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: 1.45). 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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    ABSTRACT: We present a simple mathematical model to replicate the key features of the sterile insect technique (SIT) for controlling pest species, with particular reference to the mosquito Aedes aegypti, the main vector of dengue fever. The model differs from the majority of those studied previously in that it is simultaneously spatially explicit and involves pulsed, rather than continuous, sterile insect releases. The spatially uniform equilibria of the model are identified and analysed. Simulations are performed to analyse the impact of varying the number of release sites, the interval between pulsed releases and the overall volume of sterile insect releases on the effectiveness of SIT programmes. Results show that, given a fixed volume of available sterile insects, increasing the number of release sites and the frequency of releases increases the effectiveness of SIT programmes. It is also observed that programmes may become completely ineffective if the interval between pulsed releases is greater that a certain threshold value and that, beyond a certain point, increasing the overall volume of sterile insects released does not improve the effectiveness of SIT. It is also noted that insect dispersal drives a rapid recolonisation of areas in which the species has been eradicated and we argue that understanding the density dependent mortality of released insects is necessary to develop efficient, cost-effective SIT programmes.
    Mathematical Biosciences 01/2014; · 1.45 Impact Factor
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    ABSTRACT: The Sterile Insect Technology (SIT) is a nonpolluting method of control of the invading insects that transmit disease. The method relies on the release of sterile or treated males in order to reduce the wild population of anopheles mosquito. We propose two mathematical models. The first model governs the dynamics of the anopheles mosquito. The second model, the SIT model, deals with the interaction between treated males and wild female anopheles. Using the theory of monotone operators, we obtain dynamical properties of a global nature that can be summarized as follows. Both models are dissipative dynamical systems on the positive cone R+4. The value R=1R=1 of the basic offspring number RR is a forward bifurcation for the model of the anopheles mosquito, with the trivial equilibrium 00 being globally asymptotically stable (GAS) when R≤1R≤1, whereas 00 becomes unstable and one stable equilibrium is born with well determined basins of attraction when R>1R>1. For the SIT model, we obtain a threshold number λˆ of treated male mosquitoes above which the control of wild female mosquitoes is effective. That is, for λ>λˆ the equilibrium 00 is GAS. When 0<λ≤λˆ, the number of equilibria and their stability are described together with their precise basins of attraction. These theoretical results are rephrased in terms of possible strategies for the control of the anopheles mosquito and they are illustrated by numerical simulations.
    Computers & Mathematics with Applications 08/2012; 64(3):374–389. · 2.07 Impact Factor
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    ABSTRACT: The anthropophilic and peridomestic female Aedes aegypti bites humans to suck blood to matu-rate fertilized eggs, which are laid in appropriate recipients (breeding sites). These eggs can hatch in contact with water releasing larvae, or can be stored in a dormant state (quiescence), which last for extended periods. Taking into account this ability of eggs of A. aegypti mosquitoes, mathemat-ical model is developed taking into account four successive quiescence stages. The analysis of the model shows that the ability of the eggs surviving in dormant state in adverse abiotic conditions, depending on the model parameters, can increase the fitness of mosquito population; in other words, the capacity of the mosquitoes generating offsprings is increased.
    Applied Mathematics 10/2014; 5(17):2696-2711. · 0.19 Impact Factor


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