اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the use of Traveling Waves for Pest/Vector elimination using the Sterile Insect Technique
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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.
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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 o
f 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.
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 con
trol 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.
Vector control is critical to limit the circulation of vector-borne diseases like chikungunya, dengue or zika which have become important issues around the world. Among them the Sterile Insect Technique (SIT) and the Incompatible Insect Technique (II
T) recently aroused a renewed interest. In this paper we derive and study a minimalistic mathematical model designed for Aedes mosquito population elimination by SIT/IIT. Contrary to most of the previous models, it is bistable in general, allowing simultaneously for elimination of the population and for its survival. We consider dierent types of releases (constant, periodic or impulsive) and show necessary conditions to reach elimination in each case. We also estimate both sucient and minimal treatment times. Biological parameters are estimated from a case study of an Aedes polynesiensis population, for which extensive numerical investigations illustrate the analytical results. The applications of this work are twofold: to help identifying some key parameters that may need further eld investigations, and to help designing release protocols.
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.
The deer tick, $textit{Ixodes scapularis}$, is a vector for numerous human diseases, including Lyme disease, anaplasmosis, and babesiosis. Concern is rising in the US and abroad as the population and range of this species grow and new diseases emerge
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