Control of mixed pattern AID S-tuberculosis co-infection a sub-optimal approach of the resource allocation

This work concerns a problem of decision in the field of epidemiological control. The main objective is the optimal allocation of a limited amount of resources in such a way that the direct and social costs are minimized in terms of co-infection: acquired immune deficiency syndrome (AIDS) and tuberculosis. A mathematical model for the dynamics of the co-infection found in the literature is used together with a cost functional of quadratic type to yield an optimal control problem. The class of admissible controls was then restricted to be piecewise constant functions, characterized by the heights and the breakpoints, to reflect the form that the financial resources from health authorities are made available. The sub-optimal control problem is to choose a piecewise constant function that minimizes the cost functional, now written in as a mathematical programming problem which is solved using a numerical method that searches for global solutions. In this work the method of flexible polyhedra with simulated annealing and multiple random initializations is used. Numerical simulations in a digital computer show that the increase in the fraction of the population affected by AIDS tends to be significantly slowed, although not reduced as no cure is yet known.