Mathematical analysis of a non‐convex optimal control problem for age‐structured mosquito populations

We present a rigorous mathematical analysis of a non‐convex optimal control problem for mosquito populations. The nonlinear model for the dynamics of the mosquito population takes in consideration the iterations among the immature (aquatic) subpopulation, the adult winged subpopulation, and the environment resources; the immature subpopulation is assumed to be age‐structured. Moreover, the action of certain control mechanisms on these subpopulations is also taken in account. The cost functional to be minimized is non‐convex. The proof of the existence of an optimal control is done by using fixed point arguments and a special minimizing sequence obtained with the help of Ekeland's variational principle.