A feedback control perspective on biological control of dengue vectors by Wolbachia infection

Abstract

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. 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 feedback-based release strategies, enforceable to a variety of models and situations. These principles are exemplified by several feedback control laws whose stabilizing properties are demonstrated, illustrated numerically and compared, when applied to a model retrieved from [P.-A. Bliman et al., Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control. J. of Math. Bio. 76(5):1269–1300, 2018]. The contribution is believed to be also of potential interest to tackle other important issues related to the biological control of vectors and pests. A crucial use of the theory of monotone dynamical systems is made in the derivations.