OSCILLATORY DYNAMICS OF SMALLPOX AND THE IMPACT OF VACCINATION

The evolution of smallpox epidemics in London, 1647-1893, was studied by time series analysis of deaths from the disease in the Bills of Mor tality. The interepidemic interval (T) evolved progressively from 4 ye ars 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) T is determined by the product of population size (N) and su sceptibility (beta), (ii) T determines the mean age of catching the di sease, (iii) the system will settle at its steady-state, endemic level unless the epidemics are driven. It is suggested that (i) the progres sive change in T was initially caused by a rise in N and later by an i ncreased beta related to malnutrition and (ii) the epidemics were driv en by an oscillation in delta beta associated with seasonal dry condit ions. The effects of variolation and vaccination became apparent after 1800: the endemic level fell progressively, the epidemics were reduce d in amplitude and they were not driven. The dynamics of the disease c an now be described by an SEIR model: severe outbreaks of smallpox are followed by decaying epidemics. Endemic smallpox mortality also inter acts with the dynamics of the population so that a long wavelength osc illation (associated with recovery after the plague) and a 5/6 year (a ssociated with immigration) oscillation are generated. (C) 1996 Academ ic Press Limited