  We derive and asymptotically analyze mass-action models for disease spread
that include transient pair formation and dissociation. Populations of unpaired
susceptibles and infecteds are distinguished from the population of three types
of pairs of individuals; both susceptible, one susceptible and one infected,
and both infected. Disease transmission can occur only within a pair consisting
of one susceptible individual and one infected individual. By considering the
fast pair formation and fast pair dissociation limits, we use a perturbation
expansion to formally derive a uniformly valid approximation for the dynamics
of the total infected and susceptible populations. Under different parameter
regimes, we derive uniformly valid effective equations for the total infected
population and compare their results to those of the full mass-action model.
Our results are derived from the fundamental mass-action system without
implicitly imposing transmission mechanisms such as that used in
frequency-dependent models. They provide a new formulation for effective
pairing models and are compared with previous models.
