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作用。人类和畜牧业中抗生素的滥用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”的抗菌治疗新范例，它指的是一种权衡，即细菌对一种抗生素获得的耐药机制可能使它们更容易受到另一种抗生素的影响。然而，利用附带敏感性来安排抗生素治疗的顺序和时间是具有挑战性的，而且很大程度上尚未探索。通过这个 LEAPS-MPS 项目，研究团队将为模拟抗生素耐药和敏感细菌的种群动态奠定数学基础。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。所开发的方法将有可能指导更有效的药物治疗方案，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应用数学研究的培训。 PI 将接触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。为了提高可及性，教育和研究材料将通过出版物、会议演示、研讨会和免费在线视频来传播。该项目的技术方面围绕开发一个基于附带敏感性概念的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使用非线性切换系统来描述。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。将创建计算算法来近似相关非线性切换系统的原点之外的区域内的控制不变集和持久集。通过识别控制不变集，将有可能设计控制策略，将系统维持在这些集合内，从而执行可预测和理想的系统行为。模型预测控制将解决受系统动力学以及涉及状态和控制的约束影响的在线有限视野开环最优控制问题。这套数学工具将帮助医生决定循环疗法，以减少抗生素耐药性，从而根除宿主体内的细菌感染。这个跨学科项目为计算数学、工程和生物学不同领域的学生提供了培训机会。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。