An hypothesis for the periodicity of smallpox epidemics as revealed by time series analysis.
Parish registers have been studied by time series analysis to detect smallpox epidemics in England during 1600-1800. Confirmatory evidence was provided by the seasonality of child mortality. A 5-year cycle in smallpox epidemics was detected in medium-sized, rural towns. Consideration of the mathematics of the dynamics of viral diseases suggests that the true interepidemic period where smallpox is endemic should be 2-3 years and it is concluded that, in the towns studied, the disease was not endemic but that the oscillations were established by 5-year cycles of periods of famine associated with high wheat prices. The cross-correlation function between the two cycles shows zero lag and the input-output function shows significant coherence. Another epidemic follows only when a sufficient density of susceptibles has been established by births, so that the cycles become phase-locked. It is predicted that smallpox (i) was endemic in London and other large cities, with 2-3 year epidemics, (ii) was epidemic with a 5-year oscillation in rural towns, (iii) did not reach epidemic proportions in scattered communities.
Duncan
S R
SR
Department of Electrical Engineering and Electronics, UMIST, Manchester, U.K.
Scott
S
S
Duncan
C J
CJ
D001723:Birth Rate; D002648:Child; D004196:Disease Outbreaks; D004739:England; D006801:Humans; D007223:Infant; D007226:Infant Mortality; D008954:Models, Biological; D015233:Models, Statistical; D010507:Periodicity; D012042:Registries; D012621:Seasons; D012899:Smallpox / Q000453:epidemiology*; D013217:Starvation