Patterns of smallpox mortality in London, England, over three centuries

Abstract

Smallpox is unique among infectious diseases in the degree to which it devasted human populations, its long history of control interventions, and the fact that it has been successfully eradicated. Mortality from smallpox in London, England, was carefully documented, weekly, for nearly 300 years, providing a rare and valuable source for the study of ecology and evolution of infectious disease. We describe and analyze smallpox mortality in London from 1664 to 1930. We digitized the weekly records published in the London Bills of Mortality and the Registrar General's Weekly Returns. We annotated the resulting time series with a sequence of historical events that appear to have influenced smallpox dynamics in London. We present a spectral analysis that reveals how periodicities in smallpox dynamics changed over decades and centuries, and how these changes were related to control interventions and public health policy changes. We also examine how the seasonality of smallpox epidemics changed from the 17th to 20th centuries in London.

Fast estimation of time-varying infectious disease transmission rates

“…Thus, the S method is defined by Eq (13), coupled with Eqs (8) and (15) for the reconstruction of S and I. The S method requires users to specify (i) input parameters S 0 = S(t 0 ) and t gen = γ −1 , and (ii) values of Z(t k ), B(t k ), and μ(t k ) from incidence, birth, and natural mortality data, respectively.…”

“…Eq (21) has the limitation that multiplying by p À 1 rep does not correct for under-reporting if, by chance, C(t + [t rep ] Δt ) = 0. In this situation, not only is the result Z(t) � 0 incorrect, but we divide by zero in the FC and S methods when we substitute Eqs (5) and (15) in Eqs 7and (13), respectively. If C(t + [t rep ] Δt ) = C(t + [t rep ] Δt + Δt) = 0, then the SI method also suffers: Eq (20) gives β(t) � 0.…”

“…While some existing infectious disease time series span several centuries [15], in practice, averaging as in Fig 3B and 3C is sensible only over time intervals during which the underlying seasonal pattern in transmission is roughly stationary. [Details] A reported incidence time series with 1000 years of weekly observations (Δt = 1 week, n = 52153) was simulated with environmental noise in transmission (� = 0.5), demographic stochasticity, and random under-reporting of cases (p rep = 0.25), using reference values (Table 1) for the remaining parameters.…”

“…Utilizing historical mortality records, it is possible to identify patterns in transmission dating far back in time. Most notably, the London Bills of Mortality and the Registrar General's Weekly Returns enable investigation of transmission patterns continuously from the mid-17th century to the present, for a number of infectious diseases including cholera [14] and smallpox [15].…”

“…A mechanistic understanding of long infectious disease time series-three centuries of weekly data in the case of smallpox [15]-requires methods of transmission rate estimation that are both accurate and fast, and therefore tractable for long time scales. Simulation-based methods of transmission rate estimation from reported incidence or mortality have been developed using the susceptible-infected-removed (SIR) model for infectious disease dynamics [16].…”