Dynamic analysis of a pest management SEI model with saturation incidence concerning impulsive control strategy

Xiang, Zhongyi; Li, Yongfeng; Song, Xinyu

doi:10.1016/j.nonrwa.2008.04.017

Cited by 31 publications

(15 citation statements)

References 15 publications

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“…Impulsive differential equations are widely used in many different areas such as physics, ecology, and pest control. Most of them use impulses at fixed time such as [17] [18]. By using constant functions, some properties of the solution of predator-prey system with Beddington-DeAnglis type functional response and impulse impact are studied in [19] for continuous case.…”

Section: Introductionmentioning

confidence: 99%

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

Güvenilir

Kaymakçalan²,

Pelen³

2015

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In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.

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Section: Introductionmentioning

confidence: 99%

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

Güvenilir

Kaymakçalan²,

Pelen³

2015

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“…Compared to chemical treatment, nonchemical methods are safer to man and are generally effective for longer periods of time. One example of nonchemical pest control methods is biological treatment [13][14][15][16][17], including microbial control with pathogens, as disease can be important natural controls of some pests. Insects, like humans and other animals, can be infected by disease-causing organisms such as bacteria, viruses, and fungi.…”

Section: Introductionmentioning

confidence: 99%

Two Generalized Predator-Prey Models for Integrated Pest Management with Stage Structure and Disease in the Prey Population

Shi

Tang

Feng

2013

Abstract and Applied Analysis

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Stage-structured predator-prey models with disease in the prey are constructed. For the purpose of integrated pest management, two types of impulsive control strategies (impulsive release of infective prey and impulsive release of predator) are used. For Case 1, infective prey applications are more frequent than releases of predator (natural enemies). For Case 2, predator (natural enemies) releases are more frequent than infective prey applications. In both cases, we get the sufficient conditions for the global attractivity of the susceptible prey-eradication periodic solution. In addition, the persistence of the systems is also discussed. At last, the results are discussed and some possible future work is put forward.

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“…The epidemiological approach has been employed to model many biological and ecological phenomena such as the viral propagation of memes [34]. There also has been some work on pest control management within a single patch (see, for example, [13,35]). In both [13] and [35], impulsive biological control strategies were proposed for pest control management purposes.…”

mentioning

confidence: 99%

“…There also has been some work on pest control management within a single patch (see, for example, [13,35]). In both [13] and [35], impulsive biological control strategies were proposed for pest control management purposes. However, no patch-structure or control related costs were considered in [13,35].…”

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confidence: 99%

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Modeling the spread of bed bug infestation and optimal resource allocation for disinfestation

Gharouni

Wang

2016

Mathematical Biosciences and Engineering

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A patch-structured multigroup-like $SIS$ epidemiological model is proposed to study the spread of the common bed bug infestation. It is shown that the model exhibits global threshold dynamics with the basic reproduction number as the threshold parameter. Costs associated with the disinfestation process are incorporated into setting up the optimization problems. Procedures are proposed and simulated for finding optimal resource allocation strategies to achieve the infestation free state. Our analysis and simulations provide useful insights on how to efficiently distribute the available exterminators among the infested patches for optimal disinfestation management.

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Dynamic analysis of a pest management SEI model with saturation incidence concerning impulsive control strategy

Cited by 31 publications

References 15 publications

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

Two Generalized Predator-Prey Models for Integrated Pest Management with Stage Structure and Disease in the Prey Population

Modeling the spread of bed bug infestation and optimal resource allocation for disinfestation

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