San Francisco’s flu-shot campaign is off to a slower start than last year, with pharmacies and medical practices reporting fewer vaccinations so far this season as flu cases begin rising earlier than expected. Warm weather — with temperatures near 80 degrees on Oct. 7 — may be one reason residents are putting off vaccination. Some providers also received vaccine shipments later than usual, while federal promotion of flu shots has been scaled back, according to reporting cited in discussions of the season. Flu season typically runs from October through May. Health experts recommend that most people get an annual vaccine in early fall because it takes about two weeks for the body to build antibodies. San Francisco reported its first influenza death of the season last week. One Medical, the Amazon-owned primary care practice, has administered thousands of flu shots in the Bay Area this year, but its offices have seen slightly fewer patients for vaccinations than at the same time last year, said Dr. Brian Cogburn, a San Francisco-based primary care physician and the company’s senior medical director. Cogburn said waiting until mid- or late October can sometimes extend protection later into the season, but he said that timing may not be advisable this year given the earlier increase in cases. He encouraged patients to get vaccinated as soon as possible. The slower uptake comes as providers ask residents not to let warm fall weather obscure the start of flu season. Vaccination can help protect individuals and reduce the risk of illness spreading through households and the broader community.