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Register a new userModelling and control of Mendelian and maternal inheritance for biological control of dengue vectors
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Added by
Pierre-Alexandre Bliman
Publication date
2020
fields
Biology
and research's language is
English
Authors
Pastor Perez Estigarribia
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Mosquitoes are vectors of viral diseases with epidemic potential in many regions of the world, and in absence of vaccines or therapies, their control is the main alternative. Chemical control through insecticides has been one of the conventional strategies, but induces insecticide resistance, which may affect other insects and cause ecological damage. Biological control, through the release of mosquitoes infected by the maternally inherited bacterium Wolbachia, which inhibits their vector competence, has been proposed as an alternative. The effects of both techniques may be intermingled in practice: prior insecticide spraying may debilitate wild population, so facilitating subsequent invasion by the bacterium; but the latter may also be hindered by the release of susceptible mosquitoes in an environment where the wild population became resistant, as a result of preexisting undesired exposition to insecticide. To tackle such situations, we propose here a unifying model allowing to account for the cross effects of both control techniques, and based on the latter, design release strategies able to infect a wild population. The latter are feedback laws, whose stabilizing properties are studied.
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Controlling diseases such as dengue fever, chikungunya and zika fever by introduction of the intracellular parasitic bacterium Wolbachia in mosquito populations which are their vectors, is presently quite a promising tool to reduce their spread. While description of the conditions of such experiments has received ample attention from biologists, entomologists and applied mathematicians, the issue of effective scheduling of the releases remains an interesting problem for Control theory. Having in mind the important uncertainties present in the dynamics of the two populations in interaction, we attempt here to identify general ideas for building release strategies, which should apply to several models and situations. These principles are exemplified by two interval observer-based feedback control laws whose stabilizing properties are demonstrated when applied to a model retrieved from [Bliman et al., 2018]. Crucial use is made of the theory of monotone dynamical systems.
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