Differential and Difference Equations in Mathematical Biology

Azmy S. Ackleh is a Professor of Mathematics, the Endowed Chair and Eminent Scholar in Computational Mathematics, and the Dean of the Ray P. Authement College of Sciences at the University of Louisiana at Lafayette. Dr. Ackleh received his Ph.D. in Mathematics from the University of Tennessee at Knoxville in 1993. He then joined the Center for Research in Scientific Computation at North Carolina State University as a postdoctoral fellow. In 1995, he came to the University of Louisiana at Lafayette as Assistant Professor of Mathematics, moving through the ranks to Professor of Mathematics and heading the Department of Mathematics from 2011-2013. He was appointed Dean of the Ray P. Authement College of Sciences in 2013.Ackleh's main research focus is Mathematical Biology. Some of his recent projects involve tick dynamics, predator-prey evolutionary interaction, and size-structured population dynamics in space of measures. He has published more than 170 peer-reviewed articles, co-edited four volumes and co-authored a graduate-level textbook. He has served as Associate Editor of the Journal of Mathematical Biosciences and Engineering since 2009. He served as the major advisor for 19 Ph.D. students who have graduated and is currently directing four additional Ph.D. students. From 2003-2011, he served as the project director of the Undergraduate Biomathematics Program and directed the research of more than 30 undergraduate students. He obtained more than $9M in grant funding from agencies including the National Science Foundation, the National Institutes of Health, and the Gulf of Mexico Research Initiative and served as the Principal Investigator on the vast majority of these grants.Hongying Shu is a Professor of Mathematics at Guangzhou University. She received her Ph.D. in Mathematics from Harbin Institute of Technology in 2010. From 2011 to 2013, she was awarded the Atlantic Association for Research in the Mathematical Sciences (AARMS) Postdoctoral Fellowship. Before joining Guangzhou University, Dr. Shu held research and teaching positions at the University of New Brunswick, York University, Ryerson University, Tongji University, and Shaanxi Normal University. Her research interests include delay differential equations, partial differential equations, and dynamical systems, with applications in mathematical biology.Xiang-Sheng Wang is an Associate Professor of Mathematics at the University of Louisiana at Lafayette. He received his Ph.D. in Mathematics in 2009 through a joint Ph.D. program between City University of Hong Kong and the University of Science and Technology of China. From 2009 to 2016, he held academic positions at City University of Hong Kong, York University, Memorial University of Newfoundland, and Southeast Missouri State University. In 2016, he joined the University of Louisiana at Lafayette as an Assistant Professor of Mathematics and was promoted to Associate Professor in 2022. His research interests include asymptotic analysis, computational mathematics, differential equations, and mathematical biology.

• Part 1: Ordinary Differential Equations 1. Scalar Equations 2. Planar Systems 3. Ordinary Differential Systems 4. Perron-Frobenius Theorem 5. Hurwitz Matrices 6. Global Analysis 7. Illustrative Examples Part 2: Continuous Age-Structured Models and Delay Equations 8. Nicholson’s Blowflies Model 9. Qualitative Analysis 10. Viral Infection Dynamics 11. More Ecological Models Part 3: Reaction-Diffusion Equations 12. Linear Equations 13. Nonlinear Equations 14. Traveling Waves Part 4: Difference Equations 15. Scalar Equations 16. Finite Dimensional Systems 17. Population Dynamics