Shifting patterns: malaria dynamics and rainfall variability in an African highland

Abstract

The long-term patterns of malaria in the East African highlands typically involve not only a general upward trend in cases but also a dramatic increase in the size of epidemic outbreaks. The role of climate variability in driving epidemic cycles at interannual time scales remains controversial, in part because it has been seen as conflicting with the alternative explanation of purely endogenous cycles exclusively generated by the nonlinear dynamics of the disease. We analyse a long temporal record of monthly cases from 1970 to 2003 in a highland of western Kenya with both a time-series epidemiological model (time-series susceptible-infected-recovered) and a statistical approach specifically developed for non-stationary patterns. Results show that multiyear cycles of malaria outbreaks appear in the 1980s, concomitant with the timing of a regime shift in the dynamics of cases; the cycles become more pronounced in the 1990s, when the coupling between disease and rainfall is also stronger as the variance of rainfall increased at the frequencies of coupling. Disease dynamics and climate forcing play complementary and interacting roles at different temporal scales. Thus, these mechanisms should not be viewed as alternative and their interaction needs to be integrated in the development of future predictive models.

Figure 1

(a) Time series of cases at AHP. (b) The wavelet spectrum is shown with power increasing from blue to red colours. The continuous line corresponds to the 5% significance level (§3). The areas within this line indicate significant variability at the corresponding periods and times. A cycle of period four is apparent in the 1990s, accompanied by a shorter cycle of period between one and two. This frequency is present earlier and is already significant in the 1980s, as best seen by following the crest of the spectrum (white line) indicating the localization of local maxima in time and period. The bold continuous line is known as the cone of influence and delimits the effect of the treatment of the boundaries; only patterns within this line are therefore considered reliable. The malaria data have been square-root transformed to rescale the variance.

Figure 2

TSIR model results for the AHP malaria time series. (a) Long-term changes in the transmission rate, log(β_t). (b) Wavelet spectrum of the residuals of the TSIR model (ϵ_t in equation (2)), showing significant variability at the circa-biennial scale, which is also present in the wavelet spectrum of the AHP case data. The 4-year mode appears only weakly, with reduced intensity and significance. (Because the model is fitted using log-transformed cases, the residuals were back-transformed by exponentiation to return to the original scale of the cases; and were further square-root transformed before the wavelet analysis for purposes of comparison with the original data in figure 1. Similar patterns are apparent in the non-transformed residuals. (N=50 000; T=10 years; similar results are obtained for other values of these constants: N=10 000 and T between 5 and 20 years.)

Figure 3

Patterns of rainfall interannual variability for one of the local stations (Chagaik). (a) The time series and (b) its wavelet spectrum. To remove seasonality and focus on the interannual variability, this environmental variable was filtered with a low-pass filter (Cazelles et al. 2007).

Figure 4

Wavelet cross-coherence between malaria at AHP and rainfall at interannual time scales. (a) The cross-coherence for the average of monthly rainfall at the three local stations. (Results start in 1980 because one of the time series begins at this later time and so does the average.) Cross-coherence varies between 0 and 1, shown here in a colour scale from blue to red. The lines correspond to the 5 and 10% significance levels. Only regions within these lines exhibit significant cross-coherence at those levels. (b) The same analysis but now for a local station stating in the 1970s (Chagaik). There is no significant cross-coherence in the 1970s at interannual time scales. After 1980s, rainfall and malaria exhibit coherent cycles at the circa-biennial scales. (The rainfall time series has been filtered with a low-pass filter to remove seasonality and periods below 1 year; similar patterns are obtained without the filtering with the additional expected coherence at the 1-year scale, results not shown).

Figure 5

Seasonal patterns of malaria and rainfall. (a) Monthly average cases (continuous line) for AHP. The vertical bars correspond to 1s.d. from the mean. (b) Monthly average precipitation from the mean of the three local stations (continuous line). (c) The total cases in the first peak for February–March–April are shown as a function of total precipitation for November–December–January. (d) The number of cases from May to December is plotted as a function of the number of cases in February–March–April. Correlations values are reported in the text. The significant association is not the result of the long-term trend in the mean, since a similar result is obtained when cases are normalized by one particular month (December), which effectively detrends the data.