As Eugene Wigner stressed, mathematics has proven unreasonably
effective in the physical sciences and their technological
applications. The role of mathematics in the biological, medical
and social sciences has been much more modest but has recently
grown thanks to the simulation capacity offered by modern
computers.
This book traces the history of population dynamics---a
theoretical subject closely connected to genetics, ecology,
epidemiology and demography---where mathematics has brought
significant insights. It presents an overview of the genesis of
several important themes: exponential growth, from Euler and
Malthus to the Chinese one-child policy; the development of
stochastic models, from Mendel's laws and the question of
extinction of family names to percolation theory for the spread of
epidemics, and chaotic populations, where determinism and
randomness intertwine.
The reader of this book will see, from a different perspective,
the problems that scientists face when governments ask for reliable
predictions to help control epidemics (AIDS, SARS, swine flu),
manage renewable resources (fishing quotas, spread of genetically
modified organisms) or anticipate demographic evolutions such as
aging."
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