How population dynamics change in presence of migratory prey and predator's preference

Chatterjee, Samrat; Kesh, Dipak; Bairagi, Nandadulal

doi:10.1016/j.ecocom.2012.03.001

Cited by 8 publications

(7 citation statements)

References 39 publications

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“…If predators feed upon both susceptible prey (S) and infected prey (I) of a single species, then selectivity or preference of the predators to susceptible and infected preys plays significant role in the system dynamics (Hall et al, 2005). In this case, the traditional type II response function should be replaced by multiple-prey type II, which can be mathematically represented by nS/(a + S + uI) and unI/(a + S + uI) for susceptible and infected preys, respectively (Case, 2000;Hall et al, 2005;Flake et al, 2003;Chatterjee et al, 2012). The parameter u measures the selectivity/preference of the predator to infected prey over the susceptible one or vice-versa.…”

Section: Model Formulationmentioning

confidence: 98%

Complex dynamics of a predator–prey–parasite system: An interplay among infection rate, predator's reproductive gain and preference

Bairagi

Adak

2015

Ecological Complexity

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Section: Model Formulationmentioning

confidence: 98%

Complex dynamics of a predator–prey–parasite system: An interplay among infection rate, predator's reproductive gain and preference

Bairagi

Adak

2015

Ecological Complexity

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“…It is a well-known fact that infected prey individuals become easy to catch by the predator. This property has been considered in a various number of eco-epidemiological models [18,20,23,24,29,51]. In our model, we have considered that the predator consumes infected prey only to control the disease [52,53].…”

Section: Discussionmentioning

confidence: 99%

“…In deterministic models, parameters are all deterministic irrespective of environmental fluctuation and hence it is very difficult to predict the future dynamics of the system correctly [25]. Therefore, many authors introduced randomness in deterministic models to reveal the effect of environmental variability [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Deterministic and stochastic analysis of an eco-epidemiological model

2017

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Chronic wasting disease (CWD) is a contagious prion disease among the deer family that has the potential to disrupt the ecosystems where deer occur in abundance. To understand the dynamics of this emerging infectious disease, we consider a simple eco-epidemic model where the host population is infected by CWD. Boundedness of the system is established. The structure of equilibria and their linearized stability are investigated. The persistence condition is discussed. By constructing a suitable Lyapunov function, we discuss the global stability of the endemic equilibrium. Local bifurcation (transcritical) around the boundary equilibria is developed. Sufficient conditions for the existence of Hopf-bifurcation are derived. Further, we have also introduced white type of noise into the system to investigate stochastic stability. This suggests that the deterministic model is robust with respect to stochastic perturbation. Some numerical simulations are performed to validate our results.

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“…If predators feed upon both susceptible rabbit (S) and infected rabbit (I) of a single species, then selectivity or preference of the predators to susceptible and infected preys plays significant role in the system dynamics [23]. In this case traditional type II functional response should be replaced by multiple-prey type II, which can be mathematically represented by ω 1 S/(S + b 1 I + c 1 ) and ω 2 S/(S + b 1 I + c 1 ) for susceptible and infected rabbits, respectively [3,9,12]. The parameter b 1 measures the selectivity/preference of the predator to infected rabbit over the susceptible one or vice-versa.…”

Section: Model Development: the Eco-epidemiological Systemmentioning

confidence: 99%

Wave of chaos in a spatial eco-epidemiological system: Generating realistic patterns of patchiness in rabbit–lynx dynamics

Upadhyay

Roy

Venkataraman

et al. 2016

Mathematical Biosciences

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In the present paper, we propose and analyse an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of eco-epidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.

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How population dynamics change in presence of migratory prey and predator's preference

Cited by 8 publications

References 39 publications

Complex dynamics of a predator–prey–parasite system: An interplay among infection rate, predator's reproductive gain and preference

Complex dynamics of a predator–prey–parasite system: An interplay among infection rate, predator's reproductive gain and preference

Deterministic and stochastic analysis of an eco-epidemiological model

Wave of chaos in a spatial eco-epidemiological system: Generating realistic patterns of patchiness in rabbit–lynx dynamics

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