Using the EM algorithm to estimate the disease parameters for smallpox in 17th century London

In predicting the spread of a disease such as smallpox, knowledge of R
₀
, the transmission parameter in a population of susceptibles is important. Previous studies have estimated R
₀
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