Modeling and Simulations of Mosquito Dispersal. The Case of Aedes albopictus

Dufourd, Claire; Dumont, Yves

doi:10.11145/j.biomath.2012.09.262

Cited by 25 publications

(25 citation statements)

References 14 publications

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“…Based on these biological properties, classical SIT and IIT (see [7,8,9,16,19,27] and references therein) or population replacement (see [4,5,11,12,13,17,21,24,28] and references therein) have been modeled and studied theoretically in a large number of papers, in order to derive results to explain the success or not of these strategies using discrete, continuous or hybrid modeling approaches, temporal and spatio-temporal models. More recently, the theory of monotone dynamical systems [26] has been applied efficiently to study SIT [1,27] or population replacement [2,18] systems.…”

Section: Introductionmentioning

confidence: 99%

Implementation of control strategies for sterile insect techniques

Bliman

Cardona-Salgado

Dumont

et al. 2019

Mathematical Biosciences

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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.

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Section: Introductionmentioning

confidence: 99%

Implementation of control strategies for sterile insect techniques

Bliman

Cardona-Salgado

Dumont

et al. 2019

Mathematical Biosciences

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“…Such a model requires knowledge of the properties of the trap such as the active area [5] and the strength of attraction, as well as some properties of the population, like its diffusion rate [25]. These parameters are seldom exactly known, and also tend to vary with changing weather [23] and landscape heterogeneity [11], [10].…”

Section: Introductionmentioning

confidence: 99%

Parameter Identification in Population Models for Insects Using Trap Data

Dufourd¹,

Weldon²,

Anguelov³

et al. 2013

BIOMATH

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BIOMATH h t t p : / / w w w. b i o m a t h f o r u m . o r g / b i o m a t h / i n d e x . p h p / b i o m a t h /Abstract-Traps are used commonly to establish the presence and population density of pest insects. Deriving estimates of population density from trap data typically requires knowledge of the properties of the trap (e.g. active area, strength of attraction) as well as some properties of the population (e.g. diffusion rate). These parameters are seldom exactly known, and also tend to vary in time, (e.g. as a result of changing weather conditions, insect physiological condition). We propose using a set of traps in such a configuration that they trap insects at different rates. The properties of the traps and the characteristics of the population, including its density, are simultaneously estimated from the insects captured in these traps. The basic model is an advection-diffusion equation where the traps are represented via a suitable advection term defined by the active area of the traps. The values of the unknown parameters of the model are derived by solving an optimization problem. Numerical simulations demonstrate the accuracy and the robustness of this method of parameter identification.

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“…By(15)-(17), we have ∈ X + . Since the functions B(W) are positive, it is clear that(19) satisfies the assumptions in Corollary 7.3.2 in,49 which complete the proof.The following result establishes the global well-posedness result for (13)-(17). For any ∈ X + , system (13)-(17) admits a unique solution u(t, x, ) defined on [0, ∞) × Ω, and the solution semiflow t ∶ X + → X + has a global compact attractor.…”

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confidence: 57%

Mathematical analysis of a spatio‐temporal model for the population ecology of anopheles mosquito

Manyombe

Mbang

Tsanou

et al. 2020

Math Methods in App Sciences

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We propose a novel model for the population dynamics of mosquitoes by considering the dispersal states of female mosquitoes of oviposition's cycle and spatial variations. From the modeling perspective, a general functional form of eggs oviposition rate is used including the Malthusian, the Verhlust‐Pearl logistic, the Hassell, and the Maynard‐Smith‐Slatkin functions. From the theoretical and numerical perspectives, the study is done in two steps using the more realistic birth Maynard‐Smith‐Slatkin function. First, we consider an ordinary differential equations model and show that the mosquito‐free equilibrium (MFE) is globally asymptotically stable, whenever the basic offspring number scriptR0ode is less than unity. Using a fluctuation argument, we prove that the unique mosquito‐persistent equilibrium (MPE) is globally attractive, whenever scriptR0ode exceeds the unity. Moreover, the temporal model undergoes a Hopf bifurcation in the absence of density‐dependent mortality in the aquatic stage of mosquitoes. Second, the temporal model is extended into an advection‐reaction‐diffusion model in order to account for the movement of mosquitoes and their spatial source of heterogeneity. We establish the uniform persistence and the existence of at least one positive steady state whenever the spatial basic offspring number scriptR0pde is greater than unity. Finally, for the case study of malaria vector agent (Anopheles mosquito), we construct a nonstandard finite difference scheme that is dynamically consistent with the features of the continuous model to illustrate our results, including the spatial heterogeneity of mosquito resources.

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Modeling and Simulations of Mosquito Dispersal. The Case of Aedes albopictus

Cited by 25 publications

References 14 publications

Implementation of control strategies for sterile insect techniques

Implementation of control strategies for sterile insect techniques

Parameter Identification in Population Models for Insects Using Trap Data

Mathematical analysis of a spatio‐temporal model for the population ecology of anopheles mosquito

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