where year tZ1 corresponds to 1954. The binomial distribution B(N, p) can be accurately approximated by a Poisson distribution with parameter Np for the range of values of N and p of interest. We considered fitting a distribution for values of p; however, provided individual p-values are low there is minimal improvement in model fit. Thus, for a set of model parameters, the likelihood of observing data, XZ{x i }, the number of viruses discovered for years 1 to k, is given by