TSU Computational Mathematics research group

Research interests of some members of the department include

Dr. Jesse Crawford – Multivariate Statistics, Data Science, Environmental Science, and Health Care Analytics

Dr. Crawford research has involved the study of multivariate normal distributions with covariance matrices determined by group symmetries and acyclic mixed graphs, including the generalization of canonical correlations to group symmetry models, and developing a likelihood ratio test for testing equality of natural parameters for generalized Riesz distributions. 

 He is currently working on a project sponsored by Blue Cross and Blue Shield of Texas under the Affordability Cures Initiative to minimize improper payments for health insurance claims.  Previous projects include ensemble models of climate variability, identification of nitrate contamination in water wells, SIR disease models in amphibian populations, development of general canonical correlations for group symmetry models, and likelihood ratio tests for generalized Riesz distributions.

Dr. Keith Emmert – Mathematical Biology

Dr. Emmert research is focused on the development of new deterministic and stochastic epidemic models for the spread of disease in a structured host population. Past models have been included difference as well as differential equations with both fixed or periodic coefficients. I use theory as well as simulations to investigate the richness of the models.

Future directions in research include investigating the robustness of stability results, improved visualization techniques for bifurcations in higher dimensions, animal movement models, epidemic models that incorporate a spatial component, and population genetics. Parallel algorithms and genetic algorithms will most likely be of great use in exploring these new topics.

Dr. Bryant Wyatt- Particle Modeling

Dr. Wyatt and his students work in a high performance computing lab doing Particle Modeling research. In the old days to run large N-body simulations you needed a CRAY supercomputer which cost tens of millions of dollars. Today with the advances Graphics Processing Units (GPUs) supercomputing can be done in your living room. The lab was built with a grant from Tarleton State University and donations from Mellanox Technology and NVIDIA. We are grateful for their support.

N-body Simulations of Late Lunar Forming Impacts

The Giant Impact Hypothesis is currently the most widely accepted explanation for the formation of the Earth-Moon system. Though this mode of formation is stated in text books it has never been modeled. Dr. Robin Canup (Associate Vice President at the Southwest Research Institute) made the problem popular when she was featured on the history channel. Researchers have been able to create impact models that produce a disk of debris around the earth with enough mass to create the moon. They have also created models that can start with a disk of debris around the earth and coalesce into a moon. But no one to date has been able to produce both from a single model. Brett and Justin were able to produce models using only a single GPU with very similar results to Dr. Canup’s.

Brett Hokr graduated from Tarleton in May 2011 and moved on to Texas A&M to work on his Ph.D. in Quantum Optics studying under Dr. Marlan Scully.

Justin Highland graduated from Tarleton December 2011 and will be joining the team down at Texas A&M in the fall of 2012.

We are still trying to create a single model that will produce the accretion disk from an impact that will then coalesce into a moon.

N-body Study of the Thermodynamic Properties of Water

Student: Travis Salzillo is working on a model of the water molecule and trying to check the validity of the model to known thermodynamic properties of water. Once we have an understanding of the models temperature we will study the phase changes of water using the model.

Travis is scheduled to graduate in May 2013 and hopes to continue his studies toward his Ph.D.

Particle Based Simulation of Oscillating String

Student: Robert Pierce is working on comparing a particle based model to a continuum based model. He is building a physical vibrating string apparatus that he can set the amount of tension. He can also find the mass per unit length of the string. Using these two parameters he will build a continuous model that he solves using partial differential equations and a discrete case which he will solve using particle modeling. He will then compare both back to the physical vibrating string.

Particle Modeling Optimization on a CUDA-enabled High-performance Cluster

Student: David Gibson is working on ways of optimizing different N-body problems to run most efficiently on a CUDA cluster.

Student: Eli Symm has just joined our group and is working on finding a problem to study.

Graduation parties on the Paluxy River at Wyatt’s in Glen Rose.

If you would like more information on our group drop us a line at wyatt@tarleton.edu

Dr. José Herrera-Diestra – Modeling Infectious Diseases

Mobility-Informed Epidemic Surveillance and Forecasting

Human mobility plays a fundamental role in shaping how infectious diseases spread across communities. In this line of research, I investigate whether mobility patterns observed before an epidemic season can be used to anticipate where disease burden will be greatest. By combining large-scale mobility data, network science, statistical modeling, and machine learning, I develop methods to identify communities that may be at elevated risk before outbreaks occur.

Recent work has focused on influenza and respiratory syncytial virus (RSV), using mobility networks constructed from millions of movements between communities to predict hospitalization burden across Texas. This research aims to transform mobility data into practical tools for early warning, epidemic preparedness, and public health planning.

Key question: Can mobility data collected before an epidemic season be used to predict where disease burden will be highest?

Surveillance and Vaccination Strategies for Respiratory Diseases

Public health resources are often limited, making it essential to identify where surveillance and intervention efforts can have the greatest impact. My research explores how mobility networks, demographic information, and epidemiological models can be combined to improve the placement of surveillance systems and optimize vaccination strategies for respiratory diseases.

Current projects focus on identifying communities that could serve as effective sentinel locations for early outbreak detection and evaluating how vaccination resources can be allocated to reduce disease burden most efficiently. These studies integrate mathematical models with real-world mobility and hospitalization data to support evidence-based public health decision-making.

Key question: Can mobility networks improve the effectiveness of disease surveillance and vaccination programs?

Infectious Disease Importation Risk During Mass Gathering Events

Large international events create unique opportunities for infectious diseases to spread across countries through increased travel and population mixing. This research investigates how publicly available data can be used to estimate disease importation risk during mass gathering events, providing rapid and transparent assessments that can support preparedness efforts.

A recent project examines the 2026 FIFA World Cup, integrating international travel data, disease incidence estimates, and tournament schedules to evaluate the potential risk of importing infectious diseases into host cities. More broadly, this work seeks to develop scalable frameworks for assessing epidemic risk in highly connected global systems and to provide actionable information before more detailed proprietary datasets become available.

Key question: How can publicly available data be used to rapidly assess infectious disease importation risk during global events?

Social Vulnerability, Mobility, and Health Disparities

Communities do not experience epidemics equally. Differences in socioeconomic conditions, demographics, and mobility patterns can lead to substantial disparities in disease burden. My research examines how social vulnerability interacts with human mobility to influence the spatial distribution of infectious diseases.

Using data from Texas communities, I investigate how mobility reduction, network connectivity, and measures of social vulnerability contribute to differences in hospitalization rates and epidemic outcomes. This work aims to improve our understanding of why certain communities experience disproportionately severe impacts during outbreaks and how public health interventions can be targeted more effectively.

Key question: Why do some communities experience disproportionately higher disease burden than others?

Livestock Mobility Networks and Disease Surveillance

The movement of animals between farms creates transportation networks that can facilitate the spread of infectious diseases. In this line of research, I apply methods from network science and epidemiology to study livestock movement systems and evaluate their role in disease surveillance and outbreak risk.

Past work has examined cattle transportation networks and their ability to explain patterns of epidemic burden. Ongoing efforts explore how publicly available movement-network data can be used to support surveillance for emerging livestock diseases such as H5N1, particularly in situations where access to proprietary industry data is limited. These projects extend concepts developed in human epidemiology to agricultural systems and food security.

Key question: Can livestock transportation networks be used to identify high-risk locations and improve disease surveillance?

Mathematical Modeling of Infectious Diseases

Mathematical models provide a framework for understanding how infectious diseases spread through populations and how interventions can alter epidemic trajectories. My research develops and analyzes compartmental and metapopulation models that incorporate demographic structure, vaccination, climate effects, and human mobility.

Recent projects include age-structured models of influenza transmission calibrated to hospitalization data and simulations designed to evaluate the impact of vaccination strategies and surveillance systems. These models help bridge theoretical epidemiology and real-world public health applications by providing quantitative tools to evaluate competing intervention scenarios.

Key question: How can mathematical models help explain and predict epidemic dynamics?

Complex Systems and Network Dynamics

Many biological and social phenomena emerge from interactions among large numbers of interconnected individuals. My research in complex systems seeks to understand how local interactions generate large-scale collective behavior, drawing on tools from statistical physics, nonlinear dynamics, and network science.

This work includes studies of adaptive networks, social dynamics, opinion formation, collective behavior, and the interplay between network structure and dynamics. Although my recent research focuses primarily on epidemiological applications, these ideas continue to provide the theoretical foundation for many of the network-based approaches used throughout my work.

Key question: How do local interactions generate large-scale collective behavior in complex systems?