1 Aim and Scope

Despite advances in health care, women continue to have disparate outcomes. Women experience higher morbidity and mortality, especially with regard to cancer, cardiovascular disease, and recently COVID-19 [1]. Reproductive health and maternity are also a continued source of health risk.

Mathematical modeling can be used to identify some of the underlying causes for the different outcomes experienced by women and begin to suggest possible solutions and pathways forward. The goal of the work is to use data and biological insight from experimental publications and collaborations and develop mathematical frameworks to explore questions of disparity.

This volume contains the scientific work from the Collaborative Workshop for Women in Mathematical Biology. The workshop brought together 44 researchers (Fig. 1) to collaborate on six problems that used mathematics to understand complex biological systems with implications for women’s health. The workshop was held at the UnitedHealth Group campus in Minnetonka, Minneapolis during June 20–24, 2022 and was organized by Ashlee N. Ford Versypt, Rebecca Segal, Blerta Shtylla, and Suzanne S. Sindi. The articles contained in this volume were initiated during the intensive 1-week workshop and continued through follow-up collaborations afterward. Ashlee N. Ford Versypt served as the primary editor of this volume with generous support from 13 anonymous peer reviewers.

Fig. 1
A photograph of a group of women from the collaborative Workshop for Women in Mathematical Biology posing for a photo on a staircase.

Group photograph of the 2022 Collaborative Workshop for Women in Mathematical Biology participants at UnitedHealth Group Optum of Minnetonka, MN

Full size image

2 History and Context

Historically, women have been underrepresented in the mathematical sciences. Although progress has been made, the numbers remain unbalanced. In the most recent American Mathematical Society survey from 2018, only 17% of tenure-track mathematics faculty in doctoral departments are female [2]. Research reports from the American Association of University Women provide evidence on challenges that many early and midcareer women face that are likely contributors to leaving science, technology, engineering, and mathematics (STEM) professions [3, 4]. Two aspects explicitly recommended to enhance persistence of women in STEM are (1) cultivating a sense of belonging in the workplace and the profession and (2) making the work socially relevant. These aspects give an even more compelling picture of why research workshops such as this one can be so valuable for the mathematics community. As the COVID-19 pandemic impacted the workshop participant recruitment, timing, and other logistics, the challenges faced by untenured and/or teaching-focused female professors as well as research trainees [5, 6] were motivation for our emphasis on supporting these vulnerable groups of women in mathematics. Research mentoring and support from senior mentors is one key to success, and a workshop environment provides a significant amount of interaction in a concentrated amount of time. Interactions with women across various career stages from graduate and postdoctoral training to all ranks of faculty careers provide a rich support network of other technical women, particularly those who have faced similar recent challenges. The emphasis in our particular workshop was women’s health, which also has clear social impacts toward addressing health disparities.

The primary aim of the Women in Mathematical Biology (WIMB) workshops is to foster research collaboration among women in mathematical biology. Participants spend a week making progress on a research project and encouraging innovation in the application of mathematical, statistical, and computational methods in the resolution of significant problems in the biosciences. The workshops have a special format designed to maximize the opportunities to collaborate. The groups are structured to facilitate tiered mentoring. Each group has a senior researcher who presents a problem. This person is matched with a co-leader, typically a researcher in their field but with whom they have not previously collaborated. The groups are rounded out with researchers at various career stages. By matching senior research mentors with junior mathematicians, we expand and support the community of scholars in the mathematical biosciences. At the 2022 workshop, a panel session on career paths in industry was also included to connect participants with women in mathematics and statistics careers, primarily from the local Minneapolis area in addition to co-organizer Blerta Shtylla who works at Pfizer in California. To date, WIMB workshops have occurred at the Institute for Mathematics and its Applications (IMA, https://www.ima.umn.edu/), the National Institute for Mathematical and Biological Synthesis (NIMBioS, http://www.nimbios.org/), the Mathematical Biosciences Institute (MBI, https://mbi.osu.edu/), and the Institute of Pure and Applied Mathematics (IPAM, https://www.ipam.ucla.edu/). These workshops were sponsored by an ADVANCE grant from the National Science Foundation to the Association for Women in Mathematics. This award helped establish research networks in 26 different areas of mathematics research including Control, Commutative Algebra, Geometry, Data Science, Materials, Operator Algebras, Analysis, Number Theory, Shape, Topology, Numerical Analysis, and Representation Theory.

For the WIMB workshops, each group continues its project together to obtain results that are submitted to the peer-reviewed volume in the book series for the workshop. The benefit of such a structured program with leaders, projects, and working groups planned in advance is based on the successful Women In Numbers conferences and works in both directions: senior women meet, mentor, and collaborate with the brightest young women in their field on a part of their research agenda of their choosing, and junior women faculty and students develop their network of colleagues and supporters and encounter important new research areas to work in, thereby improving their chances for successful research careers.

3 Research

This volume contains six research papers loosely grouped into the following general application areas: infectious diseases, contraceptives, breast cancer, and infant respiratory distress. Throughout this research are discussions of detailed mathematical models for complex physiological processes and treatments, integration with data, reviews on the state of the art, and development of potentially impactful new methods. The following descriptions of the projects were proposed by the team mentors during project team formation. The mentors’ affiliations at the time of the workshop are listed. The papers in this volume follow the arbitrary order of the project team numbers. Each paper is contained in a separate chapter with all authors and affiliations listed there and abstracts updated accordingly for the work conducted during and after the workshop.

Project 1: HIV, Pre-exposure Prophylaxis, and Drug Resistance. Team Mentors: Katharine Gurski, Howard University and 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 1 month apart and then every 2 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, parameter estimation, and numerical simulation.

Project 2: Modeling the Stability and Effectiveness of Dosing Regimens of Oral Hormonal Contraceptives. Team Mentors: Lisette de Pillis, Harvey Mudd College and 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.

Project 3: Effects of Exogenous-Hormone Induced Perturbations on Blood Clotting. Team Mentors: Karin Leiderman, Colorado School of Mines and 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.

Project 4: Development of Effective Therapeutic Schedules in Breast and Gynecological Cancers. Team Mentors: Morgan Craig, University of Montreal and 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 on 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.

Project 5: Modeling Neonatal Respiratory Distress. Team Mentors: Laura Ellwein Fix, Virginia Commonwealth University and 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 equation (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 model, or the connections of 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.

Project 6: On Stable Estimation of Disease Parameters and Forecasting in Epidemiology. Team Mentors: Alexandra Smirnova, Georgia State University and Ruiyan Luo, 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.

4 Concluding Remarks

This workshop was originally postponed due to the COVID-19 pandemic; we are grateful for the continuing support of our team leaders who repeatedly made space for this workshop in their schedules until we could safely hold the workshop. We were able to accommodate a few needs for virtual participation while maintaining a vibrant collaborative event and are proud of the hard work of our participants during these challenging times.

Workshop groups are continuing to work on furthering the projects and presenting their work at conferences. Several teams presented their work at the 2023 Society for Mathematical Biology Annual Meeting. Past workshops have had successful research collaborations last for years following the workshop. The more community building we can accomplish, the higher the rate of success for women and mathematics. This means more innovative research will be produced and built upon by the entire mathematics community.