Section: New Results

Epidemiology

Participants : Luis Lopes Neves de Almeida, M. Soledad Aronna [FGV, Rio de Janeiro] , Pierre-Alexandre Bliman, Flávio C. Coelho [FGV, Rio de Janeiro] , Martin Strugarek, Nicolas Vauchelet, Jorge Zubelli [IMPA, Rio de Janeiro] .

Establishing Wolbachia by feedback

The releases of Wolbachia-positive mosquitoes are usually completed on an open-loop approach, that is, with a schedule computed once for all before the beginning of the experiment. Using the fact that measurements are achieved and available during the whole release process, we applied feedback control technique 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. A major advantage of feedback compared to open-loop approaches is its ability to cope with the uncertainties in the model dynamics (typically in the modelling of the life stages and the population structure), in the parameters (population size, mortality, reproductive rates, etc.), and in the size of the population to be treated.

Travelling waves in the problem of infestation by Wolbachia

As described above, a new method of control of dengue fever consists in releasing Wolbachia-infected mosquitos in the field, in the aim to replace the whole existing population by a population unable to transmit Dengue fever. In the study of the feasibility of such a strategy, an important issue concerns the spacial propagation of the mosquitoes. More precisely, releasing infected mosquitoes in a given domain (which can be a part of the city of Rio de Janeiro), the hope is to invade the whole area. The study of this propagation phenomena falls into the study of existence of traveling wave. In a recent paper [30], the authors have proposed a mathematical model to study such phenomena and they have simplified it to recover a well-know simple bistable system for which existence of traveling wave is known. The study of the probability of success of spacial invasiveness has been performed in [53].