Computational and Mathematical Population Dynamics

This book is a collection of works that represent the recent advancements in computational and mathematical methods applied to population dynamics. It concentrates on both development of new tools as well as on innovative use of existing tools to obtain new understanding of biological systems. The volume introduces new state-of-the-art techniques for defining and solving numerically control problems in mathematical biology in which the control appears linearly. Such problems produce simpler optimal controls that can be implemented in practice. The book further develops tools for fitting multi-scale models to multi-scale data and studying the practical identifiability of the parameters from multi-scale data. Novel model of Zika with Wolbahia infection in mosquitoes suggests that the most suitable control strategy to control Zika in the absence of Wolbahia is killing mosquitoes but the most suitable strategy when mosquitoes are Wolbahia infected is the treatment of humans.

A completely novel methodology of developing discrete-continuous hybrid models of multi-species interactions is also introduced together with avantgarde techniques for discrete-continuous hybrid models analysis. A mathematical model leads to new observations of the within-host virus dynamics and its interplay with the immune responses. In particular, it is observed that the parameters promoting CTL responses need to be boosted over parameters promoting antibody production to obtain a biologically relevant steady state. A novel stochastic model of COVID-19 investigates quarantine and lock down as important strategies for control and elimination of COVID-19.

Necibe Tuncer is an Associate Professor in the Department of Mathematical Sciences at Florida Atlantic University, where she teaches undergraduate and graduate students. She received her PhD from Auburn University in 2007. Her postdoctoral position was as John Thompson Assistant Professor at the University of Florida. Before joining Florida Atlantic University in 2014, she worked as an Assistant Professor of mathematics at the University of Tulsa. She is now a member of the editorial boards of Mathematical Biosciences and Journal of Biological Systems. Since 2012, the National Science Foundation has been funding for her research in mathematical epidemiology.

Maia Martcheva is a professor of mathematics at University of Florida. She obtained her PhD at Purdue University in 1998. After that she was a postdoc at IMA, University of Minnesota, Arizona State university and an NSF Advance Fellow at Cornell University in 2002-2003. Since 2003 she has been an Assistant, Associate and Full Professor at the Department of Mathematics, University of Florida. Maia Martcheva has published over 130 papers. Maia Martcheva has also published 3 books: Gender Structured Population Modeling (2005, SIAM), An Introduction to Mathematical Epidemiology (2015, Springer), and Age Structured Population Modeling (2020, Springer). Her research has been supported by the National Science Foundation. In 2016-2018 Maia Martcheva was a Managing Editor of Journal of Biological Systems. Currently, she serves on the editorial boards of Journal of Biological Systems, Journal of Biological Dynamics and Journal of Difference Equations with Applications.

Olivia Prosper is an Assistant Professor of mathematics at the University of Tennessee. She earned her PhD from the University of Florida in 2012, held the postdoctoral position of Instructor of Applied and Computational Mathematics at Dartmouth College from 2012 to 2015, and spent four years as an Assistant Professor of Mathematics at the University of Kentucky before joining the Department of Mathematics at the University of Tennessee in 2019. Since 2018, her research has been supported by NSF grants, including the NSF CAREER Award, awarded in 2021. In 2021, she also received the Intercollegiate Biomathematics Alliance Excellence in Research Award.

Lauren M Childs is an Assistant Professor in the Department of Mathematics at Virginia Tech. She received her BS in Mathematics and Chemistry from Duke University followed by her MA and PhD in Applied Mathematics from Cornell University. Lauren Childs was a Postdoctoral Fellow at Georgia Tech joint between the School of Biology and the School of Mathematics. Following her work at Georgia Tech, she was a MIDAS Postdoctoral Fellow and Research Scientist in the Center for Communicable Disease Dynamics at the Harvard T H Chan School of Public Health. In 2016, she joined the faculty at Virginia Tech. Her research program involves the development, analysis and simulation of mathematical and computational models to examine biologically-motivated questions. Her work includes modeling with diverse techniques for a wide variety of applications in epidemiology, immunology, and ecology. Lauren Childs has published over 35 peer-reviewed articles and book chapters. Her research has been supported by the National Science Foundation, the National Institutes of Health, the Simons Foundation and the Jeffress Trust.