Prologue
No problem facing humanity in the next century is more compelling than the
changing epidemiological environment of infectious and other diseases. The World
Cancer Report estimates that global cancer rates could increase by 50% in the next
15 to 20 years (http:/ /www.who.int/mediacentrejnewsfreleases/2003/pr27 fen/).
Emerging pathogens-some variants on familiar themes such as influenza, some
reemergent enemies of the past such as tuberculosis, and some apparently novel
forms such as SARS and HIV-plague humanity. Emergence of novel pathogens has
always been part of our evolutionary history, but the rates of change and emergence
have been greatly accelerated through our own activities: directly through the
emergence of drug resistance because of our profligate use, for example of antibiotics
and anti-malarials, and indirectly through our increased mobility and our impacts
upon our environment.
Such challenges mandate the integration of a wide variety of disciplines, from
cell biology, immunology and genomics, to population and community ecology, to
climatology and the social sciences. These require that researchers relate phenom-
ena on diverse scales of space and time, and translate the actions of individual
agents into their macroscopic consequences, bridging scales of organizational com-
plexity. Such integration mandates the application of mathematical and computa-
tional modeling, and the expansion of the frontiers of the mathematics of infectious
diseases. Infectious disease modeling is one of the oldest and richest topics in math-
ematical biology, and has become accepted as integral to public health practice, in
large part because researchers have maintained close contact with the empirical
dimensions of the subject. But as the potential for high-speed computation has
advanced, threats such as pandemic flu and bioterrorism have fueled the creation
of ever-more-detailed models that track individual agents, and incorporate reams
of information on their demographic and epidemiological characteristics, and their
behavioral patterns. This is a welcome advance, but has run ahead of comple-
mentary analytical investigations to aid in understanding the behavior of these
high-dimensional models, and in developing more robust reduced-dimensional ver-
sions.
Gumel et al. have taken an important step in that direction, bringing together
a diverse collection of researchers in a book that provides a fair sampling of current
mathematical research and challenges in human diseases. Most notable is that
this book recognizes the central role of developing nations in the emergence of
novel pathogens, and the need to involve researchers from these developing nations
in addressing these problems. Over the last quarter century, there has been a
remarkable expansion of research capacity in developing nations concerned with
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