For a class of epidemiological SIRS models that include public health
policies, the stability at the uninfected state and the prevalence at
the infected state are investigated. Backward bifurcation from the uni
nfected state and hysteresis effects are shown to occur for some range
of parameters. In such cases, the reproduction number does not descri
be the necessary elimination effort; rather the effort is described by
the value of the critical parameter at the turning point. An explicit
expression is given for this quantity. The phenomenon of subcritical
bifurcation in epidemic modeling is also discussed in terms of group m
odels, pair formation, and macroparasite infection. (C) 1997 Elsevier
Science Inc.