In this paper, we use control theory to determine optimal treatment regimens for HIV patients, taking into account treatment-resistant mutations of the virus. We perform optimal control analysis on a model developed previously for the dynamics of HIV with strains of various resistance to treatment (Moore and Gu, 2005). This model incorporates three types of resistance to treatments: strains that are not responsive to protease inhibitors, strains not responsive to reverse transcriptase inhibitors, and strains not responsive to either of these treatments. We solve for the optimal treatment regimens analytically and numerically. We find parameter regimes for which optimal dosing is substantially better than constant dosing, but we also find parameter regimes for which optimal dosing is only marginally better than constant dosing. We propose the following open problem: Classify the settings in which variable-dose regimes determined by optimal control methods yield significantly better outcomes than comparable constant-dose regimes.
© 2006 American Mathematical Society
Gu, Weiqing; Moore, Helen. "Optimal therapy regimens for treatment-resistant mutations of HIV." Mathematical studies on human disease dynamics, 139–152, Contemp. Math., 410, Amer. Math. Soc., Providence, RI, 2006.