Dynamical Models in Biology

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Academic Press, Jun 15, 2001 - Mathematics - 187 pages
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Dynamic Models in Biology offers an introduction to modern mathematical biology. This book provides a short introduction to modern mathematical methods in modeling dynamical phenomena and treats the broad topics of population dynamics, epidemiology, evolution, immunology, morphogenesis, and pattern formation.

Primarily employing differential equations, the author presents accessible descriptions of difficult mathematical models. Recent mathematical results are included, but the author's presentation gives intuitive meaning to all the main formulae. Besides mathematicians who want to get acquainted with this relatively new field of applications, this book is useful for physicians, biologists, agricultural engineers, and environmentalists.

Key Topics Include:

  • Chaotic dynamics of populations
  • The spread of sexually transmitted diseases
  • Problems of the origin of life
  • Models of immunology
  • Formation of animal hide patterns
  • The intuitive meaning of mathematical formulae explained with many figures
  • Applying new mathematical results in modeling biological phenomena

Miklos Farkas is a professor at Budapest University of Technology where he has researched and instructed mathematics for over thirty years. He has taught at universities in the former Soviet Union, Canada, Australia, Venezuela, Nigeria, India, and Columbia. Prof. Farkas received the 1999 Bolyai Award of the Hungarian Academy of Science and the 2001 Albert Szentgyorgyi Award of the Hungarian Ministry of Education.

  • A 'down-to-earth' introduction to the growing field of modern mathematical biology
  • Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra
 

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Contents

Chapter 1 Discrete Population Models
1
Chapter 2 Population Dynamics in Continuous time
17
Chapter 3 Epidemics
63
Chapter 4 Evolution And population Genetics
79
Chapter 5 Morphogenesis And Pattern Formation
105
Appendix 1 Discrete Mathematics
125
Appendix 2 Ordinary Differential Equations
143
Appendix 3 Partial Differential Equations
157
Appendix 4 Riemannian Geometry
171
References
179
Index
184
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About the author (2001)

Miklos Farkas received his Ph.D. in applied mathematics at Eötvös Loránd University of Budapest. He has been a professor of mathematics for over 30 years and has published a number of books and nearly 80 research papers. His research interest include stability theory nolinear oscillations, bifurcations, and population dynamics. He received the Bolyai Award of the Hungarian Academy of Science in 1999.

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