ABSTRACT
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 H1N1 (1918-19), Asian influenza H2N2 (1957-58) and Hong Kong influenza H3N2 (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.
Subject(s)
Disease Outbreaks , Influenza, Human/epidemiology , Morbidity/trends , Sentinel Surveillance , Cohort Studies , Female , Hong Kong/epidemiology , Humans , Iceland/epidemiology , Influenza A Virus, H1N1 Subtype , Influenza A Virus, H2N2 Subtype , Influenza A Virus, H3N2 Subtype , Influenza, Human/diagnosis , Male , Models, Theoretical , Predictive Value of Tests , Prevalence , Sensitivity and Specificity , Spain/epidemiology , Survival Analysis , United Kingdom/epidemiologyABSTRACT
While there is a large literature on the form of epidemic waves in the time domain, models of their structure and shape in the spatial domain remain poorly developed. This paper concentrates on the changing spatial distribution of an epidemic wave over time and presents a simple method for identifying the leading and trailing edges of the spatial advance and retreat of such waves. Analysis of edge characteristics is used to (a) disaggregate waves into 'swash' and 'backwash' stages, (b) measure the phase transitions of areas from susceptible, S, through infective, I, to recovered, R, status (S --> I --> R) as dimensionless integrals and (c) estimate a spatial version of the basic reproduction number, R(0). The methods used are illustrated by application to measles waves in Iceland over a 60-year period from 1915 to 1974. Extensions of the methods for use with more complex waves are possible through modifying the threshold values used to define the start and end points of an event.
ABSTRACT
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.
