on the disease if they have contracted it. A second consideration is that it is generally thought unethical to carry out direct experiments to establish per-contact infection risks as this would require the deliberate exposure of individuals to infectious agents. The Common Cold Unit that researched cold transmission in the UK between 1946 and 1989 was a notable exception. It is also possible to estimate the transmission risk in certain circumstances where exposures to infection have been documented, for example the rate of infection among nurses who have accidentally pricked their fingers with a needle that had previously been used with contaminated blood. A more direct assessment of transmission risks can be provided by a contact study, which is often carried out because of an outbreak (such a study was carried out during the SARS outbreak of 2002–3). The first (or primary) case within a defined group (such as a school or family) is identified and people infected by this individual (called secondary cases) are documented. If the number of susceptibles in the group is n and the number of secondary cases is x, then an estimation of the transmission risk is Here, p is the same parameter as before but it has been calculated in a different way. To reflect this, it is called the secondary attack rate (it is really a risk, of course, and not a rate, but the term is still commonly used). Even if the whole group in question is susceptible, x is generally smaller than the basic reproduction number for the disease. That is defined as the number of individuals each infected individual will go on to infect themselves, in a population with no resistance to the disease. The basic reproduction number includes all secondary cases infected by a primary case, while x is only the number of secondary cases within the group in question. Secondary attack rates are useful for comparisons between vaccinated and unvaccinated groups and hence assessing the efficacy of vaccinations against the disease under inspection. However, there are inevitably complications with such contact studies. It is not always obvious which members of the group are susceptible and distinguishing between secondary and subsequent cases (for example, those infected by the secondary cases are tertiary cases and so on) can be difficult. Also, the possibility of infection from an outsider must be ignored. Despite these problems, the parameters p and β are