On the use of the sterile insect release technique to reduce or eliminate mosquito populations

Mathematical Biosciences

et al. 2019

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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 mosquitofree 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.

Section: Introductionmentioning

confidence: 99%

Implementation of control strategies for sterile insect techniques

Bliman

Cardona-Salgado

Mathematical Biosciences

et al. 2019

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“…In this manuscript we complete the work done in [20], when no Allee effect can be exploit in the SIT treatment strategy. We know that without Allee effect, a permanent SIT treatment is necessary to maintain the population under a certain threshold and eventually to drive it to extinction, at a minimal cost.…”

Section: Resultsmentioning

confidence: 99%

“…where the parameters and state variables are described in Table 1. Contrary to [20], we assume a density-dependent mortality rate in the aquatic stage. This may correspond to an intra-specific competition between the larvae stages, for instance.…”

Section: A Minimalistic Entomological Modelmentioning

confidence: 99%

See 1 more Smart Citation

Sustainable vector/pest control using the permanent sterile insect technique

Anguelov

Math Methods in App Sciences

Djeumen

2020

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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 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 0 is globally asymptotically stable when the basic offspring number, R, is lower or equal to one, whereas 0 becomes unstable and one stable positive equilibrium exists, with well determined basins of attraction, when 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.

“…Several types of perturbations, or instantaneous phenomena, have been considered as pulse events in mathematical models. These include events such as birth, vaccination, release, harvest, or fire events : see Mailleret and Lemesle [36] where various examples are given and references therein; see also White et al [57], Dumont and Tchuenche [13], Strugarek et al [45], Bliman et al [9], Anguelov et al [4], Liu et al [31], Zhao et al [65], Yatat Djeumen and Dumont [61], Yatat Djeumen et al [63] and references therein. The resulting impulsive models were rigorously analyzed by the well-known theory due to Lakshmikantham et al [26], Bainov and Simeonov [6] and [5], or Lakmeche and Arino [25].…”

Section: Space-implicit Impulsive Modelsmentioning

confidence: 99%

Spreading Speeds and Traveling Waves for Monotone Systems of Impulsive Reaction–Diffusion Equations: Application to Tree–Grass Interactions in Fire-prone Savannas

Banasiak

Djeumen

2020

Differ Equ Dyn Syst

Many systems in life sciences have been modeled by reaction-diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events, etc) such that an appropriate formalism like impulsive reaction-diffusion equations is necessary to analyze them. While several works tackled the issue of traveling waves for monotone reaction-diffusion equations and the computation of spreading speeds, very little has been done in the case of monotone impulsive reaction-diffusion equations. Based on vector-valued recursion equations theory, we aim to present in this paper results that address two main issues of monotone impulsive reaction-diffusion equations. Our first result deals with the existence of traveling waves for monotone systems of impulsive reaction-diffusion equations. Our second result tackles the computation of spreading speeds for monotone systems of impulsive reaction-diffusion equations. We apply our methodology to a planar system of impulsive reaction-diffusion equations that models tree-grass interactions in fire-prone savannas. Numerical simulations, including numerical approximations of spreading speeds, are finally provided in order to illustrate our theoretical results and support the discussion.