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Books > Medicine > Nursing & ancillary services > Biomedical engineering
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Spatial Dynamics and Pattern Formation in Biological Populations (Hardcover)
Loot Price: R6,744
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Spatial Dynamics and Pattern Formation in Biological Populations (Hardcover)
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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
numerical methods can understand the analysis. The results are also
illustrated with figures. Focuses on mathematical modeling and
numerical simulations using basic conceptual and classic models of
population dynamics, Virus and Brain dynamics. Covers wide range of
models using spatial and non-spatial approaches. Covers single, two
and multispecies reaction-diffusion models from ecology and models
from bio-chemistry. Models are analysed for stability of
equilibrium points, Turing instability, Hopf bifurcation and
pattern formations. Uses Mathematica for problem solving and MATLAB
for pattern formations. Contains solved Examples and Problems in
Exercises. The Book is suitable for advanced undergraduate,
graduate and research students. For those who are working in the
above areas, it provides information from most of the recent works.
The text presents all the fundamental concepts and mathematical
skills needed to build models and perform analyses.
General
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