Unified bio-simulate framework
Hub or rebate: what moves stable patients.
Friction vs hub mitigation
Four barriers to switching, each netted against its own hub lever.
Friction f and hub strength Hmax are in utility units, the same scale as copay savings in 02. Each lever cancels only its own friction, so spend past its neutralize point is wasted.
Friction vs hub mitigation
F = fadmin + fpsych + fnav + flogist
Hk = Hmax,k · (1 − e−γ·KH)
net friction = Σ max(0, fk − Hk)
K*k = ln(Hmax,k / (Hmax,k − fk)) / γ
Netting each friction against its own lever keeps a strong PA engine from cancelling anxiety nobody addressed. If H_max ≤ f, that friction is never fully neutralized.
Total friction
4.50
F
Hub cancels
2.40
Σ min(H_k, f_k)
Net friction
2.10
47% of F left
Phase
A
High brand inertia · B at $19.5M
Administrative · EHR enrollment portal
cancels 0.79 of 1.50 · neutralized at $13.9M
Psychological · Nurse navigator calls
cancels 0.55 of 1.20 · neutralized at $19.5M
Navigational · e-PA and copay engine
cancels 0.59 of 1.00 · neutralized at $11.0M
Logistical · Specialty pharmacy triage
cancels 0.47 of 0.80 · neutralized at $11.0M
Switch probability
The monthly odds a stable patient switches, and the share of switches that get filled.
Choice probability bridge
Uswitch = β₀ + α·ΔC − net friction + ε
P(Switch) = eU / (1 + eU) ΔC = βc·R
C = e−η·(net admin + nav + logist)
Everyone modeled is stable on the brand, so the stable gate is 1. β₀ keeps switching realistic once friction is gone: without it a patient with no savings would switch half the time each month. Admin, navigation and logistics friction also stop switches from being filled (C); psychological friction only affects the decision.
Copay savings
$16
ΔC per month
Switch utility
-6.12
no hub -8.52
P(Switch) per month
0.22%
no hub 0.02%
Switches filled
31%
no hub 7%
Market share shift velocity
Direct switching, peer diffusion and the payer strike, all limited by fulfillment.
Market share shift velocity
dM/dt = [P·(1 + k·M) + δ·Φt] · C · (M̄ − M)
Φ = 1 / (1 + e−θ(R − Rcrit))
P·(1 + k·M) is direct switching plus peer diffusion, so share can grow from zero. δ·Φ is the payer strike from the exclusion month. Both pass through fulfillment C and stop at M̄; in monthly steps they combine as 1 − (1 − a)(1 − b), so share never overshoots.
Exclusion odds
12%
Φ at your rebate
Share at month 12
7.6%
no hub 1.6%
Share at month 36
32.0%
best split 90.0%
Months to half of M̄
—
not within 36 mo
Capital allocation
NPV across hub capital and rebate levels, and where the next dollar should go.
Hub capital is spent once up front; the rebate is held flat across the horizon. Tap a cell in the map to load that split into 01 and 03.
NPV objective and budget
Π = Σ (1 + r)−t · Mt · Q · (Pgross − R) − KH
B = Σ (1 + r)−t · R · Mt · Q + KH
next dollar → higher ΔG / ΔB, hub vs rebate
r is the monthly rate from your annual input. B counts rebates on every biosimilar unit plus hub capital. G is gross revenue at WAC. The next dollar goes where it adds more G per budget dollar over the whole horizon; below $1 it lowers NPV.
NPV, your split
$68.4M
hub $5.0M · rebate $800
NPV, best split
$295.9M
hub $15.0M · rebate $1,000
Revenue per $1 of hub
$2.79
next $100k
Revenue per $1 of rebate
$2.61
next $25 per unit
Next dollar → hub capital.
NPV by hub capital (across) and rebate per unit (up). Tap a cell to try that split.
Best $295.9MYour splitDarker = higher NPV