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

Regents Of The University Of Idaho, Moscow ID

Investigators

Abstract

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.