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

在抗生素耐药性对全球公共健康造成的日益严重的威胁中，细菌逃脱了旨在杀死它们的药物的影响。人类和畜牧业滥用抗生素正在加剧常见呼吸道病原体的多重耐药性。生物技术的进步揭示了一种被称为“附带敏感性”的抗菌治疗的新范式，它指的是一种交易，即细菌对一种抗生素获得的耐药性机制可能使它们对另一种抗生素更容易受到伤害。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，而且在很大程度上是未被探索的。通过这个LEAPS-MPS项目，研究小组将建立数学基础，对抗生素耐药和敏感细菌的种群动态进行建模。计算机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。开发的方法可能会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。该项目还支持本科生和研究生在应用数学研究方面的培训。国际学生联合会将接触到历史上代表性不足的少数族裔学生，并招募他们从事STEM活动。为了增加可及性，将通过出版物、会议演示文稿、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根据附带敏感性的概念开发一个预测细菌种群进化的数学框架。抗生素耐药性的细菌种群动态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，以确保期望的性质，如稳定性、安全性和性能。将创建计算算法，用于在相关非线性切换系统的原点之外的区域内逼近控制不变集和永久集。通过识别控制不变集合，可以设计控制策略来维持这些集合中的系统，执行可预测和期望的系统行为。模型预测控制解决的是一个受系统动力学和状态与控制约束的在线有限时间开环最优控制问题。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，从而根除宿主中的细菌感染。这一跨学科项目为学生提供了在计算数学、工程和生物学的不同领域进行培训的机会。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.