Article

Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique

Departamento de Matemáticas, Facultad de Ciencias, UNAM 04510 México, D.F., Mexico.
Mathematical Biosciences (Impact Factor: 1.49). 01/2006; 198(2):132-47. DOI: 10.1016/j.mbs.2005.06.004
Source: PubMed

ABSTRACT We propose a mathematical model to assess the effects of irradiated (or transgenic) male insects introduction in a previously infested region. The release of sterile male insects aims to displace gradually the natural (wild) insect from the habitat. We discuss the suitability of this release technique when applied to peri-domestically adapted Aedes aegypti mosquitoes which are transmissors of Yellow Fever and Dengue disease.

Download full-text

Full-text

Available from: Hyun Mo Yang, Feb 07, 2014
0 Followers
 · 
137 Views
  • Source
    • "There have been numerous mathematical papers discussing application of optimal control scenario to the mosquito reduction issue (see e.g. [28] [29] [8] [24] [7] [18] [30] and some references therein). The authors used prototypic autonomous model utmost, encouraging us to propose a novel approach adopting non-autonomous dynamical system theory. "
    [Show abstract] [Hide abstract]
    ABSTRACT: It is preliminarily known that Aedes mosquitoes are very close to humans and their dwellings, also give rises to a broad spectrum of diseases: dengue, yellow fever, chikungunya. In this paper, we explore a multi-age-class model for mosquito population secondarily classi- fied into indoor-outdoor dynamics. We accentuate a novel design for the model in which periodicity of the affecting time-varying environ- mental condition is taken into account. Application of the optimal control with collocated measure as apposed to the widely-used pro- totypic smooth time-continuous measure is also considered. Using two approaches: least-square and maximum likelihood, we estimate several involving undetermined parameters. We analyze the model enforceability to biological point of view such as existence, unique- ness, positivity and boundedness of solution trajectory, also existence and stability of (non)trivial periodic solution(s) by means of the basic mosquito offspring number. Some numerical tests are brought along at the rest of the paper as a compact realistic visualization of the model.
    Mathematical Methods in the Applied Sciences 03/2015; DOI:10.1002/mma.3517 · 0.88 Impact Factor
  • Source
    • "Contemporary, eradication and control methods of mosquitos are similar to those arranged over half a century back. In the academic article [13], author has exhibited one of the controlling strategies named Sterile Insect Technique (SIT) for the control of Aedes aegypti mosquitoes. Further, RIDL (Release of Insects Carrying a Dominant Lethal) based on new genetic sexing system for male mosquitoes is introduced by which allow only to born of male mosquitoes by blocking of female production of Aedes aegypti [20]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: This article presents a new eco-epidemiological deterministic delay differential equation model considering a biological controlling approach on mosquitoes, for endemic dengue disease with variable host (human) and variable vector (Aedes aegypti) populations, and stage structure for mosquitoes. In this model, predator-prey interaction is considered by using larvae as prey and mosquito-fish as predator. We give a complete classification of equilibria of the model, and sufficient conditions for global stability/global attractivity of some equilibria are given by constructing suitable Lyapunov functionals and using Lyapunov-LaSalle invariance principle. Also, numerical simulations are presented to show the validity of our results.
    Electronic Journal of Differential Equations 01/2015; 2015 (2015)(10):1. · 0.42 Impact Factor
    • "The dynamics of system (1) was considered in [6]. According to Esteva and Yang [6] the trivial equilibrium point í µí±ƒ 0 = (0, 0, 0, 0, 0) of system (1) without SIT control is stable if í µí±… = í µí¼™í µí±Ÿí µí»¾í µí»½/(í µí¼‡ í µí°´+ í µí»¾)(í µí¼‡ í µí°¼ + í µí»½)í µí¼‡ í µí°¹ < 1; that is, in the absence of sterile insects (í µí»¼ = 0), the condition for existence of natural insects is í µí±… > 1. In affected areas the last inequality is satisfied, and an application of IVM is necessary. "
    [Show abstract] [Hide abstract]
    ABSTRACT: We formulate an infinite-time quadratic functional minimization problem of Aedes aegypti mosquito population. Three techniques of mosquito population management, chemical insecticide control, sterile insect technique control, and environmental carrying capacity reduction, are combined in order to obtain the most sustainable strategy to reduce mosquito population and consequently dengue disease. The solution of the optimization control problem is based on the ideas of the Dynamic Programming and Lyapunov Stability using State-Dependent Riccati Equation (SDRE) control method. Different scenarios are analyzed combining three mentioned population management efforts in order to assess the most sustainable policy to reduce the mosquito population.
    Journal of Applied Mathematics 01/2015; 2015:1-8. DOI:10.1155/2015/918194 · 0.72 Impact Factor
Show more