Collaborative Workshop for Women in Mathematical Biology: Mathematical Approaches to Support Women’s Health

• Katharine Gurski, Howard University
• Yeona Kang, Howard University

In December 2021, the FDA approved an injectable pre-exposure prophylaxis (PrEP) for use in at-risk adults and adolescents to reduce the risk of sexually acquired HIV.  The cabotegravir extended-release injectable suspension is given first as two initiation injections administered one month apart, and then every two months thereafter. In this project, we aim to study how dynamics of drug-sensitive and drug-resistant HIV strains within hosts affect the prevalence of drug-resistant strains in the population when injectable pre-exposure prophylaxis enters the picture.  This project will use methods from dynamical systems, statistics as it relates to sensitivity analysis, data, and parameter estimation and numerical simulation.

• Mentor Lisette de Pillis, Harvey Mudd College
• Heather Zinn Brooks, Harvey Mudd College

Oral contraceptives are a leading form of birth control in the United States, but consistent daily use and unwanted side effects can pose challenges for some users. Existing mathematical models of the effects of hormonal contraception on the menstrual cycle do not incorporate the dynamics of the on/off dosing regimens or the metabolism of the exogenous hormones, although methods from differential equations and dynamical systems are well-positioned to investigate these questions. We aim to explore the stability of the contraceptive state achieved by oral hormonal contraceptives using a mechanistic mathematical model of the menstrual cycle. Such a model could provide insight into when a contraceptive state is lost due to inconsistency or changes in hormonal birth control use, which may further inform the advisement of care providers and the choices of birth control users.

• Mentor Karin Leiderman, Colorado School of Mines
• Anna Nelson, Duke University

Exogenous hormones are used by hundreds of millions of people worldwide for contraceptives and hormonal replacement therapy (HRT). However, estrogen in combined oral contraceptives (OC) and HRT have been shown to significantly increase the risk of both arterial and venous thrombosis.The objectives for this project are to use a mechanistic mathematical model of flow-mediated coagulation to investigate the effects of exogenous-hormone induced perturbations that have been observed on blood clotting. We will use the model to simulate specified hormone induced perturbation profiles, i.e., percent changes in plasma levels of proteins and blood platelets caused by estrogen and progesterone, in varying doses, separately and together. The first objective will be to verify the observations from the literature showing increased clotting for specified profiles and doses. It is also well known that plasma levels of clotting factors vary among individuals. Variation that is considered normal and still healthy is a range between 50 and 150% of the mean value of the healthy population. Our second objective will be to identify individuals that may be more susceptible to thrombosis due to certain hormones and doses. We will accomplish this by performing global sensitivity analysis on model output metrics where variance is due to uncertainty in the input levels of clotting factors, platelets, and hormones. 

• Morgan Craig, University of Montreal
• Adrianne Jenner, Queensland University of Technology

After lung cancer, breast cancer continues to be projected as the second most commonly diagnosed cancer in Canada. Leveraging data cancer growth, pharmacokinetic and pharmacodynamic models of various cancer therapies, and models of therapeutic resistance, this project aims to identify responders/non-responders to treatments and establish effective therapeutic schedules in breast and gynecological cancers. For this, we will develop mathematical and pharmacokinetic/pharmacodynamic models, integrated with patient data, to construct and implement in silico clinical trials. Familiarity with MATLAB, Python, and/or R is recommended. Other data fitting software including Monolix may be introduced, but prior knowledge is not necessary.

• Laura Ellwein Fix, Virginia Commonwealth University
• Sharon Lubkin, North Carolina State University

Respiratory distress in the newborn, a condition characterized by difficulty breathing, occurs in about 7% of newborns. This team’s project will address a question related to modeling of respiratory mechanics in the neonatal population. We previously developed an ordinary differential equations (ODE) model describing dynamic breathing volumes and pressures in aggregate compartments depicting the airways, lungs, chest wall, and intrapleural space, in an ideal spontaneously breathing preterm infant. Current areas of inquiry include application to ventilated infants and parameter identification using clinical data from a neonatal intensive care unit or an animal model. Alternatively, a specific unsolved problem could arise that requires the incorporation of a different dynamic model type such as spatially dependent or stochastic, or connects the organ level respiratory system with different physiology. The team’s co-leaders have interests in physiology, biotransport, tissues, cardiovascular and respiratory systems, and the use of noninvasive data in modeling. Our expertise centers on physiological mechanistic modeling, spatiotemporal systems and dynamics, parameter identification, numerics, and model development starting from simple to complex. Ideal team members would have interest and knowledge in some of these areas and embrace the opportunity to learn in other areas.

• Ruiyan Luo, Georgia State University
• Alexandra Smirnova, Georgia State University

Real-time reconstruction of disease parameters for an emerging outbreak helps to provide crucial information for the design of public health policies and control measures. The goal of our team project is to investigate and compare parameter estimation algorithms that do not require an explicit deterministic or stochastic trajectory of system evolution, and where the state variable(s) and the unknown disease parameters are reconstructed in a predictor-corrector manner in order to mitigate the excessive computational cost of a quasi-Newton step. We plan to look at uncertainty quantification and implications of parameter estimation on forecasting of future incidence cases. Theoretical study will be combined with numerical experiments using synthetic and real data for COVID-19 pandemic.