Mathematical Models for the Use of Sterile Insects

Barclay, Hugh J.

doi:10.1007/1-4020-4051-2_6

Cited by 77 publications

(66 citation statements)

References 48 publications

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“…The dearth of population models to guide SIT based on inherited sterility is demonstrated by a recent review of 50 years of SIT modelling ( Barclay, 2005 ) mentioning inherited sterility only once. An accompanying review of inherited sterility in insects ( Carpenter et al , 2005 ) cites only four peerreviewed population models ( Walker & Pedersen, 1969;Knipling, 1970;Brower & Tilton, 1975;Carpenter et al , 1987 ), each of which is tailored to a specific pest species.…”

Section: Discussionmentioning

confidence: 99%

“…Similarly, the competitiveness of adult males, in terms of locating and successfully mating with a female, relative to that of wild males is denoted c M , c S , and c Y , where c M = 1. The model assumes only one effective mating per female, which is the case if only the first mating of a female results in sperm retention, or if all sperm from previous matings is replaced at each successive mating, or if that the sperm of irradiated males is fully competitive ( Berryman, 1967 ), and if all matings occur before oviposition begins ( Barclay, 2005 ). In this case, matings can be modelled by a simple extension of Knipling's (1955) formula, so that the probability of a female successfully mating with a fertile male is M /( M + c S S + c Y Y ), whereas that of successfully mating with an IL male is c Y Y / ( M + c S S + c Y Y ), and that of successfully mating with an irradiated male released into the population is c S S / ( M + c S S + c Y Y ).…”

Section: Discrete Generations Modelmentioning

confidence: 99%

“…We believe that this is an opportune time for new population models to inform inherited sterility SIT programmes, particularly models that incorporate further biological realism such as demographic stochasticity, Allee effects and spatial structure, all of which are known to have major influences on the viability and dynamics of small populations. Hypotheses generated by such models need to be tested critically in the field, and further theory is needed to optimize integrated eradication programmes in which SIT is used simultaneously with other population controls ( Barclay, 2005 ).…”

Section: Figurementioning

confidence: 99%

“…Although a wide range of mathematical models have been published to underpin the use of SIT (for a comprehensive review, see Barclay, 2005 ), few have considered inherited sterility and its effects. Knipling's (1970) numerical analysis lacks biological detail, whereas others ( Walker & Pedersen, 1969;Brower & Tilton, 1975;Carpenter et al , 1987 ) are tailored for specific pest species.…”

Section: Introductionmentioning

confidence: 99%

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Modelling the effects of inherited sterility for the application of the sterile insect technique

Kean

Wee

Stephens

et al. 2008

Agri and Forest Entomology

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1 The sterile insect technique (SIT) involves the release of large numbers of sterile or partially-sterile insects into a wild pest population to dilute the number of successful wild matings, with the eventual aim of eradication or area-wide suppression. General population models, encompassing a wide range of SIT types, were used to derive principles for optimizing the success of SIT, with particular emphasis on the application of partial sterility leading to inherited sterility in the F 1 population. 2 The models show that inherited sterility can only be guaranteed to be more effective than complete sterility if matings between irradiated-lineage partners are unsuccessful. This is widely assumed but rarely examined experimentally. 3 The models allow the critical overflooding ratio, c , to be calculated for a particular target species, suggesting the release rate required to prevent population increase. Successful eradication using SIT alone should aim for a substantially higher release rate than suggested by c . 4 The models show that pest populations may continue to increase in the first few generations of SIT releases, regardless of release rate, as irradiated-lineage individuals infiltrate the population. This does not necessarily imply that the SIT programme will be unsuccessful in the longer term. 5 For pests with overlapping generations, the models suggest that frequent small releases may be more effective than less frequent large releases, particularly when the average release rate is close to the critical threshold for success.

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Section: Discussionmentioning

confidence: 99%

Section: Discrete Generations Modelmentioning

confidence: 99%

Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling the effects of inherited sterility for the application of the sterile insect technique

Kean

Wee

Stephens

et al. 2008

Agri and Forest Entomology

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“…Therefore, it is necessary to consider new sustainable alternatives or additional tools, like the Sterile Insect Technique (SIT). SIT consists in releasing sterilized male mosquitoes that will mate with wild females which won't be able to deposit hatching eggs [32] (see also [6,1,23] for extended references about SIT), driving slowly the wild population to decline. Thus, the release of sufficiently many sterile males over a sufficiently long period of time can lead to local reduction or elimination of the wild population.…”

Section: Introductionmentioning

confidence: 99%

Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control

Dufourd

Dumont

2013

Computers & Mathematics with Applications

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The aim of this paper is to develop a mathematical model to simulate mosquito dispersal and its control taking into account environmental parameters, like wind, temperature, or landscape elements. We particularly focus on Aedes albopictus mosquito which is now recognized as a major vector of human arboviruses, like chikungunya, dengue, or yellow fever. One way to prevent those epidemics is to control the vector population. Biological control tools, like the Sterile Insect Technique (SIT), are of great interest as an alternative to chemical control tools which are very detrimental to environment. The success of SIT is based on a good knowledge of the biology of the insect, but also on an accurate modeling of the insect's distribution. We consider a compartmental approach and derive temporal and spatio-temporal models, using Advection-Diffusion-Reaction equations to model mosquito dispersal. Periodic releases of sterilized males are modeled with an impulse differential equation. Finally, using the splitting operator approach, and well-suited numerical methods for each operator, we provide numerical simulations for mosquito spreading, and test different vector control scenarios. We show that environmental parameters, like vegetation, can have a strong influence on mosquito distribution and in the efficiency of vector control tools, like SIT.keyword Advection diffusion reaction equation, impulse differential equation, mosquito dispersal, sterile insect technique, operator splitting, nonstan-

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Management of a stage‐structured insect pest: an application of approximate optimization

Hackett

Bonsall

2018

Ecological Applications

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Ecological decision problems frequently require the optimization of a sequence of actions over time where actions may have both immediate and downstream effects. Dynamic programming can solve such problems only if the dimensionality is sufficiently low. Approximate dynamic programming (ADP) provides a suite of methods applicable to problems of arbitrary complexity at the expense of guaranteed optimality. The most easily generalized method is the look-ahead policy: a brute-force algorithm that identifies reasonable actions by constructing and solving a series of temporally truncated approximations of the full problem over a defined planning horizon. We develop and apply this approach to a pest management problem inspired by the Mediterranean fruit fly, Ceratitis capitata. The model aims to minimize the cumulative costs of management actions and medfly-induced losses over a single 16-week season. The medfly population is stage-structured and grows continuously while management decisions are made at discrete, weekly intervals. For each week, the model chooses between inaction, insecticide application, or one of six sterile insect release ratios. Look-ahead policy performance is evaluated over a range of planning horizons, two levels of crop susceptibility to medfly and three levels of pesticide persistence. In all cases, the actions proposed by the look-ahead policy are contrasted to those of a myopic policy that minimizes costs over only the current week. We find that look-ahead policies always out-performed a myopic policy and decision quality is sensitive to the temporal distribution of costs relative to the planning horizon: it is beneficial to extend the planning horizon when it excludes pertinent costs. However, longer planning horizons may reduce decision quality when major costs are resolved imminently. ADP methods such as the look-ahead-policy-based approach developed here render questions intractable to dynamic programming amenable to inference but should be applied carefully as their flexibility comes at the expense of guaranteed optimality. However, given the complexity of many ecological management problems, the capacity to propose a strategy that is "good enough" using a more representative problem formulation may be preferable to an optimal strategy derived from a simplified model.

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Mathematical Models for the Use of Sterile Insects

Cited by 77 publications

References 48 publications

Modelling the effects of inherited sterility for the application of the sterile insect technique

Modelling the effects of inherited sterility for the application of the sterile insect technique

Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control

Management of a stage‐structured insect pest: an application of approximate optimization

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