In predicting the spread of a disease such as smallpox, knowledge of R0, the transmission
parameter in a population of susceptibles is important. Previous studies have estimated
R0 from outbreaks of the disease, but these estimates are prone to uncertainties due
to the small population sizes and the short data runs. This study uses data from smallpox
deaths in London over the period 1708 to 1748. Although smallpox was endemic in the
population at this time, by using the EM algorithm to estimate the parameters of an
age-structured nonlinear model of the disease dynamics, an estimate of R o is obtained.
The algorithm exploits the structure of the model in which the parameter vector is
affine, once estimates of the states have been obtained from an extended Kalman smoother.
The model also reveals the importance of temperature and rainfall on the transmissibility
of the disease.