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    Interval observer for uncertain time-varying SIR-SI model of vector-borne disease
    (EMAp, 2017) Aronna, Maria Soledad; Bliman, Pierre-Alexandre
    The issue of state estimation is considered for an SIR-SI model describing a vector-borne disease such as dengue fever, with seasonal variations and uncertainties in the transmission rates. Assuming continuous measurement of the number of new infectives in the host population per unit time, a class of interval observers with estimate-dependent gain is constructed, and asymptotic error bounds are provided. The synthesis method is based on the search for a common linear Lyapunov function for monotone systems representing the evolution of the estimation errors.
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    Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control
    (EMAp, 2015-03-19) Bliman, Pierre-Alexandre; Aronna, Maria Soledad; Coelho, Flávio Codeço; Silva, Moacyr Alvim Horta Barbosa da
    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 which is proved to guarantee that the population converges to a stable equilibrium where the totality of mosquitoes carry Wolbachia.