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

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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.