Yunnan province (Figure 1) has an area of 394,000 square kilometres and a population during the 2000 census of 42.9 million. The province is divided into 16 prefectures, 128 counties, and over 1,400 townships. The climate is characterized by a cool, dry winter and a warm, wet summer, with peaks in rainfall in July–August and temperature in May–August. Elevation is highly variable, with county median elevation ranging from just over 600 metres above sea level in the south-east (Hekou county) to over 3,600 metres in the north-west, close to Tibet (Deqin county). See the additional file 1 for more information on the climate and geography of Yunnan.

The Chinese Centre for Disease Control lists malaria as a notifiable disease and maintains routine surveillance of clinical malaria nationwide. Diagnosis of malaria is based on clinical signs and, in an unspecified proportion of cases, laboratory confirmation. Cases of malaria diagnosed at health facilities are reported to the township-level authorities, and collated up through the county, prefecture and provincial administrative levels. For the purposes of the present study, reported numbers of P. vivax and P. falciparum malaria cases were assembled by month for each of the 128 counties between January 1991 and December 2006.

High-resolution (1 square kilometre) raster maps of interpolated long-term average monthly rainfall and minimum and maximum temperature were obtained from the WORLDCLIM website 1920. Digital elevation (in meters above sea level for cells of a 1 square kilometre grid), were also obtained from the same source. Rainfall, temperature and elevation maps were imported into a geographical information system (GIS; ArcView version 9, ESRI, Redlands, CA) and linked spatially to a digitized boundary map of the 128 counties across Yunnan. The county median values of rainfall, temperature and elevation were computed in the GIS to define attribute parameters in subsequent models. Data from national censuses conducted in 1990 and 2000 were used to impute inter-censual growth rates at the county level and to estimate population counts for each month between January 1991 and December 2006.

An initial descriptive analysis of malaria incidence was conducted. Crude standardized morbidity ratios (SMRs) for each county were calculated by dividing the observed number of cases across 1991–2006 by the expected number, where the expected was calculated by multiplying the provincial incidence by the average population for each county across 1991–2006. Pairwise Pearson cross-correlations for each month (January–December) were calculated to investigate temporal correlation in the case incidence data. Due to the strong correlations between rainfall and minimum temperature (Pearson's correlation = 0.83) and minimum and maximum temperature (0.89), only rainfall and maximum temperature were included in subsequent models. Poisson regression suggested that elevation was not significantly associated with P. vivax or P. falciparum case incidence after accounting for the effects of rainfall and temperature and elevation was thus excluded from the final models.

Bayesian spatiotemporal Poisson regression models were constructed using the WinBUGS software, version 1.4.3 (MRC Biostatistics Unit, Cambridge, UK). The Bayesian approach is advantageous in that it provides a convenient platform for modelling hierarchical datasets and incorporating spatiotemporal autocorrelation. Similar Bayesian spatiotemporal models of malaria surveillance data have been reported previously 2122. The outcome was the monthly number of cases of P. vivax or P. falciparum malaria in each county and the offset was the expected number of cases based on the population of each county for the months January 1991 to December 2006.

Fixed effects were added for monthly rainfall and maximum temperature and random effects were added for inter-annual variation in incidence in January–February and June–September, with incidence in January–February modelled (using a linear regression) as a predictor of incidence in June–September (this was justified by strong correlations of raw incidence in the summer with raw incidence in the preceding January and February). Additional components included a spatial county-level random effect, modelled using a conditional autoregressive (CAR) prior structure 23 and fixed-effect temporal trends (i.e., where the number of months passed since the index month, January 1991, was regressed against the outcome) with: 1) an overall provincial mean trend and 2) spatially smoothed county-level trends, where spatial variation was modelled by fitting a CAR prior to the trend coefficients as per Bernardinelli and Montomoli 24. Statistical notation of the final model is provided in additional file 2.

Three chains of the model were run consecutively, with each model parameter monitored after an initial burn-in of 1,000 iterations. Convergence was assessed by visual inspection of history and density plots of the three chains. Convergence occurred within the first 10,000 iterations for each model, but some parameters were slow-mixing, with considerable autocorrelation. Therefore, subsequent iterations were thinned by a factor of 10. Ten thousand values from the posterior distribution of each parameter were stored and summarized using descriptive statistics (posterior mean, 95% posterior credible interval [CrI]). Choropleth maps of model outputs were created in the GIS.

In Yunnan, there was a total of 250,070 cases of P. vivax malaria documented over the 16 years of observation (1991–2006), representing a crude incidence of 3.12 cases per 100,000 person years at risk. There were 44,465 cases of P. falciparum malaria reported during the same period representing a crude incidence of 0.55 cases per 100,000 person years at risk. Across the entire time-series, 10 counties had no reported cases of P. vivax and 29 counties had no reported cases of P. falciparum. The monthly incidence for both P. vivax and P. falciparum is shown in Figure 2 (note the natural log scale of the y-axis, used to help visualisation of temporal variation). Some features are immediately apparent for both types of malaria: there was a strong seasonal pattern characterized by a peak of malaria incidence in summer (June–September, peak month August) and a trough in winter (November–January). A smaller peak preceding the summer peak was also apparent, occurring in February of most years. A downward temporal trend was apparent, with some inter-annual variation around the trend.

Pearson correlations between overall incidence in the months January to December and the preceding 1–12 months are presented in additional file 1. Two clear patterns were apparent: firstly, there was strong temporal autocorrelation between incidence in each month and the preceding month; second, there were strong correlations between the months May–October and the preceding January and February. There was relatively little correlation between any month and a month in the preceding year, except that the summer peaks for P. vivax were correlated with the magnitude of the preceding summer peak.

Maps of crude SMRs for the 128 counties of Yunnan for 1991–2006 (Figure 3) show a high incidence of both types of malaria among counties bordering Myanmar, Laos and Vietnam and counties located in the Red River (Hong He) valley. Low incidence counties were mainly located in the central region, around Kunming, the provincial capital, the eastern regions bordering Guizhou province and the north-western regions bordering Tibet.

The final spatio-temporal models are presented in Table 1. For both types of malaria, incidence in January–February was a significant predictor of incidence in the following June–September (as indicated by 95% CrI of the regression slope that excluded zero) meaning that higher than average incidence in January–February could predict higher than average incidence in the subsequent June–September period. Time series plots of the modelled relative risks in January–February and June–September highlighted the dependence of the summer incidence on the preceding January–February (Figure 4). Interestingly for P. vivax, the relative risks appeared to cycle every 3 to 4 years, with noticeably higher risks in 1992, 1995, 1999 and 2003, whereas for P. falciparum the pattern was less regular, with peaks in 1993–1994 and 2003. There were significant positive relationships between malaria incidence and both rainfall and maximum temperature (Table 1). There was a significant downward temporal trend in malaria incidence between 1991 and 2006, with an average decrease in incidence of 5.2% per year (95% CrI 4.8, 5.6%) for P. vivax and 4.3% per year (95% CrI 3.5, 5.1%) for P. falciparum across the province.

Maps of the spatial random effect, representing residual spatial clustering after accounting for the climate variables, are presented in Figure 5. For both types of malaria, clusters of high-incidence counties were located in south-western Yunnan and far northern Yunnan, whereas clusters of low-incidence counties were located in eastern and north-western Yunnan. A map of the spatial variation in county-level temporal trend is presented in Figure 6. Clusters of counties with higher than average temporal trend (i.e., a gentler decline in incidence over the 16 years) were interspersed with clusters of counties with lower than average temporal trend, throughout the province. Clusters of counties in north-western and north-eastern Yunnan actually showed an increasing trend in incidence for P. vivax, albeit with very low overall SMRs.