具有细胞感染和抗病毒治疗的HIV感染模型的最优控制

Optimal control of HIV infection model with cell-to-cell transmission and antiretroviral therapy

对一类具有病毒-细胞感染和细胞-细胞传播的HIV感染模型的最优控制问题进行了讨论.该最优控制问题通过控制抗病毒药物RTIs和PIs的治疗效果,实现在有限的治疗时间内使未感染的CD4+T细胞浓度最大,而药物副作用最小.通过分析模型解的非负性和有界性证明了最优控制的存在性,利用Pontryagin最大值原理得到了最优系统,使用四阶龙格库塔算法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 a kind of HIV infection model with virus-cell infection and cell-cell transmission is discussed.This optimal control problem can maximize the concentration of uninfected CD4+T cells and minimize the side effects of drugs within a limited treatment time by controlling the therapeutic effects of antiviral drugs RTIs and PIs.The existence of optimal control is proved by analyzing the nonnegativity and boundedness of the solution of the model.The optimal system is obtained by using the Pontryagin maximum principle.The treatment effect under the optimal control strategy is numerically simulated by using the fourth-order Runge Kutta algorithm.