Optimizing thymic recovery in HIV patients through multidrug therapies - Costanza, Vicente (2012)
A control-theoretic approach to the problem of designing `low-side-effects´ therapies for HIV patients based on highly active drugs is substantiated here. The evolution of side-effects during treatment is modelled by an extra differential equation coupled to the dynamics of virions, healthy T-cells, and infected ones.  The new equation reflects the dependence of collateral damages on the amount of each dose administered to the patient, and on the evolution of the viral load detected by periodical blood analyses.  The cost objective accounts for recommended bounds on healthy cells and virions, and also penalizes the appearance of collateral malignancies caused by the medication.  The problem is solved by a hybrid Dynamic Programming scheme that adhere to discrete-time observation and control actions, but maintaining the continuous-time setup for predicting states and side-effects.  The resulting optimal strategies employ less drugs than those prescribed by previous optimization studies, but maintaining high doses at the beginning and the end of each period of six months.  If an inverse discount rate is applied to favor early actions, and under a mild penalization of the final viral load, then the optimal doses are found to be high at the beginning and decrease afterwards, causing a desirable stabilization of the main variables.