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

• ##### Lourdes Esteva
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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##### Article: Assessing the Influence of Quiescence Eggs on the Dynamics of Mosquito Aedes aegypti
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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.
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##### Article: A mathematical model of dengue transmission with memory
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ABSTRACT: We propose and analyze a new compartmental model of dengue transmission with memory between human-to-mosquito and mosquito-to-human. The memory is incorporated in the model by using a fractional differential operator. A threshold quantity R0, similar to the basic reproduction number, is worked out. We determine the stability condition of the disease-free equilibrium (DFE) E0 with respect to the order of the fractional derivative $\alpha$ and R0. We determine $\alpha$ dependent threshold values for R0, below which DFE (E0) is always stable, above which DFE is always unstable, and at which the system exhibits a Hopf-type bifurcation. It is shown that even though R0 is less than unity, the DFE may not be always stable, and the system exhibits a Hopf-type bifurcation. Thus, making R0 < 1 for controlling the disease is no longer a sufficient condition. This result is synergistic with the concept of backward bifurcation in dengue ODE models. It is also shown that R0 > 1 may not be a sufficient condition for the persistence of the disease. For a special case, when $\alpha$ = 1/2 , we analytically verify our findings and determine the critical value of R0 in terms of some important model parameters. Finally, we discuss about some dengue control strategies in light of the threshold quantity R0.
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• ##### Article: A spatial model with pulsed releases to compare strategies for the sterile insect technique applied to the mosquito Aedes aegypti
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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 08/2014; · 1.45 Impact Factor

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