Optimal control in world health problems: onchocerciasis control

In some regions of the world black flies are the vector of serious endemic diseases such as onchocerciasis (river blindness). Theoretical and numerical solutions to the control of black fly larvae in running waters are presented. The problem is modeled by a diffusion-transport partial differential equation with impulse controls and state constraint. A mixed finite element method is used to solve the diffusion-transport equations. A special technique is developed to get around the combinatorial problem which naturally arises from the discretization of the impulse control problem. Solutions are presented for the 1D equations