To obtain estimates of R a requires consideration of the length of stay distribution. To simplify matters we ignore any potential additional length of ICU stay caused by infection, but account for the facts that the longer a susceptible patient stays the greater the risk of acquiring MRSA, and the longer an MRSA-positive patient stays the greater the expected number of secondary transmission events they will cause. In simple models it is often assumed that there is constant hazard of hospital discharge and the length of stay distribution is exponential. In such cases the risk of a patient acquiring MRSA is unrelated to the subsequent length of stay and R a is trivially calculated as the product of mean length of stay, the mean number of exposed patients on the ward, and the daily probability of transmission from a single source to a single exposed patient. In practice, the hazard of ICU discharge is likely to be dependent on the day of stay, and typically decreases with increasing day of stay. In this case, the patients at greatest risk of acquiring MRSA (i.e. those who have stayed longest on the ward) will also have longer expected future stays and will therefore tend to cause more secondary infections. To account for this we partition patients into groups defined by the number of ICU days a randomly-selected patient on the ward would stay after becoming MRSA positive (assuming no additional stay due to MRSA). To do this we use the empirical length of stay distribution and calculate the probability, p i , that a randomly selected patient on the ICU is a member of group i. This is given by p i~P ? k~1 l kzi{1 = P ? k~1 kl k , where l k is the probability that a newly admitted patient stays for k days. Assuming an average of n exposed patients per day on the ward, and that each patient has a daily probability, q, of acquiring MRSA from a single MRSA positive patient on the ward, an MRSA patient in group j will, on average, transmit MRSA to k ij~pi |q|j|n patients in group i (ignoring saturation effects, which will be negligible for sufficiently small q). These k ij values are the elements of the next generation matrix. The dominant eigenvalue of this matrix gives the reproduction number, R a [20] .