Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We present a versatile framework to systematically explore the trade-offs that arise in designing combination therapy protocols using optimal control. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.

中文翻译：

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使用多个最佳对照设计联合疗法。

相互作用的生物物种种群的战略管理通常需要结合多种治疗或疗法的干预措施。这在生态学、流行病学、伤口愈合和肿瘤学等关键研究领域非常重要。尽管用于确定单一最佳控制的理论和技术得到了很好的发展，但支持联合治疗实施的实际指导却很有限。在这项工作中，我们使用最优控制理论来计算将联合疗法应用于急性髓细胞白血病模型的最佳策略。我们提出了一个通用框架来系统地探索在使用最佳控制设计联合治疗方案时出现的权衡。我们考虑连续和 bang-bang（离散）控制的各种组合，我们研究了控制动态如何相互作用并响应表征最优性的回报的权重和形式的变化。我们证明，由于物种之间的相互作用，最佳控制对处理强度和控制参数呈非线性响应。我们讨论了在多重控制设置中适当表征最优性的挑战，并为应用多重最优控制提供了实用指导。GitHub 上提供了在这项工作中用于实现多个优化控制的代码。我们讨论了在多重控制设置中适当表征最优性的挑战，并为应用多重最优控制提供了实用指导。GitHub 上提供了在这项工作中用于实现多个优化控制的代码。我们讨论了在多重控制设置中适当表征最优性的挑战，并为应用多重最优控制提供了实用指导。GitHub 上提供了在这项工作中用于实现多个优化控制的代码。