Optimal control of epidemiological models

We apply optimal control theory to a Tuberculosis (TB) and a TB-HIV/AIDS co-infection models. The models are given by systems of ordinary differential equations. 
For the TB model, optimal control strategies are proposed to minimize the number of active infectious and persistent latent individuals, as well as the cost of interventions. A cost-effectiveness analysis is done, to compare the application of each one of the control measures, separately or in combination. 
We introduce delays in the TB model, representing the time delay on the diagnosis and commencement of treatment of individuals with active TB infection. The stability of the disease free and endemic equilibriums is investigated for any time delay. Corresponding optimal control problems, with time delays in both state and control variables, are formulated and studied.
We propose a model for TB-HIV/AIDS coinfection transmission dynamics. We analyze separately the HIV-only, TB-only and TB-HIV/AIDS models. The respective basic reproduction numbers are computed, equilibria and stability are studied. Optimal control theory is applied to the TB-HIV/AIDS model and optimal treatment strategies for co-infected individuals with HIV and TB are derived. Numerical simulations to the optimal control problem show that non intuitive measures can lead to the reduction of the number of individuals with active TB and AIDS.