{"id":970,"date":"2022-05-23T13:53:51","date_gmt":"2022-05-23T13:53:51","guid":{"rendered":"https:\/\/web.tarleton.edu\/math\/?page_id=970"},"modified":"2026-06-24T18:05:27","modified_gmt":"2026-06-24T18:05:27","slug":"research","status":"publish","type":"page","link":"https:\/\/www.tarleton.edu\/math\/research\/","title":{"rendered":"New and Ongoing Research"},"content":{"rendered":"\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-a822f0453c1dc733e0318ca3cd92a3d5 wp-block-paragraph\"><a href=\"https:\/\/www.tsucomputationalmathematics.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">TSU Computational Mathematics<\/a>&nbsp;research group<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-76593f364e4160f13e3c6a7408690a2f wp-block-paragraph\">Research interests of some members of the department include<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.tarleton.edu\/math\/research\/#wyattmodeling\">Dr. Bryant Wyatt &#8211; Particle Modeling<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.tarleton.edu\/math\/research\/#biology\">Dr. Keith Emmert &#8211; Mathematical Biology<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.tarleton.edu\/math\/research\/#datamining\">Dr. Jesse Crawford &#8211; Mathematical Statistics and Data Mining<\/a><\/li>\n\n\n\n<li>Dr. Madhur Wyatt &#8211; Atrial Fibrillation Study<\/li>\n\n\n\n<li>Dr. Jos\u00e9 Herrera-Diestra &#8211; Modeling Infectious Diseases<\/li>\n<\/ul>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 id=\"datamining\" class=\"wp-block-heading\">Dr. Jesse Crawford &#8211; Multivariate Statistics, Data Science, Environmental Science, and Health Care Analytics<\/h2>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-da65483c5b92387e61289160191bbfe1 wp-block-paragraph\">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.&nbsp;<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-32adc8a5c85877b6b6b1a471f90d6799 wp-block-paragraph\">&nbsp;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.&nbsp; 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.<\/p>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 id=\"biology\" class=\"wp-block-heading\">Dr. Keith Emmert &#8211; Mathematical Biology<\/h2>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-7184327eec6a43879218983e371126ca wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-62043cbf2ee6b4bce2071cb3165b792d wp-block-paragraph\">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.<\/p>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 id=\"wyattmodeling\" class=\"wp-block-heading\">Dr. Bryant Wyatt- Particle Modeling<\/h2>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-771126f2f1938399d3b8d8cf398432ee wp-block-paragraph\">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.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">N-body Simulations of Late Lunar Forming Impacts<\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-8ef721805e15c2408409615aa092d2dc wp-block-paragraph\">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&#8217;s.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-3265f67c83a221af6064d67d209f7dcc wp-block-paragraph\">Brett Hokr graduated from Tarleton in May 2011 and moved on to Texas A&amp;M to work on his Ph.D. in Quantum Optics studying under Dr. Marlan Scully.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-c9dbf01325889becf7b50550e581f23a wp-block-paragraph\">Justin Highland graduated from Tarleton December 2011 and will be joining the team down at Texas A&amp;M in the fall of 2012.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-2056ca2ce40d508efc8d9e4ce74f3be0 wp-block-paragraph\">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.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">N-body Study of the Thermodynamic Properties of Water<\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-4d7d77428e4ff09d46172f7ff8372728 wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-1d81c546108f8ec8f8dac250a2b19640 wp-block-paragraph\">Travis is scheduled to graduate in May 2013 and hopes to continue his studies toward his Ph.D.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Particle Based Simulation of Oscillating String<\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-45723723bab73ec3d89647a8e46a60a1 wp-block-paragraph\">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.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Particle Modeling Optimization on a CUDA-enabled High-performance Cluster<\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-02bd3884c7a28b13620d083354358cc4 wp-block-paragraph\">Student: David Gibson is working on ways of optimizing different N-body problems to run most efficiently on a CUDA cluster.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-6285989fa250993e87d10f5e7cfea2f8 wp-block-paragraph\">Student: Eli Symm has just joined our group and is working on finding a problem to study.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-40630955515f587a91dc955e5c7c723b wp-block-paragraph\">Graduation parties on the Paluxy River at Wyatt&#8217;s in Glen Rose.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-673afca8e19b5ee0172e917cf4d10a67 wp-block-paragraph\">If you would like more information on our group drop us a line at\u00a0<a href=\"mailto:wyatt@tarleton.edu\">wyatt@tarleton.edu<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Dr. Jos\u00e9 Herrera-Diestra &#8211; Modeling Infectious Diseases<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Mobility-Informed Epidemic Surveillance and Forecasting<\/strong><\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-2e1d0fba556c5fe7d150cece2bc1f30b wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-937721121555cbc41c4450a3ed0502da wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-8afcd69aaca94684275f5aafa4237e23 wp-block-paragraph\"><strong>Key question:<\/strong>&nbsp;Can mobility data collected before an epidemic season be used to predict where disease burden will be highest?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Surveillance and Vaccination Strategies for Respiratory Diseases<\/strong><\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-8a2fcb17319ff5bf28b2cd43abf299da wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-256c64e4abe722abd27a202a0b398c86 wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-9e770fb0f1fe9327409fbca358791387 wp-block-paragraph\"><strong>Key question:<\/strong>&nbsp;Can mobility networks improve the effectiveness of disease surveillance and vaccination programs?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Infectious Disease Importation Risk During Mass Gathering Events<\/strong><\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-2e2503e382fd90e27079532cfdff12ea wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-5080da358faf77dc80fbb733a089b667 wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-f07ec3ccb7db0c5fee8d031ed192d3d4 wp-block-paragraph\"><strong>Key question:<\/strong>&nbsp;How can publicly available data be used to rapidly assess infectious disease importation risk during global events?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Social Vulnerability, Mobility, and Health Disparities<\/strong><\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-248d8d23260359ed1f423de89dda6a08 wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-deca63a29adb9c90bb4e2dcb547dcc4b wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-24e3b6f285e29c0da7e98c99e555f80b wp-block-paragraph\"><strong>Key question:<\/strong>&nbsp;Why do some communities experience disproportionately higher disease burden than others?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Livestock Mobility Networks and Disease Surveillance<\/strong><\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-50da2ec1664f80f733dede9e0407e97d wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-1b83f9d31337c8565cca0a10138e501e wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-8836fdc378a21037a5f886f5f6dbcfe2 wp-block-paragraph\"><strong>Key question:<\/strong>&nbsp;Can livestock transportation networks be used to identify high-risk locations and improve disease surveillance?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Mathematical Modeling of Infectious Diseases<\/strong><\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-a186c140d77f2d24230a1d0d33c334bd wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-68a92a45d3ad6b27edf637683264e9a0 wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-3e92190a5b8ac008bffa8f90937a43f8 wp-block-paragraph\"><strong>Key question:<\/strong>&nbsp;How can mathematical models help explain and predict epidemic dynamics?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Complex Systems and Network Dynamics<\/strong><\/h3>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-07170ab379d0b471c0b53bc544aa2250 wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-cb0d59e049a783ef982a07fc51f9eced wp-block-paragraph\">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.<\/p>\n\n\n\n<p class=\"has-tarleton-black-color has-text-color has-link-color wp-elements-c8e6af532aae1b9fd680ea132470b8a1 wp-block-paragraph\"><strong>Key question:<\/strong>&nbsp;How do local interactions generate large-scale collective behavior in complex systems?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>TSU Computational Mathematics&nbsp;research group Research interests of some members of the department include Dr. Jesse Crawford &#8211; Multivariate Statistics, Data Science, Environmental Science, and Health Care Analytics Dr. Crawford research &#8230;<\/p>\n","protected":false},"author":62,"featured_media":580,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-fullwidth.php","meta":{"_acf_changed":false,"inline_featured_image":false,"advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","footnotes":""},"class_list":["post-970","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"coauthors":[],"author_meta":{"author_link":"https:\/\/www.tarleton.edu\/math\/author\/kyle-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-3\/","display_name":"kyle"},"relative_dates":{"created":"Posted 4 years ago","modified":"Updated 2 weeks ago"},"absolute_dates":{"created":"Posted on May 23, 2022","modified":"Updated on June 24, 2026"},"absolute_dates_time":{"created":"Posted on May 23, 2022 1:53 pm","modified":"Updated on June 24, 2026 6:05 pm"},"featured_img_caption":"","featured_img":false,"series_order":"","_links":{"self":[{"href":"https:\/\/www.tarleton.edu\/math\/wp-json\/wp\/v2\/pages\/970","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.tarleton.edu\/math\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.tarleton.edu\/math\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.tarleton.edu\/math\/wp-json\/wp\/v2\/users\/62"}],"replies":[{"embeddable":true,"href":"https:\/\/www.tarleton.edu\/math\/wp-json\/wp\/v2\/comments?post=970"}],"version-history":[{"count":4,"href":"https:\/\/www.tarleton.edu\/math\/wp-json\/wp\/v2\/pages\/970\/revisions"}],"predecessor-version":[{"id":2397,"href":"https:\/\/www.tarleton.edu\/math\/wp-json\/wp\/v2\/pages\/970\/revisions\/2397"}],"wp:attachment":[{"href":"https:\/\/www.tarleton.edu\/math\/wp-json\/wp\/v2\/media?parent=970"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}