Effect of delay in a Lotka–Volterra type predator–prey model with a transmissible disease in the predator species

Haque, Mainul; Sarwardi, Sahabuddin; Preston, Simon; Venturino, Ezio

doi:10.1016/j.mbs.2011.06.009

Cited by 55 publications

(26 citation statements)

References 20 publications

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“…In [66] the following delayed ecoepidemic model with disease in the predators is considered, taking into account the time needed for the predators to digest their prey and generate newborns, µ ∈ R expressing the predators net birth rate:…”

Section: Effects Of Time Lagsmentioning

confidence: 99%

Ecoepidemiology: a More Comprehensive View of Population Interactions

Venturino

2015

Math. Model. Nat. Phenom.

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Abstract. Models proposed for the description of population interactions with pathogenic agents are presented. We review some basic quadratic-interactions models, then move to more complex demographics, structured models, models involving several populations, delays, plankton dynamics, the Allee effect and group behavior. In most of these cases basic reproduction numbers are evaluated and commented.

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Section: Effects Of Time Lagsmentioning

confidence: 99%

Ecoepidemiology: a More Comprehensive View of Population Interactions

Venturino

2015

Math. Model. Nat. Phenom.

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“…Incorporating the system controls the size of the populations. Venturino [17,18], Haque and Venturino [19], Haque et al [20,21,22], Xiao and Chen [23,24], Tewa [25], Hethcote [26], Rahman [27], Chattopadhyay et.all [28,29,30] discussed the dynamics of preypredator system with disease in prey population.…”

Section: Introductionmentioning

confidence: 99%

A Leslie-Gower Holling Type-II Predator-Prey Mathematical Model with Disease in Prey Population Incorporating a Prey Refuge

Mandal¹,

Das²,

Pal³

2016

JMSS

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Abstract:We formulate and analyze a predator-prey model followed by Leslie-Gower model in which the prey population is infected by disease. We assume that the disease can only spread over prey population. As a result prey population has been classified into two categories, namely susceptible prey, infected prey where as the predator population remains free from infection. To investigate the behaviour of prey population we incorporate prey refuge in this model. Since the prey refuge decreases the predation rate then it has an important effect in our predator-prey interaction model. We have discussed the existence of various equilibrium points and local stability analysis at those equilibrium points. We investigate the Hopf-bifurcation analysis about the interior equilibrium point by taking the rate of infection parameter and the prey refuge parameter as bifurcation parameters. The numerical analysis is carried out to support the analytical results and to discuss some interesting results that our model exhibits.

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“…Recently, several authors proposed different eco‐epidemiological predator–prey models by assuming that the predator population suffers a transmissible disease (see, for example, ). In , by assuming that a transmissible disease spreads among the predator population, Haque et al . considered the following eco‐epidemiological model with a time delay representing the gestation period of the newborns:

\begin{matrix} x (t) = & x (t) (r - a_{11} x (t) - a_{12} S (t) - a_{13} I (t)), \\ S (t) = & k a_{12} x (t - τ) S (t - τ) - r_{1} S (t) - βS (t) I (t), \\ I (t) = & βS (t) I (t) + k a_{13} x (t - τ) I (t - τ) - r_{2} I (t), \end{matrix}

where x ( t ), S ( t ), and I ( t ) represent the densities of the prey, susceptible (uninfected) predator, and the infected predator population at time t , respectively.…”

Section: Introductionmentioning

confidence: 99%

Global stability and Hopf bifurcation of a delayed eco‐epidemiological model with Holling type II functional response

Tian

2014

Math Methods in App Sciences

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In this paper, a delayed eco‐epidemiological model with Holling type II functional response is investigated. By analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcations at the disease‐free equilibrium, the susceptible predator‐free equilibrium and the endemic‐coexistence equilibrium are established, respectively. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are derived for the global stability of the endemic‐coexistence equilibrium, the disease‐free equilibrium, the susceptible predator‐free equilibrium and the predator‐extinction equilibrium of the system, respectively. Numerical simulations are carried out to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.

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Effect of delay in a Lotka–Volterra type predator–prey model with a transmissible disease in the predator species

Cited by 55 publications

References 20 publications

Ecoepidemiology: a More Comprehensive View of Population Interactions

Ecoepidemiology: a More Comprehensive View of Population Interactions

A Leslie-Gower Holling Type-II Predator-Prey Mathematical Model with Disease in Prey Population Incorporating a Prey Refuge

Global stability and Hopf bifurcation of a delayed eco‐epidemiological model with Holling type II functional response

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