When a Toothbrush Stops Cleaning: A Splay-Based Replacement Rule and Its Cost per Effective Brush

Toothbrush replacement is usually governed by habit or by a calendar printed on packaging, not by how well the brush still cleans. This study models plaque-removal efficacy as falling linearly by 0.045 per week of twice-daily use from an initial index of 1.00, and computes end-of-life and mean efficacy, brushes per year, and annual cost at a bulk price of USD 0.60 for replacement intervals from 2 to 16 weeks. Efficacy first falls below 0.70 at 6.67 weeks. The longest interval whose mean efficacy over the brush's life stays at or above 0.85 is 6 weeks, using 8.67 brushes a year at USD 5.20. An 8-week interval lowers the cost to USD 3.90 with a mean efficacy of 0.82, while a 12-week interval gives a mean efficacy of only 0.73 at USD 2.60. The recommended rule is replacement at about six weeks on performance grounds, with eight weeks as a stated budget compromise. This study is simulated, not measured. SIMULATED, NOT MEASURED.