DTM.2:5 - Archetypal Grounding

DTM.2:5.1 - Transmission can reconstruct the practice

Suppose 100 eligible groups face a modeled one-period uptake probability of 0.3. Among their accepted source encounters, 60% carry A and 40% carry B. The accepted flows are therefore 18 and 12.

Assume the recipient retains A after an A encounter with probability 0.9, while a B encounter yields A with probability 0.2. The other outcomes yield B. The receiving flows are:

A: 0.9 × 18 + 0.2 × 12 = 18.6
B: 0.1 × 18 + 0.8 × 12 = 11.4.

These are expected counts, not fractions of a particular person. Thirty uptakes do not mean thirty faithful copies. If accepted encounters favour one source differently, use their composition rather than the source population’s composition.

An intervention that helps more recipients obtain the required tool changes uptake. An intervention that helps recipients preserve a needed operation changes K. They are different proposed effects and need different observations.

DTM.2:5.2 - Reinforcement is a different law

In a constructed three-neighbour case, each neighbour independently provides a relevant endorsement with probability 0.4. If one endorsement is sufficient, the chance of reaching that threshold is 1−0.6³=0.784. If two are required, it is 3×0.4²×0.6+0.4³=0.352.

Both numbers concern the specified endorsement condition, not actual adoption. A recipient may still lack resources or choose not to proceed. Dependence among neighbours invalidates this binomial calculation; three repetitions from one source are not necessarily three independent endorsements.

The useful result is a choice between mechanisms to investigate, rather than adjusting one transmission coefficient until both stories appear to fit.

DTM.2:5.3 - A demonstration reaches learners without supplying coordination

A dance workshop distributes a turn demonstration. A view count measures exposure. A learner’s attempt, successful execution with a cue, uncued execution and later teaching provide different events.

If the learner needs a coordination method not supplied by the demonstration, raising the number of views need not increase the target performance. HCD and the relevant movement methods supply the acquisition work. The transmission model records its effect on the chosen transition, rather than treating a missing capability as unwillingness or resistance.

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.