Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China; Department of Epidemiology and Biostatistics, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi, 710061, PR China.
Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China.
Math Biosci. 2019 Mar;309:107-117. doi: 10.1016/j.mbs.2019.01.007. Epub 2019 Jan 24.
Most of previous studies investigated the optimal control of HIV infection at either within-host or between-host level. However, the optimal treatment strategy for the individual may not be optimal for the population and vice versa. To determine when the two-level optimal controls are in accord or conflict, we develop a multi-scale model using various functions that link the viral load within host and the transmission rate between hosts, calibrated by cohort data. We obtain the within-host optimal treatment scheme that minimizes the viral load and maximizes the count of healthy cells at the individual level, and the coupled optimal scheme that minimizes the basic reproduction number at the population level. Mathematical analysis shows that whether the two-level optimal controls coincide depends on the sign of the product of their switching functions. Numerical results suggest that they are in accord for a high maximal drug efficacy but may conflict for a low drug efficacy. Using the multi-scale model, we also identify a threshold of the treatment effectiveness that determines how early treatment initiation can affect the disease dynamics among population. These results may help develop a synergistic treatment protocol beneficial to both HIV-infected individuals and the whole population.
大多数先前的研究都在宿主内或宿主间水平上探讨了 HIV 感染的最佳控制。然而，个体的最佳治疗策略对人群来说可能不是最佳的，反之亦然。为了确定两个层次的最佳控制是一致还是冲突，我们使用通过队列数据进行校准的各种功能建立了一个多尺度模型，这些功能将宿主内的病毒载量和宿主间的传播率联系起来。我们在个体水平上获得了最小化病毒载量和最大化健康细胞数量的最佳治疗方案，以及在群体水平上最小化基本繁殖数的最佳耦合方案。数学分析表明，两个层次的最佳控制是否一致取决于它们的切换函数的乘积的符号。数值结果表明，对于高最大药物疗效，它们是一致的，但对于低药物疗效，它们可能会发生冲突。通过使用多尺度模型，我们还确定了治疗效果的一个阈值，该阈值决定了早期治疗启动如何影响人群中的疾病动态。这些结果可能有助于制定一种协同治疗方案，既有益于 HIV 感染者个体，也有益于整个人群。
