A predator–prey model with infected prey

Hethcote, Herbert W.; Wang, Wendi; Han, Lei; Ma, Zhien

doi:10.1016/j.tpb.2004.06.010

Cited by 294 publications

(197 citation statements)

References 24 publications

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“…In the form of total prey population, prey prevalence and predators formulation, the model of [75] containing disease contagion modeled via standard incidence is:…”

Section: Use Of the Standard Disease Incidencementioning

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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“…In the form of total prey population, prey prevalence and predators formulation, the model of [75] containing disease contagion modeled via standard incidence is:…”

Section: Use Of the Standard Disease Incidencementioning

confidence: 99%

Ecoepidemiology: a More Comprehensive View of Population Interactions

Venturino

2015

Math. Model. Nat. Phenom.

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“…The parameter combinations R P1 and R P2 are similar to the reproduction ratios in epidemic theory (cf. Hethcote et al [24], Inaba and Nishiura [25], and Haque and Venturino [26]). …”

Section: Proposition 1 the Prey Population Is Always Bounded From Abovementioning

confidence: 99%

Dynamical behaviour of a two-predator model with prey refuge

Sarwardi

Mandal²,

Ray

2013

J Biol Phys

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A three-component model consisting on one-prey and two-predator populations is considered with a Holling type II response function incorporating a constant proportion of prey refuge. We also consider the competition among predators for their food (prey) and shelter. The essential mathematical features of the model have been analyzed thoroughly in terms of stability and bifurcations arising in some selected situations. Threshold values for some parameters indicating the feasibility and stability conditions of some equilibria are determined. The range of significant parameters under which the system admits different types of bifurcations is investigated. Numerical illustrations are performed in order to validate the applicability of the model under consideration.

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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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A predator–prey model with infected prey

Cited by 294 publications

References 24 publications

Ecoepidemiology: a More Comprehensive View of Population Interactions

Ecoepidemiology: a More Comprehensive View of Population Interactions

Dynamical behaviour of a two-predator model with prey refuge

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

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