DTM.2:5.4 - A recipient hazard becomes a population flow

Suppose N=100, f=0.2 and β=0.5 per week. There are 80 eligible recipients, each with current hazard 0.1 per week. The instantaneous new-uptake flow is therefore 8 events per week, or 0.08 of the population per week.

For a short interval of 0.1 week with hazards approximately unchanged, the expected first-uptake count is approximately 0.8. With constant hazard throughout that interval, it is 80[1−exp(−0.01)], approximately 0.796. Counting the remaining fraction again would incorrectly reduce the instantaneous flow to 6.4 events per week. If uptake materially changes f during the interval, evolve the changing state rather than holding its initial hazard fixed.