Anchor on the exact demand of the stem, which is prevention rather than cure. So we need the disease for which a tetracycline is given to people who are well but exposed, to stop them developing or spreading infection.
During cholera epidemics, household and close contacts of a case are offered a tetracycline, classically a short course, to suppress Vibrio cholerae carriage and curb the chain of transmission. This is the textbook setting of tetracycline as a prophylactic.
Compare the others. Brucellosis is managed with prolonged combination therapy that includes a tetracycline for treatment, not routine prevention. Leptospirosis prevention does use doxycycline in high-risk exposure, yet cholera remains the canonical answer paired with tetracycline in this list. Meningococcal contacts receive rifampicin, ciprofloxacin or ceftriaxone, never tetracycline.
The disease whose contacts are shielded with tetracycline is cholera.
\[\boxed{\text{Cholera}}\]