We analyze the temporal evolution of emerging fields within several scientific disciplines in terms of numbers of authors
and publications. From bibliographic searches we construct databases of authors, papers, and their dates of publication. We
show that the temporal development of each field, while different in detail, is well described by population contagion models,
suitably adapted from epidemiology to reflect the dynamics of scientific interaction. Dynamical parameters are estimated and
discussed to reflect fundamental characteristics of the field, such as time of apprenticeship and recruitment rate. We also
show that fields are characterized by simple scaling laws relating numbers of new publications to new authors, with exponents
that reflect increasing or decreasing returns in scientific productivity.