A behavioral model of infant sleep disturbance.

Castañe et al. (1993) built a math-style model of why babies wake at night.

They treat crying after bedtime as an operant kept alive by parent attention.

The paper is pure theory; no infants were studied and no data were collected.

The model says sleep problems grow when parents give milk, rocking, or talk each time the baby cries.

These rewards act like VI food pellets, making the crying chain stronger and longer.

Marr (1989) and Davison (1992) use the same math tools for adult lever pressing. All three papers push Newton-style equations to map how reinforcement ‘force’ changes behavior rate.

Sundram (2011) also mixes biology with contingencies, but for stereotypy in autism. Both models say you must track brain state plus reinforcement to predict when the behavior loop will lock.

Chou et al. (2010) seems to clash: they show observer bias can fake stimulus control. M et al. ignore observer drift, yet the gap is method, not message—C warns data collectors can miscount, while M warns parents can accidentally reinforce. Fix the first with staff rotation, the second with extinction.

You can test the model tonight. Chart each cry and what you did within 30 s. If attention follows crying on most bouts, you are the VI schedule. Shift to brief, fixed checks and praise any quiet 5-s period. The math says the chain will break faster than you think.