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Mathematical Structures of Epidemic Systems (Paperback, Softcover reprint of the original 1st ed. 1993)
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Mathematical Structures of Epidemic Systems (Paperback, Softcover reprint of the original 1st ed. 1993)
Series: Lecture Notes in Biomathematics, 97
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The dynamics of infectious diseases represents one of the oldest
and ri- est areas of mathematical biology. From the classical work
of Hamer (1906) and Ross (1911) to the spate of more modern
developments associated with Anderson and May, Dietz, Hethcote,
Castillo-Chavez and others, the subject has grown dramatically both
in volume and in importance. Given the pace of development, the
subject has become more and more di?use, and the need to provide a
framework for organizing the diversity of mathematical approaches
has become clear. Enzo Capasso, who has been a major contributor to
the mathematical theory, has done that in the present volume,
providing a system for organizing and analyzing a wide range of
models, depending on the str- ture of the interaction matrix. The
?rst class, the quasi-monotone or positive feedback systems, can be
analyzed e?ectively through the use of comparison theorems, that is
the theory of order-preserving dynamical systems; the s- ond, the
skew-symmetrizable systems, rely on Lyapunov methods. Capasso
develops the general mathematical theory, and considers a broad
range of - amples that can be treated within one or the other
framework. In so doing, he has provided the ?rst steps towards the
uni?cation of the subject, and made an invaluable contribution to
the Lecture Notes in Biomathematics. Simon A. Levin Princeton,
January 1993 Author's Preface to Second Printing In the Preface to
the First Printing of this volume I wrote: \ . .
General
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