Stochastic Biomathematical Models
Title | Stochastic Biomathematical Models PDF eBook |
Author | Mostafa Bachar |
Publisher | Springer |
Pages | 216 |
Release | 2012-10-19 |
Genre | Mathematics |
ISBN | 3642321577 |
Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.
Stochastic Models in Biology
Title | Stochastic Models in Biology PDF eBook |
Author | Narendra S. Goel |
Publisher | Elsevier |
Pages | 282 |
Release | 2013-10-22 |
Genre | Science |
ISBN | 1483278107 |
Stochastic Models in Biology describes the usefulness of the theory of stochastic process in studying biological phenomena. The book describes analysis of biological systems and experiments though probabilistic models rather than deterministic methods. The text reviews the mathematical analyses for modeling different biological systems such as the random processes continuous in time and discrete in state space. The book also discusses population growth and extinction through Malthus' law and the work of MacArthur and Wilson. The text then explains the dynamics of a population of interacting species. The book also addresses population genetics under systematic evolutionary pressures known as deterministic equations and genetic changes in a finite population known as stochastic equations. The text then turns to stochastic modeling of biological systems at the molecular level, particularly the kinetics of biochemical reactions. The book also presents various useful equations such as the differential equation for generating functions for birth and death processes. The text can prove valuable for biochemists, cellular biologists, and researchers in the medical and chemical field who are tasked to perform data analysis.
Methods and Models in Mathematical Biology
Title | Methods and Models in Mathematical Biology PDF eBook |
Author | Johannes Müller |
Publisher | Springer |
Pages | 721 |
Release | 2015-08-13 |
Genre | Mathematics |
ISBN | 3642272517 |
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Stochastic Models In The Life Sciences And Their Methods Of Analysis
Title | Stochastic Models In The Life Sciences And Their Methods Of Analysis PDF eBook |
Author | Wan Frederic Y M |
Publisher | World Scientific |
Pages | 476 |
Release | 2019-08-29 |
Genre | Mathematics |
ISBN | 981327462X |
Biological processes are evolutionary in nature and often evolve in a noisy environment or in the presence of uncertainty. Such evolving phenomena are necessarily modeled mathematically by stochastic differential/difference equations (SDE), which have been recognized as essential for a true understanding of many biological phenomena. Yet, there is a dearth of teaching material in this area for interested students and researchers, notwithstanding the addition of some recent texts on stochastic modelling in the life sciences. The reason may well be the demanding mathematical pre-requisites needed to 'solve' SDE.A principal goal of this volume is to provide a working knowledge of SDE based on the premise that familiarity with the basic elements of a stochastic calculus for random processes is unavoidable. Through some SDE models of familiar biological phenomena, we show how stochastic methods developed for other areas of science and engineering are also useful in the life sciences. In the process, the volume introduces to biologists a collection of analytical and computational methods for research and applications in this emerging area of life science. The additions broaden the available tools for SDE models for biologists that have been limited by and large to stochastic simulations.
Stochastic Modelling In Biology: Relevant Mathematical Concepts And Recent Applications
Title | Stochastic Modelling In Biology: Relevant Mathematical Concepts And Recent Applications PDF eBook |
Author | Tautu Petre |
Publisher | #N/A |
Pages | 456 |
Release | 1990-12-05 |
Genre | |
ISBN | 9814611921 |
These proceedings focus on future prospects as well as on the present status in some important areas of applied probability and mathematical biology. Some papers have educational intentions regarding the mathematical modelling of special biological situations. The workshop was the third one in Heidelberg dealing with stochastic modelling in biology, e.g., cell biology, embryology, oncology, epidemiology and genetics.
Stochastic Modelling for Systems Biology, Third Edition
Title | Stochastic Modelling for Systems Biology, Third Edition PDF eBook |
Author | Darren J. Wilkinson |
Publisher | CRC Press |
Pages | 366 |
Release | 2018-12-07 |
Genre | Mathematics |
ISBN | 1351000896 |
Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Having been thoroughly updated to reflect this, this third edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context. New methods and applications are included in the book, and the use of R for practical illustration of the algorithms has been greatly extended. There is a brand new chapter on spatially extended systems, and the statistical inference chapter has also been extended with new methods, including approximate Bayesian computation (ABC). Stochastic Modelling for Systems Biology, Third Edition is now supplemented by an additional software library, written in Scala, described in a new appendix to the book. New in the Third Edition New chapter on spatially extended systems, covering the spatial Gillespie algorithm for reaction diffusion master equation models in 1- and 2-d, along with fast approximations based on the spatial chemical Langevin equation Significantly expanded chapter on inference for stochastic kinetic models from data, covering ABC, including ABC-SMC Updated R package, including code relating to all of the new material New R package for parsing SBML models into simulatable stochastic Petri net models New open-source software library, written in Scala, replicating most of the functionality of the R packages in a fast, compiled, strongly typed, functional language Keeping with the spirit of earlier editions, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership. An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling.
Stochastic Epidemic Models with Inference
Title | Stochastic Epidemic Models with Inference PDF eBook |
Author | Tom Britton |
Publisher | Springer Nature |
Pages | 474 |
Release | 2019-11-30 |
Genre | Mathematics |
ISBN | 3030309002 |
Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.