LEAPS-MPS: Controllable sets for nonlinear switched models with applications to infectious diseases

在抗生素耐药性日益严重的全球公共卫生威胁中，细菌逃脱了旨在杀死它们的药物的影响。在人类和畜牧业中滥用抗生素正在加剧常见呼吸道病原体的多重耐药性。生物技术的进步已经揭示了一种新的抗菌治疗模式，称为“附带敏感性”，这是指细菌对一种抗生素获得的耐药性机制使它们更容易受到另一种抗生素的影响。然而，安排抗生素治疗的顺序和时间以利用附带敏感性是具有挑战性的，并且在很大程度上未被探索。通过这个LEAPS-MPS项目，研究小组将创建数学基础来模拟抗药性和敏感性细菌的种群动态。计算算法将预测每种抗生素的最佳时间顺序和各自的持续时间。开发的方法将可能指导更有效的药物方案，限制耐药性的发展并延长现有疗法的有效性。该项目还支持应用数学研究的本科生和研究生的培训。PI将接触历史上代表性不足的少数民族学生，并招募他们从事STEM活动。为了提高可获得性，将通过出版物、会议介绍、讲习班和免费在线视频传播教育和研究材料，该项目的技术方面围绕着开发一个数学框架，用于根据附带敏感性的概念预测细菌种群的进化。抗生素耐药性的细菌种群动力学可以用非线性切换系统来描述。将研究这类模型的控制不变集，以确保所需的性能，如稳定性，安全性和性能。计算算法将被创建为近似控制不变集和持久集的相关非线性切换系统的原点以外的区域内。通过识别控制不变集，将有可能设计控制策略，使系统保持在这些集内，进行可预测的和理想的系统行为。模型预测控制将解决在线有限时域开环最优控制问题，该问题受到系统动态和涉及状态和控制的约束。这套数学工具将帮助医生决定循环疗法，可以减少抗生素耐药性，从而消除宿主中的细菌感染。这个跨学科的项目为培养计算数学、工程和生物学不同领域的学生提供了机会。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

In the growing global public health threat of antibiotic resistance, bacteria escape the effect of drugs designed to kill them. The misuse of antibiotics in humans and livestock farming is fueling the rise of multidrug resistance among common respiratory pathogens. Advances in biotechnology have uncovered a new paradigm for antimicrobial therapy known as “collateral sensitivity”, which refers to a trade-of such that the resistance mechanisms acquired by bacteria for one antibiotic that can make them more vulnerable to another. However, scheduling the order and time of antibiotic treatment to exploit collateral sensitivity is challenging and largely unexplored. With this LEAPS-MPS project, the research team will create the mathematical foundations to model the population dynamics of antibiotic-resistant and -susceptible bacteria. Computational algorithms will predict the best chronological order and respective duration of each antibiotic. The developed approaches will potentially guide more effective drug regimens that limit resistance development and prolong available therapies' effectiveness. This project also supports the training of undergraduate and graduate students in applied mathematics research. The PI will reach out to historically underrepresented minority students and recruit them to work on STEM activities. To increase accessibility, educational and research materials will be disseminated through publications, conference presentations, workshops, and free online videos.The technical aspects of this project revolve around developing a mathematical framework for predicting bacterial populations' evolution based on the concept of collateral sensitivity. Bacterial population dynamics of antibiotic resistance can be described using nonlinear switched systems. Control invariant sets for this class of models will be investigated to ensure desired properties such as stability, safety, and performance. Computational algorithms will be created for approximating control invariant sets and permanence sets within a region outside the origin of the associated nonlinear switched systems. By identifying control invariant sets, it will become possible to design control strategies that maintain a system within these sets, conducting predictable and desirable system behavior. Model predictive control will solve an online finite horizon open-loop optimal control problem subject to system dynamics and constraints involving states and control. This set of mathematical tools will help practitioners decide on cycling therapies that can reduce antibiotic resistance and consequently eradicate the bacterial infection in the host. This interdisciplinary project provides opportunities for training students in different areas of computational mathematics, engineering, and biology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.