On Nonlinear Pest/Vector Control via the Sterile Insect Technique: Impact of Residual Fertility
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On Nonlinear Pest/Vector Control via the Sterile Insect Technique: Impact of Residual Fertility M. Soledad Aronna1
· Yves Dumont2,3,4
Received: 7 May 2020 / Accepted: 3 August 2020 © Society for Mathematical Biology 2020
Abstract We consider a minimalist model for the Sterile Insect Technique (SIT), assuming that residual fertility can occur in the sterile male population. Taking into account that we are able to get regular measurements from the biological system along the control duration, such as the size of the wild insect population, we study different control strategies that involve either continuous or periodic impulsive releases. We show that a combination of open-loop control with constant large releases and closedloop nonlinear control, i.e., when releases are adjusted according to the wild population size estimates, leads to the best strategy in terms of both number of releases and total quantity of sterile males to be released. Last but not least, we show that SIT can be successful only if the residual fertility is less than a threshold value that depends on the wild population biological parameters. However, even for small values, the residual fertility induces the use of such large releases that SIT alone is not always reasonable from a practical point of view and thus requires to be combined with other control tools. We provide applications against a mosquito species, Aedes albopictus, and a fruit fly, Bactrocera dorsalis, and discuss the possibility of using SIT when residual fertility among the sterile males, can occur. Keywords Pest control · Vector control · Sterile insect technique · Residual fertility · Closed-loop nonlinear control · Control failure · Impulsive periodic release
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M. Soledad Aronna [email protected] Yves Dumont [email protected]
1
Escola de Matemática Aplicada, FGV EMAp, Rio de Janeiro, Brazil
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CIRAD, UMR AMAP, 97410 St Pierre, Réunion Island, France
3
AMAP, Univ Montpellier, CIRAD, CNRS, INRAE, IRD, Montpellier, France
4
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa 0123456789().: V,-vol
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M. S. Aronna, Y. Dumont
1 Introduction The Sterile Insect Technique (SIT) is a biological control technique with the advantage of targeting the pest that needs to be controlled. The concept of SIT was conceived in the 30s and 40s by three key researchers in the USSR, Tanzania and the USA [see e.g., Dyck et al. (2005) for further details about the history of SIT]. The principle of SIT is very simple: it consists of releasing males that have been sterilized using ionizing radiation; these males will mate with wild females that will not produce viable offspring. However, while conceptually “simple”, SIT can be rather difficult to apply in the field as many feasibility steps need to be checked first. Since the initial field experiments, much progress has been done under the guidance of the IAEA (International Atomic Energy Agency), who is leading or involved in most of the SIT programs around the wor
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