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.

Contents:

• Wolbachia Invasion and Establishment in Aedes aegypti Populations to Suppress Zika Transmission (Cristina Korb and Maia Martcheva)
• Dynamics and Optimal Control of HIV Infection and Opioid Addiction (Archana Neupane Timsina and Necibe Tuncer)
• The Effect of Lockdown on Mean Persistence Time of Highly Infectious Diseases: A Stochastic Model Based Study (Sk Shahid Nadim, Bapi Saha, and Joydev Chattopadhyay)
• A Model of Virus Infection with Immune Responses Supports Boosting CTL Response to Balance Antibody Response (Tyler Meadows and Elissa J Schwartz)
• Structural and Practical Identifiability Analysis of a Multiscale Immuno-Epidemiological Model (Laura Nemeth, Necibe Tuncer, and Maia Martcheva)
• Multiple Dimensions of Aedes aegypti Population Growth: Modeling the Impacts of Resource Dependence on Mass and Age at Emergence (Melody Walker, Michael A Robert, and Lauren M Childs)
• Novel Hybrid Continuous-Discrete-Time Epidemic Models (Maia Martcheva, Abdul-Aziz Yakubu, and Necibe Tuncer)
• Extending Analytical Solutions to Age–Mass Models of a Population (Lauren M Childs and Olivia F Prosper)
• Solving Singular Control Problems in Mathematical Biology Using PASA (Summer Atkins, Mahya Aghaee, Maia Martcheva, and William Hager)
• Phase Locking and Lyapunov Exponent Behaviour in Brain Networks of Epileptic Patients (Heather Berringer, Kris Vasudevan, Paolo Federico, Michael Cavers, and Elena Braverman)

Readership: Academic libraries, Researchers, Professors, Postgraduate students, Graduate students.

Key Features:

• Contains state-of-the-art tools for population dynamics modeling, simulation and analysis
• Contains most recent advances in numerical optimization applied to mathematical biology
• Contains novel numerical methods for solving linear optimal control problems
• Contains entirely novel tools for modeling multi-species interactions at the interface of discrete and continuous systems
• Contains novel analytical tools for discrete-continuous hybrid models
• Contains state-of-the-art tools for fitting to data multi-scale nested models and studying their practical identifiability
• Contains new results on Zika control
• Contains HIV and opioid epidemic novel results in data fitting and strategies for control
• Contains state-of-the-art modeling of COVID-19 quarantine and lockdown strategies for control and elimination