A cannibalistic eco-epidemiological model with disease in predator population

Biswas, Santosh; Samanta, Sudip; Chattopadhyay, Joydev

doi:10.1007/s12190-017-1100-9

Cited by 12 publications

(21 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ecological, social and psychological circumstances greatly influence the dynamic cannibalistic behaviour of interacting species. Santosh et al [2] observed cannibalism as a self-regulatory mechanism to control disease transmission among the predator species. In 2009, Sun et al [25] studied the spatial patterns in the distribution of organism where they consider cannibalism in the predator population and found spatial pattern formation greatly influenced by cannibalism.…”

Section: Introductionmentioning

confidence: 99%

“…In section 2, we have proposed our spatiotemporal model system. In section 3, we have proved the local and global stability of the constant positive steady state of (2). We use linearization technique for local stability and Lyapunov method for global stability.…”

Section: Introductionmentioning

confidence: 99%

“…We use linearization technique for local stability and Lyapunov method for global stability. In Section 4, we have established a priori upper and lower bounds for non-constant positive solution of (2), and then studied the non-existence, global existence, and bifurcation of a non-constant positive solution of a spatiotemporal model (2). Turing instability studied in section 5 and the effect of disease transmission rate and cannibalistic attack rate observed in the sections 6 and 7 respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Turing instability studied in section 5 and the effect of disease transmission rate and cannibalistic attack rate observed in the sections 6 and 7 respectively. In section 8, we have obtained Turing and spatiotemporal patterns by solving the spatial model system (2), which shows the population distribution of the species in the domain. In the last section 9, a detailed discussion about various results obtained throughout this article presented.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Pattern Formation Study of an Eco-epidemiological Model with Cannibalism and Disease in Predator Population

Kumari,

Kumar,

Agarwal

2019

Preprint

View full text Add to dashboard Cite

In this work, a diffusive eco-epidemiological model where the predator's population consume their species to survive. The proposed model is studied from both points of view, theoretical and numerical. Firstly, we deal with the behaviour of the constant positive steady state then nonconstant positive steady state. Sufficient conditions for local asymptotic stability and global asymptotic stability for a constant positive steady state are derived by linearization and Lyapunov function technique. Prior estimates of the positive steady state given, conditions are obtained for the non-existence of non-constant positive solution, by Cauchy and Poincaré inequality. The existence of non-constant positive steady states is studied by Leray-Schauder degree theory. These results indicate the importance of the large diffusivity which is responsible for the appearance and non-appearance of stationary patterns. We have discussed Turing instability, which ensures the existence of Turing patterns. Further, the effect of the cannibalistic attack rate and disease transmission rate observed on the dynamics of the proposed model system. Even it followed that in the absence of cannibalism, the spatial distribution is not possible and increment in the cannibalistic attack rate and disease transmission rate promote the Turing patterns. The similar effect observed for the disease transmission rate. Further, we have calculated Lyapunov exponents and saw the chaotic and stable fixed dynamics for various parameter settings. In the last, we have performed extensive numerical simulation and obtained Turing and spatiotemporal patterns. Keywords cannibalism • local stability • global stability • nonconstant positive steady state • priori estimates • Turing instability and Turing patterns • spatiotemporal patterns • Lyapunov exponents. Diffusion gives rise to a pattern formation phenomenon. Diffusion plays an important role in population biology. Starting from the Turing seminal work [27], Brusselator model [3], Gierer-Meinhardt model [10, 30], Sel'kov model [5, 29], Lotka-Volterra predator-prey model [17, 6] and the references therein, self diffusion and cross-diffusion are

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pattern Formation Study of an Eco-epidemiological Model with Cannibalism and Disease in Predator Population

Kumari,

Kumar,

Agarwal

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Its complication is raised in presence of disease either in prey or in predator or in both. We cannot ignore these natural phenomena of regulating population structure [1]. The disease spread in prey population, generally through contact with infected prey, whereas in predator population occurred either through consumption of infected preys [3][4][5] or by contact with infected predator [3,6].…”

Section: Introductionmentioning

confidence: 99%

Propagation of disease from exotic infected predator to native population-A prey predator model

Purushwani¹,

Sinha²

2018

Malaya J. Mat.

View full text Add to dashboard Cite

In this paper, a prey predator model for native population with SI infection in exotic population is developed and analyzed. A model with prey predator interaction in native population and exotic predator having the risk of infection is suggested to observe the transmission of disease from exotic predators to native population. Disease free equilibrium points (in presence and absence of predator) and endemic equilibrium points are calculated. Conditions for the existence and boundedness of equilibrium points have been derived. The local stability analysis of the model system around the all biologically feasible equilibrium points is discussed. We perform global dynamics of the model using Lyapunov theorem for endemic equilibrium point. We compare the growth of population in terms of ecological sensitive parameters predation rate (η 3 ) , carrying capacity of environment (K) and transmission rate of disease (β ) with the help of suitable graphs.

show abstract

Exploring dynamical complexity of a cannibalistic eco‐epidemiological model with multiple time delay

Biswas

Ahmad

Khajanchi

2022

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this paper, we investigate a cannibalistic predator-prey system with Beddington-DeAngelis type response function when the infection only exists in the predator species. The predator species are subject to cannibalistic interaction and the infection spreads among the predators via cannibalism. The model is studied in presence of multiple delays for the maturation of prey and predator. Local stability analysis of the predator-prey model around the biologically realistic two essential steady states is investigated. We also investigate the bifurcation analysis of the proposed model around the co-existing steady states. Using the normal form method and center manifold theory, the direction of Hopf bifurcation and the Hopf bifurcating periodic solutions are explored. In presence of time delays, we derive the criteria for the permanence of the model. Our findings demonstrate that maturation delays destabilize the system and can produce high periodic oscillations. Cannibalism can act as a self-regulatory scenario controlling the transmission of disease among the predator species and stabilizing the oscillations in the predator-prey system. Our theoretical analysis is well supported with numerical simulation.

show abstract

A cannibalistic eco-epidemiological model with disease in predator population

Cited by 12 publications

References 50 publications

Pattern Formation Study of an Eco-epidemiological Model with Cannibalism and Disease in Predator Population

Pattern Formation Study of an Eco-epidemiological Model with Cannibalism and Disease in Predator Population

Propagation of disease from exotic infected predator to native population-A prey predator model

Exploring dynamical complexity of a cannibalistic eco‐epidemiological model with multiple time delay

Contact Info

Product

Resources

About