A method for managing health of ruminants or other animals. The method includes providing a feed dispenser for feeding ruminants nutrient supplements, and the feed dispenser includes a gas analyzer where a ruminant places its head. The method includes determining a particular ruminant has accessed the feed dispenser such as by reading an identifier from an RFID ear tag and operating the feed dispenser to provide a ration of methane-controlling nutrient supplement. The method may include using the identifier to determine that the animal should be vaccinated such as based on their age and no record of prior vaccination. The method includes dispensing a dose of a nasal vaccine into the feed dispenser near the animal's nostrils. The method may include discharging a diagnostic agent such as propane or carbon monoxide and processing data collected to diagnose the animal as having a disease or condition such as a lung-related sickness.