Figure 1.
Parametric form for seasonally varying mosquito density.
m0: mean mosquito density; c: low season density relative to the mean; t0: time of peak density; d: duration of the high season.
Figure 2.
Reduction in R0 due to seasonality.
A: Human to mosquito generation time distribution for three models. B: R0 relative to a non-seasonal model with the same mean mosquito density for different transmission models, with sinusoidal seasonal variation. The last three lines all have a mosquito latent period, and correspond to the generation times in A. The thin solid lines are the approximate formulae in equations (1) and (2). C: Seasonal mosquito density with varying duration of high season, and c = 0.05. D: R0 relative to a non-seasonal model with the same mean mosquito density. Colours for the duration of the high season are the same in C and D.
Figure 3.
Effect size of repeated annual rounds of IRS in a non-seasonal setting.
The solid blue line is the true effect size calculated numerically. The line labelled “Using mean efficacy” is found by plugging the mean efficacy over the year into a reproduction number formula; and the line labelled “Using mean R” is found by plugging the efficacy at each time into a reproduction number formula, and then finding the mean over the year. A: Varying the repellency of the insecticide: lower repellency means greater lethality. B: Varying the coverage.
Figure 4.
Effect size of IRS with seasonality according to the time of year of spraying.
IRS is repeated annually with 80% coverage. Each line is for a different length of high season, all centred around 6 months. The black dashed lines are the effect sizes without seasonality. A: Insecticide with 60% repellency and a 6 month half-life. B: Insecticide with 20% repellency and a 3 month half-life.
Figure 5.
Effect size of repeated annual rounds of MDA at varying times of year.
In all cases, the high season is centred at 6 months and MDA is repeated annually with 80% coverage. In B, C and D, the high season is three months long. A: With different lengths of the high season. The black dashed line is the effect size in a non-seasonal setting. B: Components of the effect size. C: Prophylactic and overall MDA effect size with alternative durations of prophylaxis. D: MDA effect size with alternative durations of human infectiousness.
Figure 6.
Effect size of annual rounds of both MDA and IRS in a non-seasonal setting according to their timing relative to each other.
Each intervention is repeated annually with 80% coverage. The dashed line is the product of the separate effect sizes.
Figure 7.
Effect size of two intervention rounds per year.
The dashed horizontal and vertical lines mark the optimal time of year for each intervention on its own. There is a 3 month high season centred at 6 months. A: Effect size of a single annual round each of IRS and MDA. B: Product of separate IRS and MDA effect sizes. C: Effect size of two rounds of IRS per year (same colour scheme as A and B). D: Effect size of two rounds of MDA per year.
Figure 8.
Effect size of a pre-erythrocytic vaccine.
The lines labelled “Approx.” are approximate effect sizes calculated using the mean efficacy over the cycle between vaccination campaigns. The lines labelled “Moderate efficacy” have 50% initial efficacy and 80% coverage, while “High efficacy” means 90% initial efficacy and 90% coverage. A: Vaccination every three years (triennial) in a non-seasonal setting, with varying duration of protection. B: Annual vaccination with a one year half-life or triennial vaccination with a three year half-life (so the mean efficacy is the same in both cases), with a three-month high season and varying time of vaccination. Annual vaccination with a high efficacy transmission-blocking vaccine (TBV) is also shown.
Table 1.
Effect size of ITNs with 80% coverage.
Table 2.
Effect size of combinations of interventions.
Figure 9.
Recorded seasonally varying mosquito densities from published papers and fitted curves.
As the sampling methods and other factors vary between the datasets, the units for the data are not comparable between sites and have been omitted. A: Ajura village, Garki, Nigeria; B: Bagamayo, Tanzania; C: Navrongo, Ghana; D: Dakar, Senegal.
Table 3.
Parameters for curves fitted to mosquito density data with 95% confidence intervals.