Let p kl represent the conditional probability that patient k acquired MRSA from patient l given that patient k acquired MRSA from one of the other P w N w {1 MRSA positive patients. We calculate the elements p kl of the P w M w | P w N w matrix P kl as follows. Define u ijt to be the probability that a susceptible patient on ward i at time t escapes cross-infection from one of the P w C wjt MRSA type j positive patients in the ICUs on that day. Therefore u ijt~Pw 1{s (1{ fwg (i)) q ijt À Á Cwjt where fwg (i) is an indicator function that equals one when w~i and zero otherwise. Now consider a single patient k on ward i who is free of MRSA on admission and whose first and last days on the ward are t k f and t k l . The probability that this patient is free of MRSA type j at the end of day s (sƒt k l ) is where the h wijt terms represent the hazards of transmission of MRSA type j from patients in ward w at time t to a patient in ward i and lijs is an indicator function that takes the value 1 if patient l is present on ward i and MRSA type j positive on day s and 0 otherwise. These hazards can be expressed in terms of the probabilities q ijt as h wijt~{ C wjt ln(1{q ijt s (1{ fwg (i))), which is approximated by C wjt q ijt s (1{ fwg (i)) when q ijt is small, as will usually be the case. The conditional probabilities, p kl , which represent the probability that patient k was infected by patient l given that patient k was infected by one other patient, are then given by the following expression, which is approximately independent of q ijt when q ijt is small: