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Background Historical data are necessary to establish long-term trends in disease incidence but pose analytical problems since their accuracy and reliability may be poorly specified. Methods A robust measure of the spatial velocity, R 0A , of epidemic waves from space-time series is proposed using binary data. The method was applied to the historical records of influenza morbidity for the island of Iceland over a 61-year period of influenza seasons from 1915-16 to 1975-76. Results The onset of influenza waves tended to speed up over the period studied and the three pandemic waves associated with viral shifts in influenza A [Spanish influenza H 1 N 1 (1918-19), Asian influenza H 2 N 2 (1957-58) and Hong Kong influenza H 3 N 2 (1968-69)] spread more rapidly around the island and struck earlier in the influenza season than did inter-pandemic waves, even when the latter were equally intensive as measured by total number of cases and case incidence. Discussion The potential for using R 0A in a real-time context is explored using French influenza data. Conclusions The new measure of wave velocity appears to be applicable to those historical time series where breakdown into regional or local areas is available. The study is being extended to (i) other countries where similar influenza time series are available and (ii) to other diseases within Iceland.

The collapse of geographical space over the last 200 years has had profound effects on the circulation of human populations and on the transfer of infectious diseases. Three examples are used to illustrate the process: (a) the impact of the switch from sail to steamships in importing measles into Fiji over a 40-year period; (b) changes in measles epidemic behaviour in Iceland over a 150-year period; and (c) changes in the spread of cholera within the United States over a 35-year period. In each case, the link between time, travel and disease has been an intimate one.

This article examines temporal and spatial patterns in the relationship between provisional and amended reports for Hepatitis A and Hepatitis B received from each state by the Centers for Disease Control and Prevention through the U.S. National Notifiable Diseases Surveillance System from 1980 to 1992. It demonstrates that, as the 1980s unfolded, the preliminary disease reports became less representative markers of final disease counts. Practitioners at the state and community levels need to be aware of the temporal and spatial instabilities in such provisional data if they are used to provide early warning of contemporary health aberrations.

This paper illustrates the use of multidimensional scaling methods (MDS) to examine space-time patterns in epidemic data. The paper begins by outlining the principles of MDS. The model is then formally specified and illustrated by application to two data sets. The first is partly a tutorial example. It uses monthly reported measles morbidity data for the 31-year period from January 1960 to December 1990, collected for the 50 states of the USA, plus New York City and the District of Columbia. These data are used to explore the various ways in which MDS may be used to identify changing spatial patterns in geographically-coded data. In addition to their tutorial use, the data are also employed to search for any substantive changes in the geographical structure of measles epidemics in the USA that may have followed the introduction of mass vaccination in 1965. New England appears to have developed an epidemic profile distinct from the rest of the USA, and there is tentative evidence of an urban-rural split in epidemic characteristics. The second data set takes annual reported measles mortality data for New Zealand and the states of Australia from 1860 to 1949. MDS is used to show how the spatial relationships among these geographical units have changed over time in response to changes in the sizes of local susceptible populations.

This paper reviews the application of statistical models to outbreaks of two common respiratory viral diseases, measles and influenza. For each disease, we look first at its epidemiological characteristics and assess the extent to which these either aid or hinder modelling. We then turn to the models that have been developed to simulate geographical spread. For measles, a distinction is drawn between process-based and time series models; for influenza, it is the scale of the communities (from small groups to global populations) which primarily determines modelling style. Applications are provided from work by the authors, largely using Icelandic data. Finally we consider the forecasting potential of the models described.

The incidence of disease across geographic space often produces distinctive regional patterns. In this paper, a modeling approach to the identification of the factors that shape the patterns is presented, and a procedure for fitting the model to observed data is given. The methodology is illustrated by an application to the geographic structure of measles epidemics among 22 states of the northeastern United States, New York City, and Washington, D.C., from 1962 to 1988. The patterns identified are interpreted in terms of the spatial behavior of measles epidemics in the region, and the implications of the methodology for surveillance and control are considered.

Background This paper outlines the ways in which a little- used archive of early public health records may throw light on longer-term trends in international epidemic behaviour and serve as a major source of epidemiological information for historians of urbanization and public health. The Weekly Abstract of Sanitary Reports was the official disease surveil- lance report of the US Public Health Service and its predecessors, and began to publish urban mortality statistics on a regular basis in 1888. Here, the authors describe the first 25 years of continuous reporting (1888-1912), when the Reports contained not only disease data for US cities, but also records sent back by US consuls based in some 250 cities in many parts of the world. Methods The content of the weekly editions of the Reports was systematically sampled and analysed using graphical techniques and the simple statistical method of running means. Results Relatively complete weekly series of mortality from all causes, and six infectious diseases (diphtheria, enteric or typhoid fever, measles, scarlet fever, tuberculosis and whooping cough) were identified for a total of 100 cities world-wide. Conclusion Reporting coverage for these cities is sufficiently complete that multivariate analysis should be possible to obtain a comparative picture of mortality for many parts of the world. Despite limitations of the data, sources of the type described in this paper form an important comparative database for studying international patterns of mortality.

Geographical coherence may be defined as the degree to which the behaviour of a time series in one geographical area corresponds with the time series behaviour in another. This paper illustrates the concept using the epidemiological time series of reported monthly measles morbidity for the states of the United States for the 27 years from January 1962 to December 1988. Over this period, as measles morbidity has declined in response to vaccination campaigns, and as the seasonal peaking of the disease in late spring has become less pronounced, the geographical coherence has altered at the national, divisional, regional and state levels. There was a steady decline in coherence from 1962 to 1980. In 1981, a dramatic reduction occurred, but there has been some recovery since. The implications for spatial forecasting models of these reducing levels of coherence are discussed.

Two approaches to the measurement of epidemic velocity are presented. The first uses the moments of the frequency distribution of reported cases of a disease against time. The second is based upon an analysis of the growth parameter of a logistic model. The methods are illustrated by applications to some hypothetical and actual epidemic waves.

SUMMARYThe changing seasonal patterns of reported measles cases in Iceland during this century are analysed. These changes are related to increased population mobility following the development of external and internal transport links, particularly since 1945. The forging of such links has resulted in a shift in the seasonal distribution of cases from one peculiar to the local social and economic conditions in Iceland to one broadly similar to that in other countries of northern temperate latitudes.

Trend-surface analysis (TSA), a form of polynomial regression used in geology, ecology and geography, was applied to analysis of the spread of an epidemic of variola minor in a small Brazilian city. Cubic surfaces gave a generalized map of the space-time distribution of the epidemic, allowing those parts of the city to be identified where variola minor was spreading rapidly or slowly. The epidemic spread relatively quickly over the core area of the city, especially to the peripherally located household dwellings in a northeast to south-west direction. The dwellings of adults and pre-school children introducing the disease into their households broadly followed the overall pattern. School child introductory cases from a southern-located school yielded a saddle-shaped contour pattern, centered about the school; but this pattern was not repeated for the school serving the northern half of the city, which showed a ridge-shaped pattern dipping toward the west. Cubic surfaces for the influence of certain household and individual characteristics were investigated, but showed only week trends. The nearest match to the bowl-shaped overall pattern of introductory dates was provided by the vaccination level of the households. From this application, it appears that TSA permits the identification of regional trends in an objective manner and gives a quantitative measure of the importance of these regional trends in terms of the overall variation in the spatial pattern.