Human contact with a calm animal engages C-tactile afferents in the skin (slow, gentle stroking fires these nerves preferentially), which promotes oxytocin release and raises vagal (parasympathetic) tone. That combination produces the well-documented three-part response seen in animal-assisted therapy (AAT) studies: heart rate falls, circulating cortisol declines, and oxytocin rises.
Each biomarker here relaxes toward a mode-and-distance-dependent target with its own time constant, first-order like a capacitor discharging:
dX/dt = (X_target − X) / τ
Heart rate τ ≈ 8 s (fast: mostly vagal reflex)
Cortisol τ ≈ 70 s (slow: HPA-axis hormone clearance)
Oxytocin τ ≈ 45 s (medium: pulsatile release + reuptake)
Targets scale with a proximity factor pf = clamp(1 − distance/3m, 0, 1) — a dog across the room barely moves the needle, one within petting range does:
- No Dog Present — everything relaxes back to resting baseline (HR 78 bpm, cortisol & oxytocin 100%).
- Calm Presence — mild relaxation from the dog simply lying nearby; small HR and cortisol drop, modest oxytocin rise.
- Active Petting — the strongest effect: slow stroking maximally engages C-tactile afferents, driving the largest cortisol drop and oxytocin rise, with HR falling as vagal tone increases.
- Play & Fetch — physical activity keeps heart rate elevated, but the social bonding still lowers cortisol and raises oxytocin substantially.
Session speed compresses a realistic 15–30 minute AAT session into a watchable simulation; the numbers themselves are the real time constants, just fast-forwarded.