Optimizing thymic recovery in HIV patients through multidrug therapies

An optimal control approach based on an enlarged nonlinear model for the dynamics of HIV infection and thymic function is composed to simulate and evaluate antiretroviral therapies. In addition to the relevant biological agents, an extra state variable is included, associated with the thymus capacity for healthy cells production. The methodology contemplates eventual deleterious effects of drugs over children's thymus recovery. The intake of ‘Reverse Transcriptase Inhibitors’ and ‘Protease Inhibitors’ are modeled as two independent control variables, each affecting a different term in the dynamics, so extending the prevailing pure-HAART-therapy analysis. The objective function designed here is also more inclusive than usual, accounting for the costs of the two drug families involved and for the thymus deterioration, in addition to penalizing eventual virus excess and healthy cells deficits. The search for the best combined therapy is treated as an optimal control problem. A hybrid version of Dynamic Programming for continuous and discrete variables is used to treat the problem numerically. Long time-horizons are explored, aiming to avoid typical peaks in drug prescriptions found at the beginning and at the end of the optimization periods. Results indicate that certain combinations of drugs are more convenient than pure protocols when the value of thymus functioning is relevant, specially for children patients.

► We present an optimal control methodology, suitable for assessing drug combinations in HIV treatment of children and adult patients. ► The context takes into account the dynamics of human thymus under viral infection and highly active medication. ► Optimal results: more PIs than RTIs drugs for children, and the converse ratio for adults, when the concern for thymus function grows in appreciation. ► Stabilization of the composition of the optimal doses after some 180 days allows a drug mix with significant PI share (milder than HAART). ► In evaluating long periods, the total amount of drugs increases slightly, but rebound risks for viral load are minimized.