DTM.9:5.2 - A local consequence and further spread can move differently

Add an illustrative local consequence stock:

L' = hB + 0.1a + 0.05v − rL.

L measures a specified local impairment in normalized units; h is its rate per unit B activity and r its restoration rate. The other terms represent local costs of response and selective checking. Useful A remains a separate result, and harm to outside recipients is not included.

With h=r=1, the three rows above give stationary L of approximately 0.37778, 0.63182 and 0.105. Broad checking worsens both useful activity and this local consequence. These results do not collapse all affected interests into L.

If groups share the same settled internal regime and between-group spread is slower, an illustrative coupling is z’=βBz(1−z)−γz, with z the fraction of groups in which B is established. At β=2 and γ=0.5, the positive stationary fractions are approximately 0.19643 for the baseline and 0.55645 for broad checking. The zero state remains invariant without an introduction.

Reducing h or increasing r can improve the local consequence without changing B and therefore without changing this spread law. Conversely, reducing β can stop continued spread while leaving the established internal activity untouched. DTM.8 explains the distinct intervention targets. If affected groups differ materially or are still learning, use DTM.3 to repair the coupling instead of inserting an unsupported average B.