Estimating the transmission rate for a highly infectious disease

It is pointed out that estimates of disease transmission parameters based on the final size of an epidemic are unsatisfactory when all susceptibles are infected and that this is an event with a substantial probability for communities of practical interest. We propose a method for estimating the transmission rate for such highly infectious diseases under the assumptions that the removal process of the disease is fully observed and that the mean duration of the infectious period is known. The method uses smoothed differentiation of the removal process. A simulation study shows that the method performs satisfactorily.