(Ebook) Spatial Dynamics and Pattern Formation in Biological Populations by Ranjit Kumar Upadhyay, Satteluri R. K. Iyengar ISBN 9780367555504, 0367555506

(Ebook) Spatial Dynamics and Pattern Formation in Biological Populations by Ranjit Kumar Upadhyay, Satteluri R. K. Iyengar ISBN 9780367555504, 0367555506

The book provides an introduction to deterministic (and some stochastic) modeling of spatiotemporal phenomena in ecology, epidemiology, and neural systems. A survey of the classical models in the fields with up to date applications is given.

The book begins with detailed description of how spatial dynamics/diffusive processes influence the dynamics of biological populations. These processes play a key role in understanding the outbreak and spread of pandemics which help us in designing the control strategies from the public health perspective. A brief discussion on the functional mechanism of the brain (single neuron models and network level) with classical models of neuronal dynamics in space and time is given. Relevant phenomena and existing modeling approaches in ecology, epidemiology and neuroscience are introduced, which provide examples of pattern formation in these models. The analysis of patterns enables us to study the dynamics of macroscopic and microscopic behaviour of underlying systems and travelling wave type patterns observed in dispersive systems. Moving on to virus dynamics, authors present a detailed analysis of different types models of infectious diseases including two models for influenza, five models for Ebola virus and seven models for Zika virus with diffusion and time delay. A Chapter is devoted for the study of Brain Dynamics (Neural systems in space and time).

Significant advances made in modeling the reaction-diffusion systems are presented and spatiotemporal patterning in the systems is reviewed. Development of appropriate mathematical models and detailed analysis (such as linear stability, weakly nonlinear analysis, bifurcation analysis, control theory, numerical simulation) are presented.

Key Features

• Covers the fundamental concepts and mathematical skills required to analyse reaction-diffusion models for biological populations.
• Concepts are introduced in such a way that readers with a basic knowledge of differential equations and numerica