Table 1.
Summary of relapse classifications.
Table 2.
Quantities in the statistical model to estimate the probabilities of clinical illness (Model variant A1).
Fig 1.
The incidence of primary infection and relapse over calendar time and for each age group.
Top row: Input parameter value set 1 (shorter mean duration of blood-stage infection). Bottom row: Input parameter value set 2 (longer mean duration of blood-stage infection). Predicted incidence for children from Ilaita village with no ITN use of: a&f primary infections; b&g first or second relapse (relapse classification A2j); c&h third or later relapse (relapse classification A2j); d&i first relapse (relapse classification B2j), e&j second or later relapse (relapse classification B2j). Age categories (dark green through blue): 1-1.5 years, 1.5-2, 2-2.5, 2.5-3, 3-3.5, 3.5-4 light blue, over 4 years: blue.
Fig 2.
Observed and predicted clinical incidence in the Ilaita cohort.
Green squares: observed clinical incidence with 95% CI; purple circles: predicted clinical incidence. Model predictions for four variants (A1, A2, B1, B2) are shown for two parameterizations for blood-stage infection duration each (purple circles are on top of each other). Each is a weighted sum of the estimated incidence for each covariate category multiplied by the number of children in that category. The patterns of observed and predicted incidence show good agreement, suggesting reasonable model fit.
Table 3.
Estimated parameter values for the model for the probability of illness following primary infections and relapses.
Fig 3.
The estimated probability of clinical illness following primary infections and relapses by cumulative number of primary infections.
Model variants A1, A2, B1, B2 are shown, all with all relevant relapses (j) (Model variants are described in Table 1). Relapse classification A (all relapses excluding those during a prophylactic period), Relapse classification B (excluding relapses occurring when there is a blood-stage infection by the same brood present or during an immune period after natural clearance or during a prophylactic period). Model variants A1 and B1: primary infections (red) and relapses as one group (blue); A2 and B2: primary infection (red), first relapse (lavender), second of later relapse (orange). Polygons are the minimum and maximum of the 95% credible intervals for the probability of clinical illness following blood-stage infection for the two parameter value sets (arising from two different assumptions about the duration of blood-stage infection - S1 Appendix). The youngest children in the cohort are already one year of age, so the darker shaded range where data are available starts only at seven cumulative primary infections. Maternal immunity is not included in this statistical model. Studies of deliberate infections studies estimate a high probability of clinical illness in naive individuals [132] but the probability is not known in natural conditions.
Fig 4.
The estimated proportion of P. vivax illness due to primary infections by season.
The estimated proportion (95% credible interval) for one model variant (B2j) and one parameter set (long duration parameter set 2) for one age-group (3-3.5 years).
Fig 5.
Observed and predicted age-incidence curves from the same geographical zone with the same relapse pattern.
(a) Blue dots: Incidence of clinical cases presenting to two health facilities in residents of 29 villages in the Wosera, Papua New Guinea [22,44], an area with an estimated 12 infectious bites pppy in 1992 [24,55] Pink ribbons: minimum and maximum predicted incidence for the four model variants with 12 infectious bites pppy for treatment coverages (from lowest polygon to highest) of 60%,50%,40%,30%,20%,10% (actual treatment coverage is unknown). (b) Observed incidence in Espiritu Santu, Vanuatu in 1992-93 (blue triangles) and 1993-94 (red circles) with 95% confidence intervals [57]. Cases were detected through weekly active surveillance and visits were not included if the individual had had anti-malaria treatment in the last 4 weeks. Green ribbons: Predicted age-incidence curves using the minimum and maximum of the four model variants assuming all cases are detected for infectious bites pppy of 50,30,20,10,5,2,1 (highest peak polygon to lowest peak). (c) Incidence of P. vivax fevers in infants with 95% confidence intervals. The observed data are from the placebo arm of a trial of intermittent preventive treatment in infants (IPTi) trial, Mugil, Papua New Guinea [60]. Infants were followed up from 3 to 15 months of age. Passive case detection was carried out at one health centre and three outlying clinics. P. vivax illness is defined as a history of fever in the last 48 hours or axillary temperature ≥37.5 with a positive blood smear. For the present study, we do not exclude from the time at risk the period within 28 days of an illness but do exclude a prophylactic period of 14 days following treatment with artemether/lumefantrine (co-artem). Predicted age-incidence curves are the same as for (b), varying by transmission intensity. The actual transmission intensity and treatment coverage are not known, but treatment coverage is expected to be high. For all scenarios, we assume stable transmission with seasonal fluctuations as for Ilaita.