具有多种治疗的HIV感染模型的最优控制

Optimal Control of an HIV Infection Model with Multiple Therapy

讨论一类具有逆转录酶抑制剂、蛋白酶抑制剂和白细胞介素-2三种药物治疗的HIV感染模型的最优控制问题,通过药物控制实现在有限治疗时间内使游离病毒的浓度和药物副作用达到最小.首先利用Pontryagin最大值原理得到相应的最优系统,证明了当治疗末端时间充分小时最优系统解的唯一性,并给出了末端时间的估计式,最后对最优控制策略下的治疗效果进行了数值模拟.

The optimal control problem of an HIV infection model is discussed with three kinds of drugs,incl-uding reverse transcriptase inhibitors,protease inhibitors and interlecukin-2.The drugs are controlled to achieve the goal of minimizing the concentration of free virus and the side effect of drugs within a limited treatment time.Firstly,the optimal system is obtained by using Pontryagin maximum principle.Then the uniqueness of the opti-mal system solution is proved as the treatment final time is small enough,and the estimation formula of the end-time is given.Finally,therapeutic effect of optimal control strategy is simulated numerically.