Am. J. Trop. Med. Hyg., 71(2), 2004, pp. 129–137 Copyright © 2004 by The American Society of Tropical Medicine and Hygiene
DEVELOPMENT OF A PREDICTIVE MODEL FOR ROSS RIVER VIRUS DISEASE IN BRISBANE, AUSTRALIA WENBIAO HU, NEVILLE NICHOLLS, MIKE LINDSAY, PAT DALE, ANTHONY J. McMICHAEL, JOHN S. MACKENZIE, AND SHILU TONG School of Public Health, Queensland University of Technology, Brisbane, Queensland, Australia; Bureau of Meteorology Research Centre, Melbourne, Australia; Department of Health, Perth, Western Australia, Australia; Australian School of Environmental Studies, Griffith University, Brisbane, Queensland, Australia; National Centre for Epidemiology and Population Health, Australian National University, Canberra, Australia; Department of Microbiology and Parasitology, University of Queensland, Brisbane, Queensland, Australia
Abstract. This paper describes the development of an empirical model to forecast epidemics of Ross River virus (RRV) disease using the multivariate seasonal auto-regressive integrated moving average (SARIMA) technique in Brisbane, Australia. We obtained computerized data on notified RRV disease cases, climate, high tide, and population sizes in Brisbane for the period 1985−2001 from the Queensland Department of Health, the Australian Bureau of Meteorology, the Queensland Department of Transport, and Australian Bureau of Statistics, respectively. The SARIMA model was developed and validated by dividing the data file into two data sets: the data between January 1985 and December 2000 were used to construct a model, and those between January and December 2001 to validate it. The SARIMA models show that monthly precipitation ( = 0.004, P ⳱ 0.031) was significantly associated with RRV transmission. However, there was no significant association between other climate variables (e.g., temperature, relative humidity, and high tides) and RRV transmission. The predictive values in the model were generally consistent with actual values (root mean square percentage error ⳱ 0.94%). Therefore, this model may have applications as a decision supportive tool in disease control and risk-management planning programs. A number of studies have examined the relationship between climate variation and RRV disease.17–22 Several models have been developed to predict the likelihood of RRV epidemics using weather and environmental data.23,24 However, some important methodologic issues such as stationarity and auto-correlation of time series data have not been formally addressed in previous research. Time series analyses have been increasingly used in epidemiologic research.25–38 Since the early 1970s, time series methods, in particular seasonal autoregressive integrated moving average (SARIMA) models, which have the ability to cope with stochastic dependence of consecutive data, have become well established in the commercial and industrial fields.28,29 This study examines the potential impact of climate variability on the transmission of RRV disease and explores the possibility of developing an epidemic forecasting system for RRV disease using the multivariate SARIMA technique in Brisbane, Australia.
INTRODUCTION There has been global resurgence of arboviral diseases.1 Ecologic changes and human behavior are important in the spread of these diseases.2 Infection with Ross River virus (RRV) is the most prevalent vector-borne disease in Australia. This virus was isolated from mosquitoes in Australia in 1963,3 from people in 1972,4 and from mosquitoes and people in the Pacific islands in 1979−1980 during epidemics of epidemic polyarthritis.5–8 The virus causes epidemic polyarthritis, with rash and fever in some patients, and joint symptoms in 95% of the cases.9–11 The arthritic symptoms may persist for months and can be severe and debilitating. There is no effective treatment of the disease and, in the absence of a vaccine, prevention remains the sole public health strategy. Over the last 11 years (1992−2002), a total of 48,242 laboratory confirmed cases of RRV disease have been identified in Australia.12 In general terms, RRV activity appears to have increased in Australia in the past decade,13,14 but causes for this increase remain largely unknown.13–15 The ecology of RRV disease is complex, and the mechanism of RRV transmission remains unclear. The virus is maintained in a primary mosquito–mammal cycle involving macropods (kangaroos and wallabies), possibly other marsupials (e.g., possums), flying fox, and native rodents.16 A human– mosquito cycle may occur in explosive outbreaks, but in Australia does not appear to extend over more than three or four cycles (Lindsay M, Mackenzie JS, unpublished data). The incubation period in humans ranges from 5 to 21 days,16 which may explain why the disease is transmitted rapidly once an outbreak occurs. Extreme weather events (e.g., heavy rainfall) often trigger outbreaks of RRV disease at a lag of one to two months.17–19 Such lags may assist disease control managers in effectively planning public health interventions in advance. Nevertheless, a quantitative relationship between climate variability and the RRV transmission remains to be determined.
MATERIALS AND METHODS Study area. Brisbane, the capital of Queensland State, is a subtropical city situated on the east coast of Australia and covers approximately 1,142 km2 (Figure 1). The coastal areas are flat, with extensive mangrove forests, salt marshes, and mudflats. Within the administrative boundaries of Brisbane City Council, which also determines the study area of this investigation, the population was 888,449 on June 30, 2001.39 Brisbane had the highest number of RRV cases notified (4376 cases) in Queensland between 1985 and 2001. The number of cases was highest in 1996 (849 cases), and lowest in 1988 (41 cases). Figure 2 shows that most of the cases occurred from February to May. The average annual incidence was 29.14/ 100,000. Data collection. Since infection with RRV is a notifiable disease, positive test results have, by law, to be reported by laboratories to the Queensland Department of Health, where
129
130
HU AND OTHERS
FIGURE 1. Location of Brisbane, Queensland, Australia (including latitude and longitude of the city).
they are archived by the Communicable Diseases Unit. The requirement for notification of RRV disease is based on a demonstration of IgM antibodies in blood, a four-fold or greater change in serum antibody titers between acute and convalescent phase sera, isolation of RRV, or demonstration of arboviral antigen or genome in blood.40 The reported place of onset for each case was generally regarded to reflect the geographic distribution of RRV infection.41 We obtained the computerized data set on the notified RRV disease cases in Brisbane for the period of 1985 to 2001 from the Queensland Department of Health. Data provided for each notification case included a unique record reference number, disease code, date and place of onset, sex, age, and the confirmation status of the report. Climate and population data were obtained for the period 1985−2001 from the Australian Bureau of Meteorology and the Australian Bureau of Statistics, respectively. There are three main meteorologic stations in Brisbane. The one with the longest history of meteorologic recordings was chosen. The information is reported to the Australian Bureau of Meteorology regularly. Climate data comprised monthly mean maximum and minimum temperature (°C), total precipitation (mm), and mean relative humidity (%). Data on monthly mean high tidal levels (cm) along the coastal regions were supplied by the Queensland Department of Transport. The reason for using monthly parameters was that the incidences of RRV disease were too low if weekly or daily indices were used. Data analysis Univariate/bivariate analyses were conducted for each independent variable. Cross-correlations were used to compute a series of correlations between climate variables and the incidence of RRV disease over a range of time lags (a time lag was defined as the time span between climatic observation and the incidence of RRV disease).42 For adequate modeling, a time series should be stationary with respect to mean and variance. If the mean increases or decreases over time, the series may need to be transformed (e.g., differenced) to make it stationary, before being modeled.37 A simple inspection of the graph of the untransformed series is the most useful approach. Similarly, if the variance (as indicated by the excursions around the mean becoming
smaller or larger over time) increases or decreases, some transformation (logarithm or square root, etc.) should also be applied. A time series with seasonal non-stationary may be transformed to stationary data by taking seasonal differences into account.25,28 Since both RRV incidence and climate variables exhibited strong seasonal variation and fluctuations in their yearly means, we adjusted for seasonality by first seasonally differencing the series (i.e., each observation is replaced by the difference between it and the observation a year before) in the analysis. However, for variables without a clear secular trend, regular differencing (each observation is replaced by the difference between it and the previous observation) was not used. The multivariate SARIMA model with environmental variables was used to estimate the independent contribution of each climate variable and of high tide in this study. Four steps were undertaken in the modeling of the relationship between climate variation and the RRV transmission. First, the monthly incidences of RRV infection were calculated using monthly counts of RRV disease cases as a numerator and population size in the middle of each year as a denominator and, then, both RRV disease incidences and environmental variables were transformed to become stationary input series with respect to yearly periodicity by seasonally differencing, before being modeled. Second, SARIMA models were developed using the monthly incidence of RRV as a response variable and monthly climate variables and high tides as explanatory variables. Six main parameters were selected when fitting the SARIMA model: the order of autoregressive (p) and seasonal autoregressive (P), the order of integration (d) and seasonal integration (D), and the order of moving average (q) and seasonal moving average (Q). The process is called SARIMA (p,d,q) (P,D,Q)s (s is the length of seasonal period). The equation of this model is yt ⳱ ⌰q(B) ⌰Q(Bs)at ⌽P(Bs)/⌽P(Bs)⌽p(B)(1 − B)d(1 − Bs)D + P (precipitation at lag 2 months), where ⌽P(Bs) is seasonal autoregressive operator, ⌽p(B) is autoregressive operator, ⌰q(B) is the operator of moving averages, ⌰Q(Bs) is seasonal operator of moving averages, at is white noise, yt is the dependent variable, and P is explanatory variables’ regressive coefficients). The selection of SARIMA processes was conducted using Akaike’s information criterion (AIC) which measures how well the model fits the series.43 Of all the models tested, an SARIMA (1,0,1) (1,1,1)12 model was found to best fit the data. Meanwhile, we used a stepwise regression method to select the environment variables. Additionally, a comparison of the SARIMA with and without environmental variables was also conducted. Third, the goodness of fit of the models was checked for adequacy, using both time series (autocorrelation functions of residuals) and classic tools (to check the normality of residuals). Finally, the model developed was verified by dividing the data file into two data sets: the data between January 1985 and December 2000 were used to construct a SARIMA model and those between January and December 2001 were then used to validate the model. Such a validation method is widely used in time series analyses.44,45 In addition, the predictive validity of the models was evaluated by using the root mean square (RMS) error and RMS ˆ ˆ 2 1/2; percentage error criterion (RMS error ⳱ [∑N t⳱1(Yt − Yt) /N] ˆ −Y ˆ )/Y ]2}1/2, where RMS percentage error ⳱ {1/N ∑N [(Y t t t t=1 ˆ is the predicted values and Y is the observed values for Y t t
131
PREDICTING OUTBREAKS OF ROSS RIVER VIRUS DISEASE
FIGURE 2. Relationships between monthly incidence of Ross River virus (RRV) disease and climate variables in Brisbane between 1985 and 2001 using seasonally differenced variables.
month t, N is the number of observations).46 The smaller the RMS error, the better the model in terms of the ability of forecast. We used the 12 monthly forecasts and calculated the RMS error of these 12 forecasts, and then compared this with the RMS error if the historical average number of RRV cases each month was used as a forecast. All analyses were performed with SPSS software using the Trends procedure.47
RESULTS Summary statistics for each independent variable are shown in Table 1. The monthly mean maximum and minimum temperatures, precipitation, relative humidity, and high tide were 25.30°C, 15.60°C, 90.76 mm, 65.78%, and 201.01 cm, respectively, between 1985 and 2001 in Brisbane. Bivariate
132
HU AND OTHERS
FIGURE 2. Continued
analyses show that there appeared to be positive relations between climate variability and the transmission of RRV disease (Figure 2). The results of the cross-correlations adjusted for season show that the incidence of RRV disease was significantly associated with maximum temperature at the current month, precipitation at lags of 0−3 months, relative humidity at lags
of 0−3 months, and high tide at a lag of two months (Figure 3). However, there was no significant association between minimum temperature and RRV transmission in any lag. The SARIMA models show that auto-regression ( ⳱ 0.364, P < 0.001), moving average ( ⳱ −0.544, P < 0.001), seasonal auto-regression ( ⳱ −0.354, P < 0.001), seasonal moving average ( ⳱ 0.641, P < 0.001), and monthly total
133
PREDICTING OUTBREAKS OF ROSS RIVER VIRUS DISEASE
FIGURE 2. Continued
precipitation ( ⳱ 0.004, P ⳱ 0.031) were significantly associated with RRV transmission. It suggests that that there may be 50 more cases a year for an increase of 100 mm precipitation on average in Brisbane. However, the maximum and minimum temperatures, relative humidities, and the high tides were not significantly associated with the monthly incidence of RRV disease after adjustment for auto-correlation, seasonality, and other covariates. The model estimated with the climate variables was a better fit than the model without these variables (i.e., the log-likelihood increased, while the values of AIC decreased) (Table 2). Figure 4 shows that there was no significant auto-correlation between residuals at different lags in the SARIMA model. The graphic analysis shows that the residuals in the model appeared to fluctuate randomly around zero with no obvious trend in variation as the predicted incidence values increased. Thus the goodness-of-fit analyses showed that the model fits the data reasonably well. The model constructed with the data between January 1985 and December 2000 was used to predict the transmission of RRV disease in Brisbane between January and December 2001, and was then validated by the actual observations (Figure 5). The validation analyses indicate that the model had reasonable accuracy over the predictive period, even though the predicted spike was slightly ahead of the actual peak. The validity of the model increased with the inclusion of precipitation (RMS error ⳱ 1.96 and RMS error percentage ⳱ 0.94%) compared with the model without this variable (RMS error ⳱ 2.01 and RMS error percentage ⳱ 1.73%). DISCUSSION This is the first attempt to develop an epidemic forecasting model for predicting RRV transmission in a metropolitan
area according to our knowledge. The results of this study suggest that climatic variability, particularly precipitation, may have played a significant role in the transmission of RRV disease in Brisbane, given that other socioecologic conditions have been unlikely to change dramatically on a monthly time scale in this city over the past two decades. The key determinants of the RRV disease transmission included autoregression, moving average, seasonal auto-regression, seasonal moving average, and precipitation at lag two months. These variables may be used to assist in forecasting outbreaks of RRV disease in Brisbane. Changes in climate and the environment may influence the abundance and distribution of vectors and intermediate hosts of RRV disease.48,49 Precipitation is important in the transmission of mosquito-borne diseases including RRV infection. All mosquitoes have aquatic larval and pupal stages and therefore require water for breeding. Quantity, timing, and pattern of precipitation would first affect the breeding of mosquitoes, especially fresh water ones, because sufficient amounts of precipitation will assist in maintaining the breeding habitats further into the summer months. In addition, precipitation can also markedly affect the breeding of salt TABLE 1 Characteristics of explanatory variables Variables
Maximum temperature (°C) Minimum temperature (°C) Precipitation (mm) Relative humidity (%) High tide (cm)
N
Mean
SD
Minimum
Maximum
204
25.30
3.04
18.97
30.73
204 204 204 204
15.60 90.76 65.78 201.01
4.24 89.27 6.69 7.09
7.37 0.00 46.30 177.43
22.72 616.80 81.37 228.82
134
FIGURE 3.
HU AND OTHERS
Cross-correlation function between Ross River virus and climate variables after seasonal differencing. CI ⳱ confidence interval.
marsh mosquitoes, allowing breeding to be prolonged after periods of high tides.50 In this study, monthly total amount of precipitation was positively correlated with the monthly incidence of RRV infection in Brisbane over the study period, with two month lagged effect. Some outbreaks of RRV infection were predominantly precipitation associated.48 Similar findings have been reported for other vector-borne diseases. For example, precipitation along with humidity and temperature were found to be related to epidemics of malaria in Pakistan.51 Nearly 40 species of mosquitoes belonging to six genera have been confirmed as vectors of RRV in Australia.49 Ochlerotatus vigilax and Ochlerotatus camptorhynchus are probably the major vectors in Brisbane region.52 Some freshwater breeding species, such as Culex annulirostris, Coquillettidia linealis, and Ochlerotatus normanensis, are also the vectors of
RRV. These freshwater mosquitoes are closely associated with human habitation.52 How hosts, vectors, and humans interact with socioenvironmental changes remains to be determined. The lagged effect of precipitation, at a lag of two months, on the incidence of RRV infection is very important. Such delays are consistent with the development of mosquitoes, the external period of incubation of RRV within mosquitoes, and the incubation period of the virus in the host. Lags of 1−3 months were considered because of biologic plausibility (i.e., the time period for the development of mosquitoes, the extrinsic incubation period, and the incubation period of the virus within host). Longer lags (e.g., ⱖ 4 months) were found less important in this study. It is crucial to use adequate research methodology in the assessment of possible impacts of environmental variability on disease transmission. Recently, increasing attention has
135
PREDICTING OUTBREAKS OF ROSS RIVER VIRUS DISEASE
TABLE 2 Regression coefficients of the seasonal autoregressive integrated moving average on the monthly incidence of Ross River virus disease in Brisbane, Australia, 1985–2000 Model without climate variables*
Model with climate variables†
Variables

SE
P

SE
P
Autoregression Moving average Seasonal autoregression Seasonal moving average Precipitation at lag 2 month
0.383 −0.510 −0.395 0.607 –
0.090 0.084 0.083 0.081 –
0.000 0.000 0.000 0.000 –
0.364 −0.544 −0.354 0.641 0.004
0.093 0.085 0.088 0.083 0.002
0.000 0.000 0.000 0.000 0.031
* Log likelihood ⳱ −488, Akaike’s information criterion ⳱ 984. † Log likelihood ⳱ −455, Akaike’s information criterion ⳱ 920. Other climate variables (i.e., minimum temperature, maximum temperature, relative humidity, and high tides) were adjusted.
focused on the use of the Box-Jenkins modeling strategy to construct SARIMA models for vector-borne disease.27,45,53 The modeling strategy analyses a long series of values in a stationary mode. However vector-borne disease and climatic variables of interest are not stationary, and analysts have to resort to preliminary transformations, such as time series differencing or variance stabilizing to achieve stationarity. In this study, a multivariable SARIMA model was used to determine the independent effects of climate variables on the transmission of RRV. The steps of model identification, parameter estimation, and diagnostic checking were performed as recommended.27,44
The SARIMA modeling is a useful tool for interpreting and applying surveillance data in disease control and prevention. Once a satisfactory model has been obtained, it can be used to forecast expected numbers of cases for a given number of future time intervals.37 Since the SARIMA model has the capacity to forecast when and where an outbreak is likely to occur, it therefore has great potential to be used as a decisionsupportive tool for planning public health interventions. This study has three strengths. First, a sophisticated timeseries model was used in this attempt to develop an epidemic forecasting system for the control and prevention of RRV disease in metropolitan areas. Second, detailed infor-
FIGURE 4. Auto-correlation, partial auto-correlation of residuals, and scatterplot of residuals at different lags in the seasonal auto-regressive integrated moving average model. CI ⳱ confidence interval.
136
HU AND OTHERS
FIGURE 5. Validated seasonal auto-regressive integrated moving average model of climate variation in Brisbane, Australia (validation period ⳱ 1/2001−12/2001, i.e., to the right of the vertical dotted line). RRV ⳱ Ross River virus.
mation on a range of climate and tidal variables was incorporated in the model. Third, the model developed in this study appeared to have a high degree of accuracy and may have implications in the disease control and risk-management planning. The weaknesses of this study must be acknowledged. First, this is a broad, ecologic assessment of the relationship between climate and tide variability and the transmission of RRV at the city level. More detailed risk assessment at community and individual levels may also be required if a comprehensive and systematic risk assessment is to be made. Inclusion of other information (e.g., virus strain, mosquito population densities and survival, human behaviors, population immunity, housing characteristics, and other mosquitorelevant environmental information) may further improve the model. Second, the model may only be applicable to Brisbane and areas with a similar socioecologic background, since only local data were used in the construction of the model. Third, under the Notifiable Diseases Surveillance System, the place of onset is assumed as the place of acquisition of infection. However, two places may differ for some cases, particularly during holiday periods. If these risk factors could be included in this model, a more effective and accurate model would be expected (e.g., predicted errors would be further improved). The development of epidemic forecasting systems is important in the control and prevention of infectious disease outbreaks in the future. Should an outbreak of RRV disease occur, a large-scale public health intervention is usually required. Early warning based on forecasts from the model can assist in improving vector control and personal protection. Increasing insecticide spraying during high-risk periods and decreasing it during low-risk periods will improve costeffectiveness of operations. Disease control programs, if anticipating an increase in RRV disease, can increase vigilance, e.g., by alerting district health offices, filling vacant positions of health staff, and requesting more frequent reporting to facilitate early identification of problem areas. Additionally, the disease surveillance data can be integrated with social,
biologic, and environmental databases. These data may provide additional input into the development of epidemic forecasting models. These attempts, if successful, may have significant implications in environmental health decision-making and practices, and may help health authorities determine public health priorities more wisely and use resources more effectively and efficiently. Received January 7, 2004. Accepted for publication March 10, 2004. Acknowledgments: We thank the Queensland Department of Health, the Australian Bureau of Meteorology, Queensland transport, and the Australian Bureau of Statistics for providing the data on notified RRV disease cases, climate, sea level, and population growth between 1985 and 2001, respectively. Financial support: This study was partly funded by the National Health and Medical Research Council, the Queensland Department of Health, and the Queensland University of Technology Authors’ addresses: Wenbiao Hu and Shilu Tong, School of Public Health, Queensland University of Technology, Brisbane, Queensland 4059, Australia, Telephone: 61-7-3864-9745, Fax: 61-7-38643369, E-mail:
[email protected]. Neville Nicholls, Bureau of Meteorology Research Centre, Melbourne, Victoria 3001, Australia. Mike Lindsay, Department of Health, Perth, Western Australia 6001, Australia. Pat Dale, Australian School of Environmental Studies, Griffith University, Brisbane, Queensland 4111, Australia. Anthony J. McMichael, National Centre for Epidemiology and Population Health, Australian National University, Canberra 0200, Australia. John S. Mackenzie, Department of Microbiology and Parasitology, University of Queensland, Brisbane, Queensland 4072, Australia.
REFERENCES 1. Reiter P, 2001. Climate change and mosquito-borne disease. Environ Health Perspect 109: 141–161. 2. Ansari M, Shope R, 1994. Epidemiology of arboviral infections. Public Health Rev 22: 1–26. 3. Doherty R, Whitehead R, Gorman B, 1963. The isolation of a third group A arbovirus in Australia, with preliminary observations on its relationship to epidemic polyarhritis. Aust J Sci 26: 183–184. 4. Doherty R, Carley J, Best J, 1972. Isolation of Ross River virus in from man. Med J Aust 1: 1083–1084.
PREDICTING OUTBREAKS OF ROSS RIVER VIRUS DISEASE
5. Aaskov J, Mataika J, Lawrence G, Rabukawaqa V, Tucker M, Miles J, Dalglish D, 1981. An epidemic of Ross River virus infection in Fiji, 1979. Am J Trop Med Hyg 30: 1053–1059. 6. Rosen L, Gubler D, Bennett P, 1981. Epidemic polyarthritis (Ross River) virus infection in the Cook Islands. Am J Trop Med Hyg 30: 1294–1302. 7. Mackenzie J, Brook A, Hall R, Johansen C, Lindsay M, Philips D, Ritchie S, Russell R, Smith D, 1998. Arboviruses in the Australian region, 1990 to 1998. Comm Dis Intell 22: 93–100. 8. Johansen CA, van den Hurk AF, Ritchie SA, Zborowski P, Nisbet DJ, Paru R, Bockarie MJ, Macdonald J, Drew AC, Khromkh TI, Mackenzie JS, 2000. Isolation of Japanese encephalitis virus from mosquitoes (Diptera: Culicidae) collected in the Western Province of Papua New Guinea, 1997−1998. Am J Trop Med Hyg 62: 631–638. 9. Mudge P, Aaskov J, 1983. Epidemic polyarthritis in Australia, 1980-1981. Med J Aust 17: 269–273. 10. Fraser J, 1986. Epidemic polyarthritis and Ross River virus disease. Clin Rheum Dis 12: 369–388. 11. Flexman J, Smith D, Mackenzie J, Fraser J, Bass S, Hueston L, Lindsay M, Cunningham A, 1998. A comparison of the diseases caused by Ross River virus and Barmah Forest virus. Med J Aust 169: 159–163. 12. Australian Department of Health and Aged Care, 2004. National Notifiable Diseases Surveillance System: http://www1.health. gov.au/cda/source/rpt-4.cfm. Accessed March 2, 2004. 13. Russell R, 2002. Ross River virus: ecology and distribution. Annu Rev Entomol 47: 1–31. 14. Tong S, Bi P, Hayes J, Donald K, Mackenzie J, 2001. Geographic variation of notified Ross River virus infections in Queensland, Australia, 1985−1996. Am J Trop Med Hyg 65: 171–176. 15. Russell R, 1998. Vectors versus humans in Australia - Who is on top down under? An update on vector-borne disease and research on vectors in Australia. J Vector Ecol 23: 1–46. 16. Harley D, Sleigh A, Ritchie S, 2001. Ross River virus transmission, infection, and disease: a cross-disciplinary review. Clin Microbiol Rev 14: 909–932. 17. Tong S, Bi P, Donald K, McMichael A, 2002. Climate variability and Ross River virus transmission. J Epidemiol Community Health 56: 617–621. 18. Mackenzie J, Lindsay M, Daniels P, 2000. The effect of climate on the incidence of vector-borne viral diseases in Australia: the potential value of seasonal forecasting. Hammer G, Nicholls N, Mitchell C, eds. Applications of Seasonal Climate Forecasting in Agriculture and Natural Ecosystems. Dordrecht, The Netherlands: Kluwer Academic Publishers, 429–452. 19. Mackenzie J, Lindsay M, Broom A, 2000. The effect of climate and weather on the transmission of Ross River and Murray Valley encephalitis viruses. Microbiol Aust 21: 20–25. 20. Lindsay M, Broom A, Wright A, Johansen C, Mackenzie J, 1993. Ross river virus isolation from the mosquitoes in arid regions of western Australia: implication of vertical transmission as a means of persistence of the virus. Am J Trop Med Hyg 49: 686–696. 21. McMichael A, Haines A, Kovats R, Slooff R, 1996. Climate Changes and Human Health. Geneva: World Health Organization. 22. Tong S, Bi P, Parton K, Hobbs J, McMichael A, 1998. Climate variability and transmission of epidemic polyarthritis (letter). Lancet 351: 1100. 23. Woodruff R, Guest C, Garner M, Becker N, Lindesay J, Carvan T, Ebi K, 2002. Predicting Ross River virus epidemics from regional weather data. Epidemiology 13: 384–393. 24. Maelzer D, Hales S, Weinstein P, Zalucki M, Woodward A, 1999. El Niño and arboviral disease prediction. Environ Health Perspect 107: 817–818. 25. Bowie C, Prothero D, 1981. Finding causes of seasonal diseases using time series analysis. Int J Epidemiol 10: 87–92. 26. Catalano R, Serxner S, 1987. Time series designs of potential interest to epidemiologists. Am J Epidemiol 26: 724–731. 27. Helfenstein U, 1986. Box-Jenkins modelling of some viral infectious diseases. Stat Med 5: 37–47. 28. Helfenstein U, 1991. The use of transfer function models, intervention analysis and related time series methods in epidemiology. Int J Epidemiol 20: 808–815.
137
29. Helfenstein U, 1996. Box-Jenkins modelling in medical research. Stat Methods Med Res 5: 3–22. 30. Checkley W, Epstein L, Gilman R, Figueroa D, Gama R, Patz J, Black R, 2000. Effect of El Niño and ambient temperature on hospital admissions for diarrhoeal disease in peruvian children. Lancet 355: 442–450. 31. Clancy L, Goodman P, Sinclair H, Dockery D, 2002. Effect of air-pollution control on death rates in Dublin, Ireland: an intervention study. Lancet 360: 1184–1185. 32. Dominici F, McDermott A, Zeger S, Samet J, 2002. On the use of generalized additive models in time-series studies of air pollution and health. Am J Epidemiol 156: 193–203. 33. Hajat S, Haines A, 2002. Associations of cold temperatures with GP consultations for respiratory and cardiovascular disease amongst the elderly in London. Int J Epidemiol 31: 825–830. 34. Pope C, Burnett R, Thun M, Calle E, Krewski D, Ito K, Thurston G, 2002. Lung cancer, cardiopulmonary mortality, and longterm exposure to fine particulate air pollution. JAMA 287: 1132–1141. 35. Borghi J, Guinness L, Ouedraogo J, Curtis V, 2002. Is hygiene promotion cost-effective? A case study in Burkina Faso. Trop Med Int Health 7: 960–969. 36. Abeku T, deVlas S, Borsboom G, Teklehaimanot A, Kebede A, Olana D, van Oortamrssen G, Habbema J, 2002. Forecasting malaria incidence from historical morbidity patterns in epidemic-prone areas of Ethiopia: a simple seasonal adjustment method performs best. Trop Med Int Health 7: 851–857. 37. Allard R, 1998. Use of time-series analysis in infectious disease surveillance. Bull World Health Organ 76: 327–333. 38. Nobre F, Monteiro A, Telles P, Williamson G, 2001. Dynamic linear model and SARIMA: a comparison of their forecasting performance in epidemiology. Stat Med 20: 3051–3069. 39. Australian Bureau of Statistics, 2002. 2001 Census Basic (Electronic resource). Canberra: Australian Bureau of Statistics. 40. Rich G, McKechnie J, McPhan I, Richards B, 1993. Laboratory diagnosis of Ross River virus infection. Comm Dis Intel 17: 103–107. 41. Selden S, Cameron A, 1996. Changing epidemiology of Ross River virus disease in South Australia. Med J Aust 165: 313– 317. 42. Chatfield C, 1975. The Analysis of Time Series: Theory and Practice. London: Chapman & Hall. 43. Venables W, Ripley B, 1999. Modern Applied Statistics with SPLUS. New York: Springer. 44. Box G, Jenkins G, 1970. Time-Series Analysis: Forecasting and Control. San Francisco: Holden-Day. 45. Tong S, Hu W, 2001. Climate variation and incidence of Ross River virus in Cairns, Australia: a time series analysis. Environ Health Perspect 109: 1271–1273. 46. Makridakes S, Wheelwright S, Hyndman R, 1998. Forecasting: Methods and Applications. New York: John Wiley & Sons, Inc. 47. Statistical Package for the Social Sciences, 1997. SPSS Trends. Upper Saddle River, NJ: Prentice-Hall, Inc. 48. Lindsay M, Mackenzie J, Condon R, 1993. Ross River virus outbreaks in western Australia: epidemiological aspects and the role of environmental factors. Ewan C, ed. Health in the Greenhouse: The Medical and Environmental Health Effects of Global Climate Change. Canberra: AGPS, 85–100. 49. Mackenzie J, Lindsay M, Coelen R, Broom A, Hall R, Smith D, 1994. Arboviruses causing human disease in the Australasian zoogeographic region. Arch Virol 136: 447–467. 50. Lindsay M, Mackenzie J, 1996. Vector-borne viral diseases and climate change in the Australia region: major concerns and public health response. Curson P, Guest C, Jackson E, eds. Climate Change and Human Health in the Asia-Pacific region. Canberra: Australian Medical Association and Greenpeace International, 47–62. 51. Bouma M, Sondorp HE, van der Kaay J, 1994. Health and climate change (letter). Lancet 343: 302. 52. Russell R, 1995. Arboviruses and their vectors in Australia: an update on the ecology and epidemiology of some mosquitoborne arboviruses. Med Vet Entomol 83: 141–158. 53. Stroup D, Thacker S, Herdon J, 1988. Application of multiple time series analysis of spread of communicable disease. Stat Med 7: 1045–1059.
