LQ control design for the containment of the HIV/AIDS diffusion

An optimal control design approach is applied to a novel HIV/AIDS model to reduce the infection diffusion. Two classes of susceptible subjects, the wise one and the incautious ones, and three classes of infectious subjects, the ones not aware of their condition and the subjects in the pre-aids or in the aids status, are considered. The control input, represented by information campaigns and the medication action, is designed by means of a linear quadratic approach on the linearized model. Moreover, a preliminary state observer for the unmeasurable number of the unconscious infectious subjects is introduced. Numerical results show the effectiveness of the solution, and its robustness with respect to the approximations introduced by the linearization.