Collaborative Research: Linking Pharmacokinetics to Epidemiological Models of Vector-Borne Diseases and Drug Resistance Prevention

这项研究的目标是开发数学工具，以提高对药物在体内的行为及其对病原体的影响如何影响耐药疾病传播的理解。针对微生物的药物（抗菌剂）挽救了数百万人的生命。但是，由于微生物是进化的，随着时间的推移，抗菌剂减少了屈服于药物的病原体的数量，留下了那些不屈服于药物的病原体——这一过程被称为选择。因此，无节制地使用抗菌素威胁到它们的长期功效——这是自1928年发现青霉素以来的一个问题。今天，耐药性被认为是一个需要紧急关注的严重问题。微分方程可以描述驱动生命系统变化的机制；控制理论可以产生最佳策略，利用这些机制来实现预期的目标。这些工具将有助于指导药物开发和给药方案，以平衡使用抗菌素的直接益处与这些药物施加的长期选择压力。一个适用于不同疾病系统的数学框架可以为减少耐药病原体对全球健康的威胁以及由此带来的社会成本的战略提供信息。此外，该项目将为霍华德大学、德克萨斯理工大学、理哈伊大学和肯塔基大学的研究生提供在洛斯阿拉莫斯国家实验室实习的机会，促进学术界以外的联系。肯塔基大学的学生还将协助首席研究员指导高中生通过一个试点的周六早晨数学项目，该项目将提供编码、建模和科学结果可视化的实践经验。研究人员的目标是构建一个通用的数学框架，以媒介传播的疾病为基准，并建立所需的工具，以弥合宿主内PK/PD（药代动力学/药效学）和群体水平流行病学之间的差距，以便其他人可以很容易地将该框架应用于他们自己对竞争病原体的研究。研究人员将通过在非线性常微分方程系统中引入一系列隔间来解决将PK/PD的快速动力学与相对缓慢的种群水平动力学联系起来的问题，这些非线性常微分方程代表了个体在不同药物浓度和不同持续时间的治疗阶段的进展。提出了一个随机子模型来参数化宿主内PK/PD与种群水平动态联系的函数之一。这项研究很重要，因为到目前为止，还没有通用的方法来分析具有不同持续时间的阶段-进展模型。这样的模型可以提供结果和见解，以减轻导致耐药性的选择压力，从而显著改善药物干预方案。例如，尚不清楚可能存在的后向分叉和具有异质阶段的分阶段进展方法将如何相互作用并影响最佳治疗策略。此外，所提出的参数估计、不确定性和可识别性分析可能会导致具有挑战性的数学和统计问题，需要现有方法的进步。本项目由数学科学部数学生物学项目和人力资源开发部资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The goal of this research is to develop mathematical tools to improve understanding of how the behavior of drugs within the body, and their effects on pathogens, influence the spread of drug-resistant disease. Drugs that target microbes (antimicrobials) have saved millions of lives. But, because microbes evolve, over time antimicrobials reduce the population of pathogens that succumb to drugs and leave behind those that do not - a process called selection. Consequently, unbridled use of antimicrobials threatens their long-term efficacy - a concern since the discovery of penicillin in 1928. Today, drug resistance is recognized as a serious problem requiring urgent attention. Differential equations can describe mechanisms that drive changes in living systems; control theory can generate the best strategies to use these mechanisms to achieve a desired goal. These tools will help guide drug development and dosing protocols that balance the immediate benefits of administering antimicrobials with the long-term selection pressure imposed by these drugs. A mathematical framework that is adaptable to different disease systems could inform strategies to reduce the threat of resistant pathogens to global health and the attendant cost to society. Furthermore, this project will provide graduate students at Howard, Texas Tech, Lehigh, and the University of Kentucky, with the opportunity to intern at the Los Alamos National Laboratory, fostering connections outside of academia. University of Kentucky students will also assist the lead investigator in mentoring high school students through a pilot Saturday Morning Math program that will provide hands-on experience with coding, modeling, and visualization of scientific results.The investigators aim to construct a general mathematical framework, with vector-borne disease serving as a benchmark example, and build the tools needed to bridge the gap between within-host PK/PD (pharmacokinetics/pharmacodynamics) and population-level epidemiology, so that others may readily adapt the framework to their own studies of competing pathogens. The investigators will approach the problem of linking the fast dynamics of PK/PD to the comparatively slow population-level dynamics by introducing serial compartments in a system of nonlinear ordinary differential equations representing the progression of individuals through stages of treatment characterized by different drug concentrations and different durations. A stochastic sub-model is proposed to parameterize one of the functions that links within-host PK/PD to the population-level dynamics. The proposed research is important because, to date, no general methods exist to analyze a staged-progression model where the stages have different durations. Such a model could provide results and insights that significantly improve the protocols for drug interventions in a way that mitigates the selection pressure leading to drug resistance. For example, it is unknown how the likely existence of backward bifurcation and the staged-progression approach with heterogeneous stages will interact and influence optimal treatment policy. Furthermore, the proposed parameter estimation, uncertainty, and identifiability analyses will likely lead to challenging mathematical and statistical problems requiring advances of existing methodologies. This project is funded by the Division of Mathematical Sciences Mathematical Biology Program and Division of Human Resource Development HBCU-UP.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.