A 28-year-old male construction worker from rural Maharashtra presents to a primary health centre with a 3-week history of productive cough, low-grade fever in the evenings, and night sweats. He shares a single-room dwelling with 6 family members, including his 65-year-old mother who had tuberculosis 2 years ago (treated and cured). Sputum smear microscopy shows acid-fast bacilli. His chest X-ray reveals cavitary lesions in the right upper lobe. Which of the following epidemiological factors is MOST significant in understanding the transmission risk in this household?