Mathematical modelling of some diseases related to water

Zusammenfassung

In this PhD Thesis we shall investigate a class of optimal control problem applied to differential equations modeling the dynamics of some mosquito borne diseases. First of all, we shall make an extensive introduction to the main ingredients of this Thesis, namely: optimal control and mathematical modeling. In this direction, recent results will be summarized and original results necessary for our purposes will be proved. With these mathematical tools, shall analyze the spread and dynamics of some diseases that are transmitted by some classes of mosquitoes. Special emphasis will be done to control problems. Moreover, we shall use specific numerical methods for solving systems of differential equations to perform numerical simulations of the proposed models, that might allow to improve them.