Malaria time series and regression estimates of relapse frequency and latency.

<p>A. The monthly <i>P. vivax</i> (red) and <i>P. falciparum</i> (black) cases between January 1987 and August 2010 are overlaid. B. The power spectrum of <i>P. vivax</i> data (red) shows a strong yearly cycle as well as different dominant periods longer than one year (i.e. interannual cycles) (The power spectrum describes how the variance of the data is distributed among different periods). The interannual cycles of period less than 6 years are also present in the rainfall spectrum (dashed black). C. The comparison of the observed seasonal patterns of <i>P. vivax</i> (red) and <i>P. falciparum</i> (solid black) shows significant relapses in <i>P. vivax</i> during January–June when rainfall is minimal (dotted black) – these are called “relapse cases” in the text. The majority of <i>P. vivax</i> cases due to transmission arise between August and November, and are likewise referred to as “transmission cases”. D. The autocorrelation values of <i>P. vivax</i> cases in each of the four transmission months - August (red), September (blue), October (light blue) and November (yellow) - and the cases in the subsequent twelve months show large correlation peaks between January and June, giving latency periods ranging between 5 and 8 months. E. A linear regression of aggregated transmission and relapse cases gives a slope of 0.31, suggesting a 31% average relapse rate. In the driest months of May–June, when entomological conditions exclude transmission, the regression gives a much tighter relation (not shown). F. The average of these autocorrelation curves suggests a relapse latency of 7 months.