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

LEAPS-MPS：非线性切换模型的可控集及其在传染病中的应用

• 批准号: 2315862
• 负责人: Esteban Hernandez Vargas
• 金额: $ 25万
• 依托单位: Regents of the University of Idaho
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-11-01 至 2025-10-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2315862&HistoricalAwards=false
• 关键词: LEAPS; MPS; Controllable; sets; nonlinear

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.

在不断增长的抗生素抗性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作用。在人类和牲畜种植中对抗生素的失误正在加剧常见呼吸道病原体中多药耐药性的兴起。生物技术的进步已经发现了一种新的抗菌治疗范式，称为“ Collat​​elar敏感性”，该疗法是指细菌对一种抗生素获得的抗药性机制的用户，可以使它们更容易受到另一种抗生素的影响。但是，安排抗生素治疗的顺序和时间来探索侧支敏感性是挑战的，并且在很大程度上是意外的。通过此LEAPS-MPS项目，研究团队将创建数学基础，以模拟抗生素耐药性和敏感细菌的种群动态。计算算法将预测每种抗生素的最佳时间顺序和相对持续时间。开发的方法可能会指导更有效的药物方案，以限制耐药性发展并延长可用疗法的有效性。该项目还支持对应用数学研究的本科生和研究生的培训。 PI将与历史上代表性不足的少数族裔学生联系，并招募他们从事STEM活动。为了提高可访问性，将通过出版物，会议演示，研讨会和免费在线视频来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，以根据附加敏感性的概念来预测细菌种群的演变。可以使用非线性开关系统来描述抗生素耐药性的细菌种群动力学。将研究此类模型的控制不变集，以确保所需的属性，例如稳定性，安全性和性能。将创建计算算法，以用于在相关的非线性开关系统的起源之外的区域内为近似控制不变集和永久集合创建计算算法。通过识别控制不变集，将有可能设计控制系统在这些集合中的控制策略，从而进行可预测且可取的系统行为。模型预测控制将解决涉及状态和控制的系统动力学和约束，在线有限的开放环最佳控制问题。这组数学工具将帮助从业人员决定可以降低抗生素耐药性并因此在宿主中的细菌感染的循环疗法。该跨学科项目为培训计算数学，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的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，被认为是通过评估而被视为珍贵的支持。