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: 1.3). 01/2006; 198(2):132-47. DOI: 10.1016/j.mbs.2005.06.004
Source: PubMed


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.

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Available from: Hyun Mo Yang, Feb 07, 2014
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    • "Dumont and Dufourd [19] developed a mathematical model with pulsed release of sterile males to simulate mosquito dispersal and studied its controllability taking into account the variability of environmental parameters. Esteva and Yang [22] employed optimal control methods to find the appropriate rate for the introduction of sterile mosquitoes. Li [41] [42] developed difference and respectively, differential models to characterize the interactions between wild and transgenic mosquitoes. "
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    ABSTRACT: This paper proposes and investigates a delayed model for the dynamics and control of a mosquito population which is subject to an integrated strategy that includes pesticide release, the use of mechanical controls and the use of the sterile insect technique (SIT). The existence of positive equilibria is characterized in terms of two threshold quantities, being observed that the " richer " equilibrium (with more mosquitoes in the aquatic phase) has better chances to be stable, while a longer duration of the aquatic phase has the potential to destabilize both equilibria. It is also found that the stability of the trivial equilibrium appears to be mostly determined by the value of the maturation rate from the aquatic phase to the adult phase. A nonstandard finite difference (NSFD) scheme is devised to preserve the positivity of the approximating solutions and to keep consistency with the continuous model. The resulting discrete model is transformed into a delay-free model by using the method of augmented states, a necessary condition for the existence of optimal controls then determined. The particular-ities of different control regimes under varying environmental temperature are investigated by means of numerical simulations. It is observed that a combination of all three controls has the highest impact upon the size of the aquatic population. At higher environmental temperatures , the oviposition rate is seen to possess the most prominent influence upon the outcome of the control measures.
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    • "There are mathematical models in the literature formulated to study the interactive dynamics of mosquito populations or the control of mosquitoes [3] [4] [6] [7] [9] [14] [15]. Models for vector-borne diseases, incorporating sterile mosquitoes, have also been formulated to investigate the disease transmission dynamics in [11] [13] [27]. We focus, in this paper, on the dynamics of the interactive wild and sterile mosquitoes and explore the impact of different strategies of releasing sterile mosquitoes. "
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    • "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. "
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