The mesh is a first-order exponential treatment-response surface — the same functional form used to describe symptom decay under an effective clinical intervention (a single dominant time-constant recovery, analogous to first-order kinetics). Two real inputs form the surface's horizontal plane: support level (X axis) and sessions elapsed (Z axis, depth). Height is predicted severity:
k(support) = 0.008 + 0.032·(support/100)·model_mult
floor(support) = 8 + 22·(1 − support/100)
S(support, t) = floor(support) + (S₀ − floor(support))·e^(−k·t)
Higher support raises the recovery-rate constant k (faster symptom decline per session) and lowers the residual "floor" — the symptom level the model asymptotically approaches, standing in for incomplete remission under weak support. The four therapy-model options apply an illustrative relative multiplier to k (CBT 1.00, DBT 0.92, Psychodynamic 0.72, Humanistic 0.80) reflecting the general ordering reported for structured, skills-based interventions versus insight-oriented ones in short courses of treatment — a simplified relative comparison, not a citation-backed absolute effect size.
The white marker sits at your current (support, t) on this fixed landscape; dragging the sliders slides it across the surface exactly as the formula predicts. "Play recovery" animates t from 0 upward at a fixed rate and draws the true exponential trajectory as a trail. Sessions-to-remission solves the same equation for t at S = 20%: t = ln[(S₀−floor)/(20−floor)] / k.
- Initial severity — where the patient starts (S₀); reshapes how far the curve has to fall.
- Support level — moves the marker along X and reshapes the whole landscape's k and floor.
- Sessions elapsed — moves the marker along Z (depth) — how far into treatment the patient is.
- Therapy model — scales the recovery-rate constant k.