We construct a mathematical model of aerosol (i.e., droplet-nuclei) transmission of influenza within a household containing one infected and embed it into an epidemic households model in which infecteds occasionally infect someone from another household; in a companion paper, we argue that the contribution from contact transmission is trivial for influenza and the contribution from droplet transmission is likely to be small. Our model predicts that the key infection control measure is the use of N95 respirators, and that the combination of respirators, humidifiers, and ventilation reduces the threshold parameter (which dictates whether or not an epidemic breaks out) by ≈20% if 70% of households comply, and by ≈40% if 70% of households and workplaces comply (≈28% reduction would have been required to control the 1918 pandemic). However, only ≈30% of the benefits in the household are achieved if these interventions are used only after the infected develops symptoms. It is also important for people to sleep in separate bedrooms throughout the pandemic, space permitting. Surgical masks with a device (e.g., nylon hosiery) to reduce face-seal leakage are a reasonable alternative to N95 respirators if the latter are in short supply.