The four processes described so far separate into two categories: those that happen at an individual level, and contact processes. Seeking treatment and the cessation of tracing take place in the population at rates proportional to a number of individuals, and so fall into the former category. Using square brackets around a quantity to indicate its expected number in the population (so that quantities in square brackets are extensive expected numbers rather than intensive proportions) we take treatment to happen at a rate g½I, where g is the treatment rate constant, and the cessation of efforts to trace a treated individual's contacts to happen at rate g T ½T, where g T is the rate constant associated with the end of tracing.