具有免疫治疗的HIV感染模型的最优控制  

Optimal Control of an HIV Infection Model with Immunotherapy

作　　者：柳玉 蔺小林 李建全 宋修朝 LIU Yu;LIN Xiao-lin;LI Jian-quan;SONG Xiu-chao(School of Arts and Science,Shaanxi University of Science&Technology,Xi'an 710021,China;Basic Department,Air Force Engineering University,Xi'an 710051,China)

机构地区：[1]陕西科技大学文理学院,西安710021 [2]空军工程大学基础部,西安710051

出　　处：《西南大学学报（自然科学版）》2020年第1期59-68,共10页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11371031,11371369);陕西科技大学学术团队项目(2013XSD39)

摘　　要：对一类具有IL-2免疫治疗的HIV感染模型的最优控制问题进行了讨论.该模型描述了血浆中CD4+T细胞、游离病毒和免疫治疗药物IL-2浓度之间的关系.通过以IL-2的注射速度为控制变量,以CD4+T细胞浓度尽可能大而IL-2注射速度尽可能小为目标函数,得到了最优注射速度的表达式和相应的最优系统,并且证明了当治疗末端时间充分小时最优系统的解唯一,同时给出末端时间充分小的估计式.最后利用四阶龙格库塔算法对所求最优控制下的治疗效果进行了数值模拟.In this paper,the optimal control model of an HIV infection model with immunotherapy of IL-2 is considered.The model describes the interaction between uninfected CD4+T cells,the free virus and IL-2 in the plasma.By using the injection rate of IL-2 as the control variable,the uninfected T cells concentration as large as possible and the injection rate of IL-2 as small as possible as the objective function,the expression of the optimal injection rate of IL-2 and its corresponding optimal system are obtained.The uniqueness of solution of the optimal system is proved as the treatment final time is small enough,and the corresponding formula estimating the final time is given.At last,the effect of the IL-2 therapy under the found optimum control strategy is simulated.

关 键 词：免疫治疗 HIV感染模型 最优控制 唯一性 

分 类 号：O232[理学—运筹学与控制论]