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Register a new userThe sterile insect technique used as a barrier control against reinfestation
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The sterile insect technique consists in massive release of sterilized males in the aim to reduce the size of mosquitoes population or even eradicate it. In this work, we investigate the feasability of using the sterile insect technique as a barrier against reinvasion. More precisely, we provide some numerical simulations and mathematical results showing that performing the sterile insect technique on a band large enough may stop reinvasion.
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In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing necessary conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-loop control strategy that relies on periodic impulsive releases of sterile males with constant release size. Under this control mode, global convergence towards the mosquito-free equilibrium is proved on the grounds of sufficient condition that relates the size and frequency of releases. If periodic assessments (either synchronized with releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, which is adjustable in accordance with reliable estimations of the wild population sizes. Under this control mode, global convergence to the mosquito-free equilibrium is proved on the grounds of another sufficient condition that relates not only the size and frequency of periodic releases but also the frequency of sparse measurements taken on wild populations. Finally, we propose a mixed control strategy that combines open-loop and closed-loop strategies. This control mode renders the best result, in terms of overall time needed to reach elimination and the number of releases to be effectively carried out during the whole release campaign, while requiring for a reasonable amount of released sterile insects.
Vector/Pest control is essential to reduce the risk of vector-borne diseases or losses in crop fields. Among biological control tools, the sterile insect technique (SIT), is the most promising one. SIT control generally consists of massive releases of sterile insects in the targeted area in order to reach elimination or to lower the pest population under a certain threshold. The models presented here are minimalistic with respect to the number of parameters and variables. The first model deals with the dynamics of the vector population while the second model, the SIT model, tackles the interaction between treated males and wild female vectors. For the vector population model, the elimination equilibrium $mathbb{0}$ is globally asymptotically stable when the basic offspring number, $mathcal{R}$, is lower or equal to one, whereas $mathbb{0}$ becomes unstable and one stable positive equilibrium exists, with well-determined basins of attraction, when $mathcal{R}>1$. For the SIT model, we obtain a threshold number of treated male vectors above which the control of wild female vectors is effective: the massive release control. When the amount of treated male vectors is lower than the aforementioned threshold number, the SIT model experiences a bistable situation involving the elimination equilibrium and a positive equilibrium. However, practically, massive releases of sterile males are only possible for a short period of time. That is why, using the bistability property, we develop a new strategy to maintain the wild population under a certain threshold, for a permanent and sustainable low level of SIT control. We illustrate our theoretical results with numerical simulations, in the case of SIT mosquito control.
The development of sustainable vector/pest control methods is of utmost importance to reduce the risk of vector-borne diseases and pest damages on crops. Among them, the Sterile Insect Technique (SIT) is a very promising one. In this paper, using diffusion operators, we extend a temporal SIT model, developed in a recent paper, into a partially degenerate reaction-diffusion SIT model. Adapting some theoretical results on traveling wave solutions for partially degenerate reaction-diffusion equations, we show the existence of mono-stable and bi-stable traveling-wave solutions for our SIT system. The dynamics of our system is driven by a SIT-threshold number above which the SIT control becomes effective and drives the system to elimination, using massive releases. When the amount of sterile males is lower than the SIT-threshold, the SIT model experiences a strong Allee effect such that a bi-stable traveling wave solution can exist and can also be used to derive an effective long term strategy, mixing massive and small releases. We illustrate some of our theoretical results with numerical simulations , and, also explore numerically spatial-localized SIT control strategies, using massive and small releases. We show that this corridor strategy can be efficient to block an invasion and eventually can be used to push back the front of a vector/pest invasion.
Mosquitoes are responsible for the transmission of many diseases such as dengue fever, zika or chigungunya. One way to control the spread of these diseases is to use the sterile insect technique (SIT), which consists in a massive release of sterilized male mosquitoes. This strategy aims at reducing the total population over time, and has the advantage being specific to the targeted species, unlike the use of pesticides. In this article, we study the optimal release strategies in order to maximize the efficiency of this technique. We consider simplified models that describe the dynamics of eggs, males, females and sterile males in order to optimize the release protocol. We determine in a precise way optimal strategies, which allows us to tackle numerically the underlying optimization problem in a very simple way. We also present some numerical simulations to illustrate our results.
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 closed-loop nonlinear control, i.e. when releases are adjusted according to the wild population size estimates, leads to the best strategy in terms both of 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, textit{Aedes albopictus}, and a fruit fly, textit{Bactrocera dorsalis}, and discuss the possibility of using SIT when residual fertility, among the sterile males, can occur.
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