taking by predator population benefits the survival of the predator population itself, more importantly, it also maintains the stability of the predator-prey system. Explicitly, immediate contest behavior of predators can promote density of the predator population and keep the preys at a lower density. However, a large cost of fighting will cause not only the density of predators to be lower but also preys to be higher, which may even lead to extinction of the predator populations.

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