Modelling the dynamics of smallpox outbreaks in london, 1647-1893

摘要

The evolution of smallpox outbreaks in London, 1647-1893, was studied using data from the Bills of Mortality. Strong coherence was observed between the epidemics of smallpox and seasonal effects such as rainfall and winter temperatures. An SIR model is used to suggest an explanation for these observations in terms of periodic variations in the force of the infection. It is suggested that the progressive change in the interepidemic period is due to the growing population and to an increase in the force of the infection. After 1800, the effects of vaccination and variolation cause the endemic level of the disease to fall and the interepidemic period to increase and the dynamics of the disease are described by an unforced SIR model exhibiting severe outbreaks of smallpox followed by decaying oscillations.