Mathematical Biology

From the infinitesimal universe of a single molecule to vast ecosystems, mathematics is providing an essential insight into the structural and behavioral aspects of biological systems.

Students entering this interdisciplinary field are on the front line of a new era of understanding and problem solving, utilizing cutting-edge computational modeling and theoretical analysis to push our understanding of how the living world operates.

Imminent challenges in epidemiology, pharmaceutical chemistry, and public health policy are critical issues for our students, who actively participate in faculty research. This student involvement is greatly advantageous. Collaborating in a dynamic project-oriented milieu, students have the opportunity to forge uniquely productive working relationships with our experienced instructors, an invaluable first step towards building a rewarding career in research, biohealth, or a variety of related industries. 

Our students and faculty together are meeting today’s challenges with tomorrow’s ideas and techniques, expanding knowledge, driving innovation, and finding solutions.

The Mathematical Biology group at Lawrence Tech uses cutting-edge mathematical and computational techniques to address important biological questions in the following areas:

math bio epidemiology

Mathematic Epidemiology

Cause, course, and control. Epidemiologists seek to guide public health policies to mitigate spread or accurately predict the spread of diseases under a variety of interventions.

Our faculty and students are actively engaged in developing data-driven forecasting models to predict and help prevent the spread of infectious diseases such as COVID-19, HIV, and Influenza. Mathematical modeling offers a quantitative approach to understanding the dynamics of disease transmission and providing informed context for public health policymaking.

Our relationship with the MDHSS gives students the opportunity to use real-world data, allowing for firsthand experience that uniquely positions LTU grads to secure rewarding jobs not just in the field of medical research, but across a diverse array of related fields. 

Involved faculty: Bruce Pell, Matthew Johnston, Patrick Nelson

math bio systems-biology

Systems Biology

Finding a “big picture” perspective by discovering how the smaller pieces interact. This is what Systems Biology is all about.

Through advanced computational modeling and simulation, we can construct a more comprehensive understanding of the underlying biochemical processes that govern cell function.

Students play an active role in this dynamic research, using cutting-edge techniques to model the complex behavior of biochemical reaction systems, such as signal transduction cascades and gene regulatory networks, contribute an essential effort towards the development of new treatments for diseases, and facilitate the design and effective implementation of new biotechnology.

Involved faculty: Matthew Johnston

mathematic bio virus-nutrient

Within-Host Virus-Nutrient Models

Mathematical modeling offers a profoundly clarifying view of life, death, and decay in the environment.

By illuminating our understanding of the energy nutrient cycle, this modeling offers not just a map by which to understand nature, but potentially a blueprint by which to safeguard human survival on Earth.

Our faculty and students are exploring the complex interplay between plant-borne viruses and their environments at a cellular and molecular level. With far-ranging applications for virology and agriculture, their work is providing a more complete understanding of the impact of diseases on selected ecosystems and is laying the foundation for the development of new medical treatments.

Involved faculty: Bruce Pell

math bio medicine

Mathematical Medicine

Mathematical Medicine represents a perfect synthesis of thought and action-- principles in practice for the benefit of humankind.

We are bringing mathematical concepts into the public health arena by using calculus, statistics, and advanced modeling and analysis to both understand and predict the spread of diseases such as Covid-19, HIV, and Influenza.

Students are active participants in this rigorous and rewarding pursuit, employing sophisticated computational modeling to provide essential insights into diabetes, cancer, and heart disease. Together, we are paving the way for new therapeutic advances for drug delivery, helping to define treatment strategies for Alzheimer’s and other mental health issues, and creating the foundation for the next generation of biotechnology, such as artificial limbs and magnetic resonance imaging.

Involved faculty: Patrick Nelson, Destiny Anyaiwe

math bio bioinformatics


The use of computer programming and statistics to analyze and interpret biological data is revolutionizing fields as diverse as genetics, medicine, and agriculture. It represents a bold new direction in the way that we use science to understand science, and it is facilitating ambitious projects such as genome sequencing, drug discovery, and the development of personalized medicine. This is the power of bioinformatics.

Students of this dynamic interdisciplinary subject benefit from a collaborative approach that puts theory into action. They are directly involved in data collection, result analysis, algorithm development, lab assistance, and writing code.

The depth and breadth of their experience here not only provides them with a solid foundation in sophisticated problem-solving techniques, but offers them an advantage in seeking rewarding positions in an ever-changing biomedical industry that demands expertise in scientific research and methodology.

Involved faculty: Destiny Anyaiwe

Our People

Academic Team


Patrick Nelson


Matthew Johnston


Bruce Pell


Destiny Anyaiwe

Relevant Publications

Tin Phan, Samantha Brozak, Bruce Pell, Anna Gitter, Amy Xiao, Kristina D. Mena, Yang Kuang, Fuqing Wu. A Simple SEIR-V Model to Estimate COVID-19 Prevalence and Predict SARS-CoV-2 Transmission Using Wastewater-Based Surveillance Data. Sci. Total Environ. 857:159326, 2023.
Bryan S. Hernandez, Patrick Vincent N. Lubenia, Matthew D. Johnston, Jae Kyoung Kim, A framework for deriving analytic long-term behavior of biochemical reaction networks. Submitted, 2022.
Bruce Pell, Samantha Brozak, Tin Phan, Fuqing Wu, Yang Kuang, A wastewater-based harmless delay differential equation model to understand the emergence of SARS-CoV-2 variants. Submitted, 2022. Preprint available at arXiv:2209.07563.
Bruce Pell, Matthew D. Johnston, and Patrick Nelson, A Data-Validated Temporary Immunity Model of COVID-19 Spread in Michigan. Math. Biosci. Eng., 19(10):10122-10142, 2022.
Matthew D. Johnston, Bruce Pell, and Patrick Nelson, A Mathematical Study of COVID-19 Spread by Vaccination Status in Virginia. Appl. Sci., 12(3):1723, 2022.
Bruce Pell, Tin Phan, Amy Kendig, Elizabeth Borer, Yang Kuang. Modeling Nutrient and Disease Dynamics in a Plant-Pathogen System Using Ordinary and Delay Differential Equations. Michigan Academician 48(1):82, 2021.
Matthew D. Johnston, Analysis of Mass-Action Systems by Split Network Translation. J. Math. Chem., 60:195-218, 2021.
Matthew D. Johnston and Bruce Pell, A Dynamical Framework for Modeling Fear of Infection and Frustration with Social Distancing in COVID-19 Spread. Math. Biosci. Eng., 17(6):7892-7915, 2020.
Darrell M. Wilson, Patrick W. Nelson, et al., 898-P: CGM Metrics Identify Dysglycemic States in Subjects with Normal OGTT from the TrialNet Pathway to Prevention Study. Diabetes, 68(Supplement_1), 2019.
Alan S. Perelson and Patrick W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo. SIAM Review, 41(1):3-44, 1999.