Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control.

*(English)*Zbl 1392.92096Summary: The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of individuals carrying the Wolbachia parasite that need to be introduced into the natural population. The introduced mosquitoes are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this study, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then use feedback control techniques to devise an introduction protocol that is proved to guarantee that the population converges to a stable equilibrium where the totality of mosquitoes carry Wolbachia.

##### MSC:

92D30 | Epidemiology |

34C12 | Monotone systems involving ordinary differential equations |

93D15 | Stabilization of systems by feedback |

93D25 | Input-output approaches in control theory |

##### Keywords:

Wolbachia; vector control; global stabilization; monotone systems; input-output characteristic
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\textit{P.-A. Bliman} et al., J. Math. Biol. 76, No. 5, 1269--1300 (2018; Zbl 1392.92096)

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