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: 1.3). 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.

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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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    ABSTRACT: To prevent the transmissions of malaria, dengue fever, or other mosquito-borne diseases, one effective weapon is the sterile insect technique in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population. To study the impact of the sterile insect technique on disease transmission, we formulate discrete-time mathematical models, based on difference equations, for the interactive dynamics of the wild and sterile mosquitoes, incorporating different strategies in releasing sterile mosquitoes. We investigate the model dynamics and compare the impact of the different release strategies. Numerical examples are given to demonstrate rich dynamical features of the models.
    Full-text · Article · Dec 2015 · Journal of Biological Dynamics
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    • "In the integrated control of Aedes aegypti, preventive measures are mainly directed at breeding grounds, being simple and effective actions, especially those that consist of care to be adopted by the population. The technology currently under study includes biological control measures, chemical, genetic and physical, (Thomé, 2007;Donalísio and Glasser, 2002;Barsante et all, 2011;Esteva and Yang, 2005;Florentino et all, 2014). Among the various biological control measures, predators of larvae-eating fish type are the most recommended due to its easy acquisition and maintenance, especially for drinkers of large animals, construction elevator pits, water features / ornamental fountains, pools and abandoned deposits of non-potable water. "
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    ABSTRACT: Although linear systems analysis techniques are well developed, the search for methods of analysis and control of nonlinear systems is expanding. Can be cited nonlinear techniques based on Lyapunov stability theory and exact linearization methods in the state space, which is the tool for analysis of this study. The exact linearization consists of a procedure to transform the dynamics of a nonlinear system in a linear dynamics through a non-linear feedback of the states or the chosen output previously. The advantage is that the resulting closed loop system is linear and time invariant, allowing it to hold a second feedback, simpler to obtain. This second control law is used to provide less sensitivity to variations and uncertainties in the parameters. Moreover, it is an essential part of the development of nonlinear controllers robust and adaptive. This methodology of analysis and nonlinear dynamic design has been used successfully in tracking problems in Engineering, as well as being used in medical and biological problems. The aim of this work is apply the input-output linearization technique to a nonlinear model that describes the dynamic of the mosquitoes population that transmits dengue. The study of the plane phase of this dynamic will be made in addition to the use of the internal dynamics of this system for local asymptotic stability analysis. Numerical experiments are presented.
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