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1 Queen’s GIS Lab, Queen’s University, Kingston, Ontario K7L3N6, Canada
2 Rabies Research and Development Unit, Ontario Ministry of Natural Resources, Trent University, Peterborough, Ontario K9J 8N8, Canada
3 Corresponding author (email: tinliner{at}qsilver.queensu.ca)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODS AND MATERIALSRESULTSDISCUSSIONLITERATURE CITED |
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Key words: Arctic fox variant, clustering, metapopulation structure, persistence, rabies, regionalization, spread of rabies, time series analysis.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODS AND MATERIALSRESULTSDISCUSSIONLITERATURE CITED |
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The patterns defined by the initial invasion of Ontario (Figs. 1
and 2) have persisted in those vectors until almost eliminated by oral vaccination, which began in 1989 (MacInnes et al., 2001; Nunan et al., 2002). Understanding the patterns and persistence of enzootic rabies in southern Ontario has been a priority of the Ontario Ministry of Natural Resources (OMNR) starting with Johnston’s work in the late 1960s. Rabies is also a major concern to public health authorities and, like other jurisdictions in the world, analysis was typically linked to political boundaries, which in Ontario were the public health units based on county boundaries. During our initial attempts to understand the patterns of occurrence and develop a forecast system for outbreaks, it became clear that different regions, defined as clusters of counties, were subject to important differences in the length and magnitude of ‘‘cycles’’ (MacInnes et al., 1988). We began to call those clusters ‘‘rabies units.’’ It also became obvious that the large size and variable shape of the county boundaries obscured our efforts to understand how local ecogeography and other physical or human factors influenced the differences in cycle characteristics, and hence our forecasts. Our first step, reported here, was to develop a methodology to redefine those geographic clusters using the smallest reporting unit for which we could assemble data, the township. As well, we report on the characteristics of the resulting rabies units and discuss how the spatial pattern of units had several practical applications in Ontario’s rabies control program. We suggest some possibilities for further understanding the spatial evolution of virus subtypes and the persistence of rabies within a region.
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METHODS AND MATERIALS |
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TOPABSTRACTINTRODUCTIONMETHODS AND MATERIALSRESULTSDISCUSSIONLITERATURE CITED |
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We chose township data for our study because the township was the smallest reported unit for which we could consistently obtain the location of rabies cases from the CFIA records (Fig. 2
). Over the study period many small townships were merged as a result of provincial restructuring initiatives. Almost all of those changes, however, involved mergers using existing boundaries so we were able to agglomerate township data to 1988 boundaries. The resulting 423 townships in this study had a median size of 256 km2 with the 25th and 75th percentiles at 188 km2 and 310 km2, respectively. The frequency distribution of township sizes was right skewed with nine large outliers (>3 standard deviations) at the northern edge of the study area responsible for the skew. With the exception of the latter, adjacent townships in the rest of the study area were approximately the same size. Therefore, in terms of the methodology described below, variations in the size of townships had little impact on our results.
Our method focused on building up units by aggregating adjacent townships on the basis of similar quarterly time series behavior for numbers of rabid foxes. The quarter (3 mo) was the smallest temporal unit we could use without having too many zero observations. Although rabid foxes also occurred in the western portion of Quebec, we did not use that information because there was no municipal unit in Quebec similar in size and compact shape to the township in Ontario. We correlated the time series of a given township with the time series of each of its adjacent townships (adjacency means sharing any common boundary including corners) using Pearson product moment correlation coefficients. Standard practice in time series analysis is to break the series in question into its trend, cycle, and random noise before analysis as the presence of a trend can influence the value of cross-correlations between series (Warner, 1998). For the period 1957–88, we examined the time series for all fox cases in southern Ontario and for the units we subsequently defined. We found a weak (R2=0.107) but significant (
=0.05) upward linear trend in the time series for all fox cases. That trend was produced by similar upward trends in the groupings of townships that we subsequently defined as units 2, 3, 7, and 9. None of the other areas, however, had significant linear trends over time. Further, those weak upward trends were diminished when the time series were re-examined for the time period that we considered rabies was established in an area (i.e., after the first peak of cases [quarters 19–47 depending on the area] to the end of the series [quarter 132]). Given these results and because cycles dominated the time series, we did not remove trend from the time series in our analysis. Our method is based on determining the cyclical influence of one township on its adjacent townships. We also made no attempt to determine the relative magnitude of submission levels between districts. Correlation analysis is not affected by the relative magnitude of the times series being examined provided the difference in magnitude is constant. Since trends were weak or not significant in the data and since we had some evidence that reporting practices were consistent over time, we felt comfortable with our approach. Once the cross-correlations were calculated, we plotted vectors on a map of townships to show the significant (=0.05) cross-correlations between adjacent townships (Fig. 3).
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). Once those cores were defined, our algorithm linked adjacent townships to the core provided those townships had significant correlations with one of more of their neighbors in the core. We continued adding townships to the expanding core until we reached a township that did not have a significant link (=0.05) with a neighbor in the core or had a higher correlation with a township in another core. When the process was finished, some townships had no significant relationship with any neighbor. If such a township was entirely surrounded by townships linked to a core unit, it was assigned to that core unit. If the township was on the periphery of a unit and was also on the periphery of an adjacent unit, we classified it as a ‘‘transition’’ township. This process is our version of ‘‘linkage’’ analysis (McQuitty, 1966) that we modified to include an adjacency constraint. The resulting agglomerations of townships defined 13 rabies units (Fig. 4) and several transition areas (for convenience denoted as unit 14). Note that unit 13 was not defined by the above ‘‘rules.’’ There were too few cases for time series analysis between townships. It was not a transition area since the townships were isolated at the southwestern tip of southern Ontario. We classified it as a unit because of the general absence of rabies over time (the first case was in quarter 62), its isolation, and its short but well-defined epizootic starting in quarter 125. The procedures for determining adjacency, plotting vectors, and linking townships were developed by the authors using spatial analysis query functions in AutoCad Map 2000i (Autodesk, 2000) in combination with the query capabilities of Microsoft Access 2000 (Microsoft, 1999). Correlations were calculated with the cross-correlation function (CCF) in SPSS Version 11.0.1 (SPSS, 2001).
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Once the rabies units were defined, we aggregated the rabies data by unit by species to investigate the characteristics of each unit. We examined species distribution by calculating their relative proportions within each unit. To measure the persistence of rabies within a unit, we calculated the percent of quarters in which rabies data occurred in foxes in each unit and then repeated the calculations using all species. We used the autocorrelation function (ACF) in SPSS version 11.0.1 (SPSS, 2001) to determine the periodicity of fox cases within each unit. Finally, we examined the lead/lag relationships between units using the CCF in SPSS. Warner (1998) provided a useful description of the use of ACF and CCF in determining the periodicity of time series.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODS AND MATERIALSRESULTSDISCUSSIONLITERATURE CITED |
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). Those same units also accounted for 65% of all fox data during the study period. As well as dominating in absolute numbers, those units had the highest density of cases expressed in rabid foxes per 100 km2. The transition areas between units accounted for 12% of total cases and 11% of fox rabies cases. The peripheral units to the north (units 5 and 12) and the peninsular units (units 7 and 13) accounted for only 5.3% of the total cases. Units 5, 12, and 13 also had the lowest density of fox rabies per 100 km2. Unit 1 is relatively small and not well defined, but it is probably part of a larger structure extending into western Quebec, which as previously indicated was not part of our analysis.
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). Units from unit 4 westward had fox/skunk ratios <3. This east to west pattern reversed for livestock. Western Ontario typically had higher proportions of cases in livestock (over 30%) than most areas in eastern and northern Ontario (units 1, 2, 3, 5, and 12; mean of combined units = 22%). There were no distinct patterns for companion animals (cats and dogs) and ‘‘others’’ with the exception of high values for unit 13, which, as noted previously, were anomalous because of very small numbers of cases.
Measures of persistence and periodicity in each unit are shown in Table 2. The five dominant units (units 2, 3, 4, 8, 9) also had high persistence; rabies was present in over 90% of the quarters during the study period whether measured in terms of foxes alone or all species. Persistence was much lower in the peripheral units, especially areas in the north (units 5 and 13) and the peninsular areas (units 1, 7, and 13). Unit 13 had very low persistence, with fox rabies appearing in only 26% of the quarters during the study period.
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. Unit 9, on the other hand, had harmonics at 4, 8, 12, 16, and 24 quarters, indicating a yearly cycle and, as noted previously, high persistence. Unit 9 had no clear core as shown in Figure 4. Together, these results suggest that unit 9 is internally complex and may not be a single unit. Results of the cross-correlation analyses between adjacent units to lead or lag of occurrence between units are shown in Figure 6. Time series within the units in southeastern Ontario are clearly separated in time from adjacent units in the order 12–16 quarters (3–4 yr). The situation is not as clear in the western portion of the study area where the lead/lag relationship between adjacent units is in the order of 1 yr. Only unit 9 had a strong (3-yr lead) relationship with adjoining unit 7 (the Niagara Peninsula).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODS AND MATERIALSRESULTSDISCUSSIONLITERATURE CITED |
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). We hypothesize that the lead/lag differences also demonstrate that, in the absence of strong physiographic barriers, the relative location of unit boundaries will vary over time and may also reflect the changing distribution of species, and possibly the virus. Unit 9 is a case in point. Although it dominated other units in terms of cases it had no clear cycle, it had ambiguous lead/lag relationships with its neighbors and no clear core area. We suspect that unit 9 is an area with two or more quasi-independent rabies outbreaks that moved around in such a way that the same townships were affected at different times. Thus, a potential extension of our analysis will be to break our time series into shorter series and examine the stability of units over time. Where there are strong physiographic barriers, we expect that the units will be stable. The remarkable feature of the initial invasion from 1957 to 1966 is that the initial paths of spread (Fig. 1) and the resulting foci of infection (Fig. 2) appear to define the spatial pattern of occurrence until 1989, and this is strongly reflected in the pattern of units we have delineated. We found only weak upward linear trends in the time series data and only in some areas despite the doubling of the population of Ontario during the study period. Past studies have demonstrated that human population density can influence the number of animals submitted for testing (Wilson et al., 1997) and the magnitude of epizootics as measured by counts of rabid animals (Childs et al., 2001). We were encouraged by the lack of corresponding increase in the number of rabid foxes over time because it supported our working assumption that the reporting of rabies cases was not unduly influenced by human population density.
Our methodology worked because our time series were long (132 observations) and data were available in reasonably small and uniform units (townships) and were collected by one agency (CFIA) in a relatively uniform manner throughout the study period. These advantages also highlight the potential weaknesses in our methodology if those conditions cannot be met. For example, our methodology did not work in the area we subsequently called unit 13 because sparse data meant that reliable correlations between townships could not be calculated. Our methodology would also be problematic if we could not assign that data collection procedures had been consistent over the study period.
The major use of rabies units to date has been to help the Ontario Ministry of Natural Resources plan the fox rabies control program and to make annual rabies forecasts published in the ministry’s Rabies Reporter. Based on an earlier analysis of units at the county level, the control program began in 1989 and focused on what we now define as unit 2 in eastern Ontario (MacInnes et al., 1988). That unit was a practical starting location for several reasons. First, the red fox was clearly the principal vector within the unit and the vaccine bait was effective in foxes but not in skunks. Second, the unit was well defined, with the Ottawa River to the northeast, the St. Lawrence River to the south, and the Canadian Shield to the west. Third, in 1989 there were not enough baits available to cover the unit completely so that the oral vaccine baits were dropped on its eastern and western borders to ‘‘wall it in’’ for subsequent control efforts. Since unit 1 was the eastern border of unit 2 and the ‘‘doorway’’ to Quebec, it was baited completely in 1989. Fourth, unit 2 had a well-defined cycle in its time series, and we had predicted that occurrence in the core area would bottom out in 1990. Finally, previous rabies simulation modeling efforts (Voigt et al., 1985) had demonstrated that, given a strong cycle, oral vaccination efforts were more likely to be successful when the susceptible population was low (i.e., when the epizootic was waning). Thus we had a coincidence of logistics and theory. With our limited resources we could start baiting on the periphery of unit 2 in 1989 and then bait the core area in accordance with our theory the following year. From 1990 to 1994 the entire area of units 1 and 2 were baited. By 1995, fox rabies had disappeared from those units (MacInnes et al., 2001).
In 1993, our wall strategy was extended to the western edges of units 4 and 6 (a line from Georgian Bay across Lake Simcoe and south to Lake Ontario) to isolate unit 3 for baiting in 1994, a period of waning cases. After baiting, there were no fox rabies cases by the third quarter of 1995. By 1996 occurrence was low throughout southwestern Ontario so that the baiting area was extended to cover all the units in southwestern Ontario except unit 13, which, we believed, could not sustain rabies. The northern units (units 5 and 12) were never baited, since our analysis indicated that rabies never originated in those units. Our thinking was that controlling rabies in adjacent units would prevent rabies from entering units 5 and 12, and that if it did, it would soon die out.
The delineation of rabies units has suggested two areas for future research. There appears to be a broad relationship between spatial distribution of rabies units and the four major subtype variations in fox rabies virus identified in southern Ontario (Nadin-Davis et al., 1999). The subtypes mirrored the initial invasion routes into southern Ontario, reflected the difference between the fox/skunk ratios in the eastern and western portions of southern Ontario, and appeared to be bounded by the same broad physiographic features that defined the boundaries of the rabies units. We suggested that, in units such as unit 9 with no clear physiographic barriers, the distribution of virus subtypes might follow the advance and retreat of rabies across the unit. These results suggest that our rabies units may either be the result of, or part of the explanation for, the subtype variations in the fox rabies virus. Presumably that indicates that there have been local adaptations by the arctic fox rabies variant. Those can be identified by their unique cyclic behaviors, as indicated by this analysis. Hopefully, more genetic data will be collected to further explore those relationships.
The second area of research concerns the spread of rabies within and between units and the comparative analysis of species distribution between units. We suspect that detailed tracking of spread will shed more light on the influence of physiography on spread and may help understand the local variations in subtype noted in the research of Nadin-Davis et al. (1999). Furthermore, Tinline (1988) hypothesized that the ability of rabies to persist in southern Ontario was related to movement between units. The enzootic may persist because an outbreak in one unit spreads to adjacent units that had a peak some time ago, so that the pool of susceptible animals has been rebuilt and is large enough to sustain another epizootic. If there were not separate units, the probability of extinction of rabies virus after a sharp peak in a single area would be high since the rabies virus violates two of the more important rules for successful pathogens: it kills most infected hosts, and it has no known resting stage outside the living host. Based on our observation that different subvariants of the virus coincided with groupings of two or more units, it may well be that the persistence of rabies depends primarily on linkages between those smaller groupings rather than linkages across the whole of southern Ontario as Tinline (1988) suggested previously. Unfortunately we do not have tissue samples from earlier decades to assess possible changes in the subvariants of the virus over the entire study period.
We believe that our set of units and the linkages between them constitutes a meta-population structure, as described by Harrison (1994), which within the limits set by May (1994) is key to understanding persistence of rabies in wild systems. The thorough review by Hassel (2000) covers insects and parasitoids, but his overall description of a metapopulation structure consisting of partially autonomous local population ‘‘patches’’ loosely connected to other such patches so that population dynamics of the local patches are asynchronous makes an excellent mental model to extend our study of the behavior of rabies.
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ACKNOWLEDGMENTS |
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LITERATURE CITED |
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TOPABSTRACTINTRODUCTIONMETHODS AND MATERIALSRESULTSDISCUSSIONLITERATURE CITED |
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CHARLTON, K. M., W. A. WEBSTER, AND G. A. CASEY. 1991. Skunk rabies. In The natural history of rabies, 2nd Edition, G. M. Baer (ed.). CRC Press, Boca Raton, Florida, pp. 307–324.
CHILDS, J. E., A. T. CURNS, M. E. DEY, L. A. REAL, C. E. RUPPRECHT, AND J. W. KREBS. 2001. Rabies epizootics vary along a north-south gradient in the eastern United States. Vector Borne and Zoonotic Diseases 1: 253–257.
HARRISON, S. 1994. Metapopulations and conservation. British Ecological Society Symposium 35: 111–128.
HASSEL, M. P. 2000. Host-parasitoid population dynamics. Journal of Animal Ecology 69: 543–566.
JOHNSTON, D. H., AND M. BEAUREGARD. 1969. Rabies epidemiology in Ontario. Bulletin of the Wildlife Disease Association 5: 357–370.
LAGACE, F. 1998. Historique de la rage au Quebec de 1958 à 1997. [History of rabies in Quebec from 1958 to 1997]. Le Médecin Vétérinaire du Quebec 28: 106–110.
MACINNES, C. D. 1987. Rabies. In Wild furbearer management and conservation in North America. M. Novak, J. A. Baker, M. E. Obbard, and B. Malloch (eds.). Ministry of Natural Resources, Toronto, Ontario, Canada, pp. 910–929.
———, 1988. Control of wildlife rabies: The Americas. In Rabies. J. B. Campbell and K. M. Charlton (eds.). Kluwer Academic, Norwell, Massachusetts, pp. 381–405.
———, R. R. TINLINE, D. R. VOIGT, L. H. BROEKHOVEN, AND R. R. ROSATTE. 1988. Planning for rabies control in Ontario. Review of Infectious Diseases 10: S665–S669.
———, S. M. SMITH, R. R. TINLINE, N. R. AYERS, P. BACHMANN, D. G. BALL, L. A. CALDER, S. J. CROSGREY, C. FIELDING, P. HAUSCHILDT, J. M. HONIG, D. H. JOHNSTON, K. F. LAWSON, C. P. NUNAN, M. A. PEDDE, B. POND, R. B. STEWART, AND D. R. VOIGT. 2001. Elimination of rabies from red foxes in eastern Ontario. Journal of Wildlife Diseases 37: 119–132.[Abstract]
MAY, R. M. 1994. The effects of spatial scale on ecological questions and answers. British Ecological Society Symposium 35: 1–18.
MCQUITTY, L. L. 1966. Similarity analysis by reciprocal pairs for discrete and continuous data. Educational and Psychological Measurement 26: 825–831.
MICROSOFT. 1999. Access. Microsoft Corporation, Seattle, Washington.
NADIN, S. A., M. I. SAMPTH, G. A. CASEY, R. R. TINLINE, AND A. I. WANDELER. 1999. Phylogeographic patterns exhibited by Ontario rabies virus variants. Epidemiology and Infection 123: 325–336.[Medline]
NUNAN, C. P., R. R. TINLINE, J. M. HONIG, D. G. BALL, P. HAUSCHILDT, AND C. A. LEBER. 2002. Post-exposure treatment and animal rabies, Ontario 1958–2000. Emerging Infectious Diseases 8: 214–217.[Medline]
SPSS, 2001. SPSS Version 11.0.1. SPSS Inc., Chicago, Illinois.
TABEL, H., A. H. CORNER, W. A. WEBSTER, AND G. A. CASEY. 1974. History and epizootiology of rabies in Canada. Canadian Veterinary Journal 15: 217–281.
TINLINE, R. R. 1988. Persistence of rabies in wildlife. In Rabies, J. B. Campbell and K. M. Charlton (eds.). Kluwer Academic Publishers, Boston, Massachusetts, pp. 301–322.
———, AND D. GREGORY. 1988. The universal transverse mercator code: A location code for disease reporting. Canadian Veterinary Journal 29: 825–829.
VOIGT, D. R., R. R. TINLINE, AND L. H. BROEKHOVEN. 1985. A spatial simulation model for rabies control. In Population dynamics of rabies in wildlife. P. J. Bacon (ed.). Academic Press, London, UK, pp. 311–349.
WARNER, R. M. 1998. Spectral analysis of time series. Guildford Press, New York, New York, pp. 225.
WILSON, M. L., P. M. BRETSKY, G. H. COOPER JR., S. H. EGBERTSON, H. J. VAN KRUININGEN, AND L. CARTTER. 1997. Emergence of raccoon rabies in Connecticut, 1991–1994: Spatial and temporal characteristics of animal infection and human contact. American Journal of Tropical Medicine and Hygiene 57: 457–463.
Received for publication 31 December 2002.
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