Abstract
The evolution of smallpox epidemics in London, 1647-1893, was studied by time series analysis of deaths from the disease in the Bills of Mortality. The interepidemic interval ( T) evolved progressively from 4 years to 2 years at 1800. The dynamics of epidemics during 1647-1800 are explicable in terms of the transmission of viral diseases which shows that (i) Tis determined by the product of population size ( N) and susceptibility (β), (ii) Tdetermines the mean age of catching the disease, (iii) the system will settle at its steady-state, endemic level unless the epidemics are driven. It is suggested that (i) the progressive change in Twas initially caused by a rise in Nand later by an increased β related to malnutrition and (ii) the epidemics were driven by an oscillation in δβ associated with seasonal dry conditions. the effects of variolation and vaccination became apparent after 1800: the endemic level fell progressively, the epidemics were reduced in amplitude and they were not driven. The dynamics of the disease can now be described by an SEIR model: severe outbreaks of smallpox are followed by decaying epidemics. Endemic smallpox mortality also interacts with the dynamics of the population so that a long wavelength oscillation (associated with recovery after the plague) and a 5/6 year (associated with immigration) oscillation are generated.
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