A Leslie–Gower predator–prey model with disease in prey incorporating a prey refuge

Sharma, Swarnali; Samanta, G. P.

doi:10.1016/j.chaos.2014.11.010

Cited by 74 publications

(32 citation statements)

References 58 publications

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“…Simple prey predator food chain models often display rich nonlinear mathematical behavior, including varying numbers and stability of equilibrium states and limit cycles (Jana et al 2014;Haque et al 2013;Holt and Barfield 2013;Gwaltney et al 2007;Kooi and Hanegraaf 2001;Upadhyaya and Iyengar 2005;Xu et al 2005). A number of studies have been carried out in recent years to study the dynamics of three trophic-level food chains comprising of prey, specialist predator and generalist predators, using mathematical models based on modified version of Leslie-Gower scheme (Aziz-Alaoui 2002; Rai and Upadhyay 2004;Hanski et al 1991;Bandyopadhyay et al 2008;Kumari 2013;Naji et al 2010;Sharma and Samanta 2015;Upadhyay 2009Upadhyay , 2003. It is observed in the marine ecosystem that the top predator is generalist predator in the food chain system consisting of phytoplankton !…”

Section: Introductionmentioning

confidence: 99%

Mathematical study of a Leslie–Gower-type tritrophic population model in a polluted environment

Misra

Babu

2016

Model. Earth Syst. Environ.

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In this paper, the effect of toxicant on the dynamics of Leslie-Gower tritrophic food chain population model is studied. Two models have been studied to visualize the dynamical behaviour of prey and predator populations under toxicant stress. All the feasible equilibria of the systems are obtained and using stability theory the conditions are derived for the survival or extinction of species. From the analysis of the models it is observed that the effect of toxicant on predator population increases the equilibrium density of prey population. Finally, we support our analytical findings with numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Mathematical study of a Leslie–Gower-type tritrophic population model in a polluted environment

Misra

Babu

2016

Model. Earth Syst. Environ.

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“…For more realistic epidemic models, we refer the readers to References 3,4. Furthermore, in the literature, many models have been formulated mathematically to interpret the dynamic relationship between the predator‐prey population with a disease in prey on the autonomous system, for example, see References 5-10 and the references therein. Several works concerning eco‐epidemiological models appeared in many papers, for example, see References 11-17.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of an optimal control problem for the predator‐prey model with disease in prey

Sowndarrajan

Nyamoradi

Shangerganesh

et al. 2020

Optim Control Appl Methods

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Summary This article deals with an optimal control problem governed by a system that models the dynamics of predator‐prey interactions. We study the minimization of the infective prey density. Furthermore, our purpose is here to establish the existence of weak solutions and derive some optimality conditions. Finally, the impact of the control terms are studied to get an insight of the predator‐prey model adopting various numerical simulations.

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“…If the predator is assumed to grow logistically where its carrying capacity depends on the size of prey, then we can apply a Leslie-Gower model. Ecoepidemic models based on the Leslie-Gower equation have been proposed by a number of researchers [14][15][16][17][18][19]. Zhou et al [19] and Sharma and Samanta [16] considered an ecoepidemic model based on Leslie-Gower model with infectious disease in prey where the functional response follows the Holling type II.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Leslie-Gower Pest-Predator Model with Disease in Pest Including Pest-Harvesting and Optimal Implementation of Pesticide

Suryanto

Darti

2019

International Journal of Mathematics and Mathematical Sciences

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We propose a model which describes the interaction between pest and its natural predator. We assume that pest can be infected with diseases or pathogens such as bacteria, fungi, and viruses. The model is constructed by combining the Leslie-Gower model and S-I epidemic model. It is also considered the effects of pest harvesting. Harvesting in this case is intended to take a number of pests as one of the pest population control strategies. The proposed model will be analyzed dynamically to study its qualitative behaviour. The dynamical analysis includes the determination of all possible equilibrium points and their stability properties. Furthermore we also discuss the implementation of pesticide control where its optimal strategy is determined by Pontryagin’s maximum principle. To support our analytical studies, we perform some numerical simulations and their interpretation.

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A Leslie–Gower predator–prey model with disease in prey incorporating a prey refuge

Cited by 74 publications

References 58 publications

Mathematical study of a Leslie–Gower-type tritrophic population model in a polluted environment

Mathematical study of a Leslie–Gower-type tritrophic population model in a polluted environment

Mathematical analysis of an optimal control problem for the predator‐prey model with disease in prey

Dynamics of Leslie-Gower Pest-Predator Model with Disease in Pest Including Pest-Harvesting and Optimal Implementation of Pesticide

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