The Critical Community Size for Measles in the United States

Bartlett, Marilyn S.

doi:10.2307/2343186

Cited by 304 publications

(248 citation statements)

References 4 publications

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“…In large cities, or densely populated areas (or countries), the magnitude of the longer-term oscillations tends to be more exaggerated than is the case in less densely populated areas. Indeed, in the latter case, stochastic factors may result in disease fade out during the troughs in the epidemic cycle (Bartlett, 1960). This factor, combined with the deterministic notion of a critical density of susceptibles necessary to support an epidemic (Kermack & McKendrick, 1927;, leads to the observation that the long-term endemic maintenance of measles is critically dependent on community size and the net birth rate (Bartlett, 1960;Black, 1966).…”

Section: Discussionmentioning

confidence: 99%

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

Anderson

Grenfell

May

1984

J. Hyg.

154

133

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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.

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Section: Discussionmentioning

confidence: 99%

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

Anderson

Grenfell

May

1984

J. Hyg.

154

133

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“…It is assumed that infectives who survived an attack of scarlet fever did not suffer again because of antitoxic and antibacterial immunity [19]. (1) and (2) can be approximated by a linearized model, by defining X = X0+X1 (5) y = Yo+Y1, (6) where xi and y1 represent the variations in x and y from their steady state values. Substituting equations (5) and (6) into equations (1) and (2) and ignoring higher order terms gives dx1 dtXI -(N3yo +,) x1-(It + )y1-(I + v)y yo6fl sin wt, (7) dytl ; Nflyo xl + (It + P) yo 0l sinwt.…”

Section: Appendix Theory Of the Dynamics Of Infectious Diseasesmentioning

confidence: 99%

“…Mathematical modelling suggests that the epidemics would decay unless they were maintained [3] and the study of nonlinear dynamics of measles epidemics has allowed the development of elegant deterministic [4] and stochastic [5,6] models which incorporate spatial dynamics, seasonal forcing and age structure to describe the pattern of these epidemics and it has been suggested that measles dynamics in developed countries may exhibit low dimensional chaos [2,4,[7][8][9]. We have shown, using a nonlinear model, how 2-yearly smallpox epidemics could be maintained by driving the system with an annual cycle of susceptibility [10].…”

Section: Introductionmentioning

confidence: 99%

The dynamics of scarlet fever epidemics in England and Wales in the 19th century

Duncan

Duncan²,

Scott

1996

Epidemiol. Infect.

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SUMMARYThere was a marked rise in scarlet fever mortality in England and Wales in the mid-nineteenth century and spectral analysis of the registration details, 1847-80, shows that the interepidemic interval was 5-6 years, but after 1880 the endemic level fell and the fatal epidemics disappeared. The dynamics of the scarlet fever epidemics can be represented by a linearized mathematical model and because the system is lightly damped, it could be driven by an oscillation in susceptibility. Epidemics were significantly correlated with dry conditions in spring/summer (P < 0-001), suggesting that these produced a low amplitude oscillation in susceptibility which drove the system. Epidemics also correlated (P < 0-001) with an oscillation in wheat prices but at a lag of 3 years, suggesting that malnutrition during pregnancy caused increased susceptibility in the subsequent children which interacted synergistically with seasonal dry conditions. Scarlet fever mortality was sharply reduced after 1880 in parallel with falling wheat prices suggesting that the remarkable period of high scarlet fever mortality (1840-80) was dependent on poor nutritive levels during that time.

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“…We find that reporting probabilities vary greatly between disease, geographical region and metapopulation. This variability directly affects patterns of observed extinctions or 'fade-outs' [2,11,38] and, if not addressed, makes comparisons between diseases and metapopulations difficult.…”

Section: Discussionmentioning

confidence: 99%

“…This measure is appealing owing to its simplicity, but has been criticized as sensitive to disease reporting. To address these concerns, Bartlett [2] employed a three-week period of observed extinction, termed fade-out. Conlan et al [11] propose several alternate measures on mechanistic grounds, including fade-outs post invasion and fade-outs post epidemic.…”

Section: (B) the Obscuring Effects Of Incomplete Observationmentioning

confidence: 99%

Conserved patterns of incomplete reporting in pre-vaccine era childhood diseases

2014

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Incomplete observation is an important yet often neglected feature of observational ecological timeseries. In particular, observational case report timeseries of childhood diseases have played an important role in the formulation of mechanistic dynamical models of populations and metapopulations. Yet to our knowledge, no comprehensive study of childhood disease reporting probabilities (commonly referred to as reporting rates) has been conducted to date. Here, we provide a detailed analysis of measles and whooping cough reporting probabilities in pre-vaccine United States cities and states, as well as measles in cities of England and Wales. Overall, we find the variability between locations and diseases greatly exceeds that between methods or time periods. We demonstrate a strong relationship within location between diseases and within disease between geographical areas. In addition, we find that demographic covariates such as ethnic composition and school attendance explain a non-trivial proportion of reporting probability variation. Overall, our findings show that disease reporting is both variable and nonrandom and that completeness of reporting is influenced by disease identity, geography and socioeconomic factors. We suggest that variations in incomplete observation can be accounted for and that doing so can reveal ecologically important features that are otherwise obscured.

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The Critical Community Size for Measles in the United States

Cited by 304 publications

References 4 publications

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

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

The dynamics of scarlet fever epidemics in England and Wales in the 19th century

Conserved patterns of incomplete reporting in pre-vaccine era childhood diseases

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