Section: New Results

Optimal control for population dynamics

Participants: Y. Privat, L. Almeida (Sorbonne University), M. Duprez (Dauphine University) and N. Vauchelet (Paris 13 University).

Particular attention is being paid to the transmission of dengue fever, an arbovirus transmitted to humans by mosquitoes [3]-[2]. There is no vaccine to immunize a population. It has been observed that when a mosquito population was infected with the Wolbachia virus, they stopped transmitting the disease. In addition, the virus is transmitted from mother to child and is characterized by cytoplasmic incompatibility (no possible crosses between infected males and healthy females). On the other hand, infected mosquitoes have a reduced lifespan and fertility. Mathematically, this situation can be modelled (in a simplified way) using a controlled reaction-diffusion system. The control term represents the strategy of releasing (time-space) mosquitoes infected by Wolbachia. The practical questions that arise and that we wish to address are:

• how to carry out these releases to ensure the invasion?

• how to optimize the domain and form of releases?

Preliminary work has made it possible to determine a plausible temporal control strategy.