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

*(English)*Zbl 1090.92048Summary: 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 the Dengue disease.

##### MSC:

92D40 | Ecology |

92D30 | Epidemiology |

93C95 | Application models in control theory |

34D20 | Stability of solutions to ordinary differential equations |

34D99 | Stability theory for ordinary differential equations |

##### Keywords:

mathematical modeling; genetic control; sterile insect release; aedes aegypti; threshold; break-point
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\textit{L. Esteva} and \textit{H. M. Yang}, Math. Biosci. 198, No. 2, 132--147 (2005; Zbl 1090.92048)

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##### References:

[1] | Knipling, E.F., Possibilities of insect control or eradication through the use of sexually sterile males, J. econ. entomol., 48, 459, (1955) |

[2] | Bartlett, A.C.; Staten, R.T., The sterile release method and other genetic control strategies, (), URL: |

[3] | Knipling, E.F., The basic principles of insect population suppression and management, Agriculture handbook, 512, (1979), US Department of Agriculture Washington, DC |

[4] | Knipling, E.F., Sterile insect technique as a screwworm control measure: the concept and its development, (), 4 |

[5] | Ito, Y., A model of sterile insect release for eradication of the melon fly dacus cucurbitae coquillett, Appl. ent. zool., 12, 303, (1977) |

[6] | Barclay, H.J., Pest population stability under sterile release, Res. popul. ecol., 24, 405, (1982) |

[7] | Costello, W.G.; Taylor, H.M., Mathematical models of the sterile male technique of insect control, (), 318 |

[8] | Dietz, K., The effect of immigration on genetic control, Theor. popul. biol., 9, 58, (1976) · Zbl 0335.92015 |

[9] | Plant, R.E.; Mangel, M., Modeling and simulation in agricultural pest management, SIAM rev., 29, 235, (1987) · Zbl 0612.92014 |

[10] | Prout, T., The joint effects of the release of sterile males and immigration of fertilized females on a density regulated population, Theor. popul. biol., 13, 40, (1978) |

[11] | Barclay, H.J., Models for the sterile insect release method with the concurrent release of pesticides, Ecol. modell., 11, 167, (1980) |

[12] | Harrison, G.W.; Barclay, H.J.; van den Driesche, P., Analysis of a sterile insect release model with predation, J. math. biol., 16, 33, (1982) · Zbl 0541.92019 |

[13] | Pates, H.; Curtis, C., Mosquito behavior and vector control, Annu. rev. entomol., 50, 53, (2005) |

[14] | Coleman, P.G.; Alphey, L., Editorial: genetic control of vector population: an imminent prospect, Trop. med. int. health, 9, 4, 433, (2004) |

[15] | Barclay, H.J., The sterile insect-released method on species with two-stage life cycles, Res. popul. ecol., 21, 165, (1980) |

[16] | Hale, J.K., Ordinary differential equations, (1969), John Wiley and Sons New York · Zbl 0186.40901 |

[17] | Bradley, D.J.; May, R.M., Consequences of helminth aggregation for the dynamics of schistosomiasis, Trans. R. soc. trop. med. hyg., 72, 3, 262, (1978) |

[18] | Gubler, D.J.; Dengue, (), 213 |

[19] | Grover, K.K.; Suguna, S.G.; Uppal, D.K.; Singh, K.R.P.; Ansari, M.A., Field experiments on the competitiveness of males carrying genetic control systems for aedes aegypti, Entomol. exp. appl., 20, 8, (1976) |

[20] | Seawright, J.A.; Kaiser, P.E.; Dame, D.A., Mating competitiveness of chemosterilized hybrid males of aedes aegypti (L.) in field tests, Mosq. news, 37, 615, (1977) |

[21] | Reuben, R.; Rahman, K.; Panicker, P.; Das, P.; Brooks, G., The development of a strategy for large-scale releases of sterile males of aedes aegypti, J. commun. dis., 7, 313, (1975) |

[22] | Singh, K.R.P.; Brooks, G.D., Semi-automatic release system for distribution of mosquitoes during genetic control operations, J. commun. dis., 7, 288, (1975) |

[23] | Reiter, P.; Amador, M.A.; Anderson, R.A.; Clark, G.C., Short report: dispersal of aedes aegypti in an urban area after blood feeding as demonstrated by rubidium-marked eggs, Am. J. trop. med. hyg., 52, 177, (1995) |

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