For many diseases an individual once infected is unable to pass on the disease for what is called the latent period. He then passes into the infectious period, which ends when his symptoms appear and he is removed from circulation. Several attempts to model this situation are described, with emphasis on a model in which the latent period and the infectious period are proportional to .chi.2 variates. The likelihood function is derived for data consisting of interremoval times from households of 2. The computational difficulties are discussed and an approximation to the likelihood is suggested. The model is generalized for a variable infection rate and used to analyze 3 sets of measles data.