Publications
Peer-reviewed journal articles and preprints.
Also available on Google Scholar, ResearchGate, and ORCID.
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M. Dogbatsey, Z. Chen, Y. Shao, and S. Zhao, Numerical solution to the three-dimensional p-Laplace equation: Finite difference methods and biological applications. Journal of Computational and Applied Mathematics, 481, 117270 (2026).
Abstract
We develop and analyze finite difference methods for the three-dimensional p-Laplace equation, a nonlinear generalization of the Laplacian with applications in biomolecular surface generation and electrostatic analysis. Efficient ADI, Crank–Nicolson, and Picard iterative schemes are implemented and benchmarked across 23 benchmark proteins. The ADI method is shown to be the most computationally efficient, enabling accurate electrostatic potential calculations for drug design and protein engineering on high-performance computing platforms.
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T. Kwofie, M. Dogbatsey, and S. E. Moore, Curtailing crime dynamics: A mathematical approach. Frontiers in Applied Mathematics and Statistics, 8, 1086745 (2023).
Abstract
We propose a compartmental ODE model for the dynamics of criminal activity and gang membership, adapted from epidemiological frameworks. The model incorporates recruitment, rehabilitation, and law-enforcement intervention parameters. Stability analysis identifies reproduction numbers governing long-term crime persistence. Numerical simulations demonstrate that targeted rehabilitation programs combined with early intervention achieve the most significant reductions in criminal activity, providing quantitative guidance for policy design.