Modeling Pulmonary Tuberculosis for Optimal Control Including Prevention

It is formulated and analyzed an optimal control problem for the transmission dynamics of the SEIS-like pulmonary tuberculosis (TB) including prevention by means of non-linear differential equations, which are linked to a functional cost. Also, it is established and analyzed the use of optimal control to reduce the latent and infectious populations by using the Pontryaguin's maximum principle (a Hamiltonian function which establishes a problem with numerical limits). After that, simulations of the problem are done. Finally, with an analysis of the viability of strategies to control the disease, we have concluded that the application of effective control measures in the prevention generates a significant decrease in the infected population as well as affects directly the propagation of the infection.