Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination: time series analysis

Abstract

SUMMARYThis paper uses the techniques of time series analysis (autocorrelation and spectral analysis) to examine oscillatory secular trends in the incidence of infectious diseases and the impact of mass vaccination programmes on these well-documented phenomena. We focus on three common childhood diseases: pertussis and mumps (using published disease-incidence data for England and Wales) and measles (using data from England and Wales, Scotland, North America and France). Our analysis indicates highly statistically significant seasonal and longer-term cycles in disease incidence in the prevaccination era. In general, the longer-term fluctuations (a 2-year period for measles, 3-year periods for pertussis and mumps) account for most of the cyclical variability in these data, particularly in the highly regular measles series for England and Wales. After vaccination, the periods of the longer-term oscillations tend to increase, an observation which corroborates theoretical predictions. Mass immunization against measles (which reduces epidemic fluctuations) magnifies the relative importance of the seasonal cycles. By contrast, we show that high levels of vaccination against whooping cough in England and Wales appear to have suppressed the annual cycle.

The epidemiology of varicella–zoster virus infections: a mathematical model

“…This seasonal pattern of incidence frequently induces longer-term regular oscillations in disease incidence [59], although it is well documented that such behaviour is not apparent in the observed incidence of varicella [6,7]. This lack of long-term periodicity may be a result of the complexities in varicella transmission mentioned here.…”

Rubella epidemiology in South East England

“…As such it provides no information on short term longitudinal changes such as those induced by seasonality in virus transmission. Seasonal changes in the incidence of childhood viral and bacterial infections may arise as a direct consequence of the influence of climatic factors on virus transmission or, more significantly, as a consequence of changes in human behaviour related to season (Anderson, Grenfell & May, 1984;Schenzle, 1984;Fine & Clarkson, 1982;Yorke & London, 1973). It is possible that the latter factor, particularly with respect to school children, alters the pattern of infection within and between age classes.…”

“…They are as follows: (i) the infection is assumed to be endemic and at some quasiequilibrium state within the population (this state may be oscillatory in nature); (ii) the infection is assumed to induce lifelong immunity to reinfection and not to increase the mortality of infected individuals; (iii) it is assumed that horizontal changes in the proportion seropositive mirror longitudinal changes for specific cohorts of individuals. Assumptions (i), (ii) and (iii) broadly hold for developed countries provided the inter-epidemic period of the oscillations in disease incidence (4-5 years for rubella, see Anderson & May, 1983a;Anderson, Grenfell & May, 1984) is short in relation to the age span over which serum samples are collected (0-75 + years in this study). The mean age, A, at which susceptibles acquire infection can be estimated directly from eqns.…”

“…Time series analyses (auto-correlation and spectral analysis) were employed to examine the data for regular oscillatory fluctuations in seropositivity and mean antibody concentrations within the male segment of the sample population (for a discussion of the statistical techniques, see Anderson, Grenfell & May, 1984). No significant correlations were found.…”

“…Recent studies of the transmission dynamics of rubella virus have highlighted the importance of quantitative information concerning age-specific rates of infection to any detailed assessment of the impact of mass immunization on the incidences of rubella and congenital rubella syndrome (CRS) (Anderson & May, 1982a, 1983a, 1985 Schenzle, 1984; Anderson, Grenfell & May, 1984;Anderson & Grenfell, 1986;Grenfell & Anderson, 1985). Advances in the development of a mathematical framework to aid in the design of immunization programmes have, to some extent, outstripped the acquisition of the relevant epidemiological data needed to compare prediction with observation.…”