If we have a duty not to infect others, how far does it go? This question is often discussed with respect to HIV transmission, but reflection on other diseases like influenza raises a number of interesting theoretical issues. I argue that a duty to avoid infection not only yields requirements for persons who know they carry a disease, but also for persons who know they are at increased risk, and even for those who definitely know they are completely healthy. Given the numerous ways in which human interaction facilitates the spread of communicable diseases, a maximum level of precaution would be very demanding--possibly unreasonably demanding. The 'over-demandingness problem' is mostly invoked as a criticism of utilitarianism, as this theory requires moral agents to always maximise general welfare, even at significant cost for themselves. However, I argue that, with respect to precautions against infectious diseases like influenza, utilitarianism is able to avoid the over-demandingness problem. A contractualist account, on the other hand, whilst able to explain how one's obligations to avoid infection can be limited, given that other persons have opportunities and responsibilities to protect themselves, in the end requires precautions that raise the over-demandingness problem.