The Sterile Insect Release Method for Pest Control: a Density-Dependent Model

Barclay, Hugh J.; Mackauer, M.

doi:10.1093/ee/9.6.810

Cited by 106 publications

(72 citation statements)

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“…Based on the works in [2][3][4][5][6], homogeneous models for the interactive wild and sterile mosquitoes were formulated in [9]. Let w(t) be the number of wild mosquitoes and g(t) the number of sterile mosquitoes at time t. Density dependence is assumed for the death rates of both wild and sterile mosquitoes.…”

Section: Model Formulationmentioning

confidence: 99%

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New revised simple models for interactive wild and sterile mosquito populations and their dynamics

2016

Journal of Biological Dynamics

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Based on previous research, we formulate revised, new, simple models for interactive wild and sterile mosquitoes which are better approximations to real biological situations but mathematically more tractable. We give basic investigations of the dynamical features of these simple models such as the existence of equilibria and their stability. Numerical examples to demonstrate our findings and brief discussions are also provided. ARTICLE HISTORY

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Section: Model Formulationmentioning

confidence: 99%

“…Mathematical models have been formulated in the literature to study the interactive dynamics and control of the wild and sterile mosquito populations [2][3][4][5][6]11,12]. In particular, models incorporating different strategies in releasing sterile mosquitoes have been formulated and studied in [9,16].…”

Section: Introductionmentioning

confidence: 99%

New revised simple models for interactive wild and sterile mosquito populations and their dynamics

2016

Journal of Biological Dynamics

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“…Since the first field releases, various modelling and/or mathematical works have been done on SIT using either discrete models [12,29], or continuous temporal models with continuous release (see for instance [5,6,19,20,28,29,38] and references therein), with pulsed releases [17,42], or spatio-temporal models with one dimensional spatial component and continuous (proportional) releases [20,34,39]. See also [7] for an overview on SIT mathematical modelling.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Sterile Insect Technology for Control of Anopheles Mosquito

Anguelov

Dumont

Lubuma

2011

AIP Conference Proceedings

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The Sterile Insect Technology (SIT) is a nonpolluting method of control of the invading insects that transmit the disease. The method relies on the release of sterile or treated males in order to reduce the wild population of anopheles mosquito. We propose two mathematical models. The first model governs the dynamics of anopheles mosquito. The second model, the SIT model, deals with the interaction between treated males and wild female anopheles. Using the theory of monotone operators, we obtain dynamical properties of global nature that can be summarized as follows. Both models are dissipative dynamical systems on the positive cone R 4 + . The value R = 1 of the basic offspring number R is a forward bifurcation for the model of the anopheles mosquito, with the trivial equilibrium 0 being globally asymptotically stable (GAS) when R ≤ 1, whereas 0 becomes unstable and one stable equilibrium is born with well determined basins of attraction when R > 1. For the SIT model, we obtain a threshold numberλ of treated male mosquitos above which the control of wild female mosquitos is effective. That is, for λ >λ the equilibrium 0 is GAS. When 0 < λ ≤λ, the number of equilibria and their stability are described together with their precise basins of attraction. These theoretical results are rephrased in terms of possible strategies for the control of the anopheles mosquito and they are illustrated by numerical simulations.

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“…There has been a long history of temporal mathematical models used in SIT (Knipling 1955;Berryman 1967;Barclay and Mackauer 1980). Typically, the models define a pest population in a single equation as either a discrete time difference equation (see Knipling (1955), for example) or as a continuous time differential equation (see Barclay and Mackauer (1980), for example), to which sterile insects are released at a constant level to reduce the pest population.…”

mentioning

confidence: 99%

“…Typically, the models define a pest population in a single equation as either a discrete time difference equation (see Knipling (1955), for example) or as a continuous time differential equation (see Barclay and Mackauer (1980), for example), to which sterile insects are released at a constant level to reduce the pest population. The critical release rate (the minimum rate of sterile release required to eradicate the pest population) is then calculated.…”

mentioning

confidence: 99%

Optimal barrier zones for stopping the invasion of Aedes aegypti mosquitoes via transgenic or sterile insect techniques

Lee¹,

Baker

Gaffney

et al. 2013

Theor Ecol

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Biological invasions have dramatically altered the natural world by threatening native species and their communities. However, when the invading species is a vector for human disease there are further substantive public health and economic impacts. The development of transgenic technologies is being explored in relation to new approaches for the biological control of insect pests. We investigate the use of two control strategies, classical sterile insect techniques (SIT) and transgenic late-acting bisex lethality (RIDL), for controlling invasion of the mosquito Aedes aegypti using a spatial stage-structured mathematical model.In particular, we explore the use of a barrier zone of sterile/transgenic insects to prevent or impede the invasion of mosquitoes. We show that the level of control required is not only highly sensitive to the rate at which the sterile/transgenic males are released in the barrier zone, but also to the spatial range of release. Our models characterise how the distribution of sterile/transgenic mosquitoes in the barrier zone can be controlled so as to minimise the number of mass-produced insects required for the arrest of species invasion. In particular, we predict that, given unknown rates of mosquito dispersal, management strategies should concentrate on larger release areas rather than more intense release rates for optimal control.

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The Sterile Insect Release Method for Pest Control: a Density-Dependent Model

Cited by 106 publications

References 0 publications

New revised simple models for interactive wild and sterile mosquito populations and their dynamics

New revised simple models for interactive wild and sterile mosquito populations and their dynamics

Mathematical Modeling of Sterile Insect Technology for Control of Anopheles Mosquito

Optimal barrier zones for stopping the invasion of Aedes aegypti mosquitoes via transgenic or sterile insect techniques

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