A predator–prey model with disease in the prey and two impulses for integrated pest management

Shi, Ruiqing; Jiang, Xiaowu; Chen, Lansun

doi:10.1016/j.apm.2008.06.001

Cited by 68 publications

(29 citation statements)

References 12 publications

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“…We note that many papers have been published on impulsive interventions of disease or pest control [17,18,19,35,36,37], in some of which the explicit expressions of thresholds for persistence of systems were obtained. However, most of the cited systems can be simplified such that the equations of infected individuals related to the calculation are actually one-dimensional.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…However, most of these mathematical models considering control measures on mosquitoes invariably assume that the pesticides affect mosquitoes continuously, but usually mosquito culling takes place only at certain times. It is known that impulsive differential equations can be used to describe pesticide sprays and analyse pest control strategies [14,15,16,17,18,19]. As mosquito culling is a common method for WNV control [14,15], we adopt it in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Models of impulsive culling of mosquitoes to interrupt transmission of West Nile virus to birds

Xiao

Cheke

2015

Applied Mathematical Modelling

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A mathematical model describing the transmission of West Nile virus (WNV)between vector mosquitoes and birds, incorporating a control strategy of culling mosquitoes and defined by impulsive differential equations is presented and its properties investigated. First, we consider a strategy of periodic impulsive culling of the mosquitoes. Theoretical results indicate that if the threshold R 0 is greater than unity the disease uniformly persists, but, if not, the disease does not necessarily become extinct. The explicit conditions determining the backward or forward bifurcation were obtained. The culling rate has a major effect on the occurrence of backward bifurcation. Analysis shows that the disease is most sensitive to mosquito-bird contacts, mosquitoculling rate and intervals between culls. The dependence of the outcomes of the culling strategy on mosquito biting rate is discussed. When the complete elimination of disease is impossible, mosquito culls are implemented once the

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Models of impulsive culling of mosquitoes to interrupt transmission of West Nile virus to birds

Xiao

Cheke

2015

Applied Mathematical Modelling

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“…Furthermore, noticing (30), we have reason to confirm that our study makes the model in [14] more general.…”

Section: Remark 12mentioning

confidence: 92%

“…The approach to biological control which we adopted is to release both infective pest individuals and natural predators periodically with constant amount at different point in time; what is more, the functional response is also a more general form. Motivated by the valuable contributions of Georgescu and Zhang [10], Wang et al [13], and Shi et al [14], in this paper general IPM model will be considered as follows:…”

Section: Introductionmentioning

confidence: 99%

“…People use natural enemy, as in some sense like a pesticide, to control pest via augmentation or releasing natural enemy once the quantity of pest has reached or exceeded the economic threshold (see [9,10,14,15]). Shi et al (see [14]) analyzed a predator-pest model with disease in the pest and functional response given by Holling-II type and the time-dependent impulsive strategy including release of infective pest individuals and those natural predators at different point in time; the threshold on pest eradication was obtained. However, little of paper has been devoted to analysis of models which combine release of infective pest individuals and those natural predators.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Analysis of General Integrated Pest Management Model with Double Impulsive Control

Teng

Wang

et al. 2015

Discrete Dynamics in Nature and Society

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A general predator-prey model with disease in the prey and double impulsive control is proposed and investigated for the purpose of integrated pest management. By using the Floquet theory, the comparison theorem of impulsive differential equations, and the persistence theory of dynamical systems, we obtain that if threshold value 0 < 1, then the susceptible pest eradication periodic solution is globally asymptotically stable and if 0 > 1, then the model is permanent. The numerical examples not only illustrate the theoretical results, but also show that when the model is permanent, then it may possess a unique globally attractive -periodic solution.

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Permanence in a periodic single species system subject to linear/constant impulsive perturbations

Liu

Tang

Qin

et al. 2010

Math. Meth. Appl. Sci.

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In this paper, a single species system with linear/constant impulsive perturbations is established. The linear and constant impulses are realized at fixed moments of time. By using the comparison principle of impulsive differential equations and analysis techniques, sufficient conditions for the permanence of the system with linear and constant impulsive perturbations are obtained, respectively. Numerical simulations are presented to substantiate our analytical results, and show that the impulsive perturbations play a crucial role.

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A predator–prey model with disease in the prey and two impulses for integrated pest management

Cited by 68 publications

References 12 publications

Models of impulsive culling of mosquitoes to interrupt transmission of West Nile virus to birds

Models of impulsive culling of mosquitoes to interrupt transmission of West Nile virus to birds

Dynamic Analysis of General Integrated Pest Management Model with Double Impulsive Control

Permanence in a periodic single species system subject to linear/constant impulsive perturbations

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