Mathematical Modeling

Mathematical modeling translates complex real-world problems into abstract mathematical structures that can be analyzed and solved. Researchers develop and apply computational and analytical techniques to understand phenomena across diverse fields. This work involves creating predictive models for systems ranging from biological processes, such as population dynamics and the spread of diseases, to the optimization of logistical networks and the behavior of engineered systems. Specific areas of focus include the study of reaction-diffusion equations and traveling wave solutions, as well as the application of mixed-integer programming, network flow optimization, and scheduling algorithms within operations research. The modeling of data from Internet of Things devices also falls within this research scope.

The application of mathematical modeling holds significant relevance for Arkansas. It supports the optimization of operations within the state's key industries, including agriculture, logistics, and manufacturing, by improving efficiency and resource allocation. Furthermore, modeling plays a critical role in public health initiatives, aiding in the understanding and prediction of disease transmission patterns and informing public health strategies. The analysis of natural resource management and environmental systems also benefits from these quantitative approaches, contributing to sustainable practices within the state.

This research area fosters interdisciplinary collaborations, drawing upon expertise in computer science, engineering, biology, and economics. The work is advanced through connections to fields like operations research and the study of complex systems. Engagement across multiple institutions within Arkansas ensures a broad application of these modeling techniques.