Heterogeneity of use, access, and retention of insecticide-treated nets: Implications for subnational tailoring to maximise malaria control
Figures
Population-weighted distribution of expected ITN retention times and duration of use by country.
Median estimates of the mean ITN retention time and duration of use for each subnational region were weighted by population to produce country-level distributions. These histograms represent probability distributions of retention time and duration of use for an individual randomly selected from each country, assuming model-derived median estimates for all subnational regions. Subnational variability in retention times and the duration of use reflects differences in model-derived estimates between regions, since the model assumes these values are constant within regions. Vertical dashed lines indicate the overall population-weighted mean (black) and the population-weighted mean for each country (coloured).
ITN use, access, and PfPR over time in rural Burkina Faso.
(A) Survey estimates of ITN use (probability someone slept under an ITN the previous night, points sized proportionally to sample size) and model mean estimates of the probability of use over time (solid lines) for rural portions of subnational regions in Burkina Faso. Mean estimates are shown for the probability of access (dotted lines) and the probability of using an ITN sourced from a continuous channel (dashed lines). The model accounts for differing probabilities of use between individuals within a region; this results in notable uncertainty around the probability an individual selected at random uses an ITN. This uncertainty is illustrated in the shaded region, with the 50%, 80%, and 95% credible intervals as indicated by progressively lighter shaded regions. (B) PfPR2−10 estimates from the transmission dynamics model (darker lines) were fitted to annual Malaria Atlas Project estimates of PfPR2−10 compiled by site (Winskill, 2024b) (hollow points); model estimates of PfPR6−59mo are also shown (lighter lines), in addition to observed DHS PfPR6−59mo and associated 95% credible intervals due to measurement uncertainty (solid points and vertical lines).
Use, access, and PfPR over time in rural Senegal.
Model estimates in a lower transmission context in Senegal are shown. All features remain unchanged from Figure 2. Note, in B, some credible intervals extend beyond the y-axis limits, which have been restricted to 30% to aid visibility.
Use of ITNs from continuous channels.
For each subnational region, coloured points indicate median estimates of the mean use of any ITN and of those sourced from continuous channels, immediately following a mass campaign (A) and over the subsequent 3 years (B) with associated 95% credible intervals. For each country, the proportion of ITNs that were used which were sourced from continuous channels immediately following a campaign (A) and over the subsequent 3 years (B) can be estimated from the slopes of the coloured population-weighted linear regression lines, which assume a zero intercept. Estimates over all countries are shown by the population-weighted linear regression line in black.
Mean use and access with 3-year campaigns in subnational rural areas.
Central estimates of mean overall proportion of people using an ITN the previous night, access to an ITN, and use given access for 3-year mass campaign intervals are shown in the top three rows. The number of months following a mass campaign where overall ITN use exceeds 80% are shown in the bottom row.
Mean use and access with 3-year campaigns in subnational urban areas.
Central estimates of mean overall proportion of people using an ITN the previous night, access to an ITN, and use given access for 3-year mass campaign intervals are shown in the top three rows. The number of months following a mass campaign where overall ITN use exceeds 80% are shown in the bottom row.
Mean rural use and access with 2-year campaigns.
Central estimates of mean overall subnational ITN use, access, and use given access for 2-year mass campaign intervals in rural areas are shown in the top three rows. The number of months following a mass campaign where overall ITN use exceeds 80% are shown in the bottom row.
Mean urban use and access with 2-year campaigns.
Central estimates of mean overall subnational ITN use, access, and use given access for 2-year mass campaign intervals in urban areas are shown in the top three rows. The number of months following a mass campaign where overall ITN use exceeds 80% are shown in the bottom row.
Equity of use and access in rural Thiès and Ziguinchor, Senegal.
Solid vertical lines denote overall ITN use and access averaged over 3 years following the last mass campaign. Coloured bars indicate the proportion of the population with different probabilities of using or having access to an ITN. For example, 10% of the population have a probability of access between 70% and 80% in rural Ziguinchor, in comparison to 20% in rural Thiès. Vertical dashed lines denote 50% credible intervals for the probability of an individual using or having access to an ITN, indicating that half of the population are expected to have a probability of use or access within this range.
Subnational equity of use in Senegal.
All features remain unchanged from Figure 4.
Subnational equity of access in Senegal.
All features remain unchanged from Figure 4.
Retention time, use given access, and changes in cases for Mali.
All coloured points indicate median estimates and associated 95% credible intervals for subnational regions in Mali. (A) Mean durations of ITN use (hollow) and retention (filled) are shown in addition to national median estimates (black solid and dashed lines, respectively). (B) Mean ITN retention and use given access under a triennial campaign strategy are shown, with black lines indicating national median estimates. (C) Points indicate mean annual clinical cases under a triennial pyrethroid-PBO campaign strategy, and the projected change in cases for alternative intervention strategies with pyrethroid-only (C.i–iii), pyrethroid-PBO (C.iv–vi), or pyrethroid–chlorfenapyr (C.vii–ix) ITNs, with continuous-only distribution (C.i, iv, vii), or in conjunction with triennial (C.ii, v, viii) or biennial (C.iii, vi, ix) campaigns. The change in clinical cases is equal to zero for equivalent comparator and intervention strategies (C.v). Labelled diagonal reference lines with positive gradients indicate percentage increases in clinical cases relative to mean annual estimates under the comparator strategy; lines of the same style with negative gradients indicate equivalent percentage decreases. Urban areas were estimated to broadly have lower use given access than in rural settings, while the capital city, Bamako, was estimated to have the lowest ITN retention time of all regions.
Retention time, use given access, and changes in cases for Burkina Faso.
All features remain unchanged from Figure 5. Note the ordering of colours differs in panel B where numerical labels should be referred to.
Retention time, use given access, and changes in cases for Ghana.
All features remain unchanged from Figure 5. In 2019, several administrative regions in Ghana were subdivided: Brong-Ahafo became Bono, Bono East, and Ahafo; the Northern Region was split into Northern, Savannah, and North East; and Volta was divided into Volta and Oti. Retrospective analyses (A, B) were conducted using the pre-2019 regional boundaries, while future projections (C) used the post-2019 subdivisions. In all subnational regions, ITN retention times and use given access were estimated to be higher in rural than in urban settings.
Retention time and use given access for Malawi.
All features remain unchanged from Figure 5A. Clinical case projections were not conducted for Malawi due to the lack of intervention data stratified to the administrative-one level, despite DHS surveys being conducted at that scale.
Retention time, use given access, and changes in cases for Mozambique.
All features remain unchanged from Figure 5.
Retention time, use given access, and changes in cases for Senegal.
All features remain unchanged from Figure 5. While use given access was estimated to be broadly similar across urban and rural settings, ITNs were generally estimated to be retained for longer in rural areas.
Change in cases vs cases with triennial pyrethroid-PBO distribution.
Points represent urban and rural areas within each subnational region, are coloured by country, and are sized proportionally to the mean annual number of ITNs distributed under each strategy. Each point shows median estimates of the change in clinical cases following a switch from triennial pyrethroid-PBO distribution to alternative strategies against the projected clinical cases under the triennial pyrethroid-PBO strategy. Concurrent distribution of continuous ITNs of the same class used in mass campaigns in assumed throughout. Vertical and horizontal lines indicate 95% credible intervals. Labelled diagonal reference lines with positive gradients indicate percentage increases in clinical cases relative to mean annual estimates under the comparator strategy; corresponding lines with negative gradients represent equivalent percentage decreases and share the same line style.
Change in cases vs cases with triennial pyrethroid-chlorfenapyr distribution.
Points show median estimates of the change in clinical cases following a switch from triennial pyrethroid-chlorfenapyr distribution to alternative strategies against projected clinical cases under the triennial pyrethroid-chlorfenapyr strategy. Figure features otherwise remain unchanged from Figure 6.
Projected cases averted under different ITN distribution strategies.
Points indicate median estimates of the mean annual clinical cases averted by different ITN distribution strategies, in comparison to ceasing ITN distribution entirely, against clinical cases under a triennial pyrethroid-PBO distribution strategy. Figure features otherwise remain unchanged from Figure 6.
Change in cases vs PfPR with triennial pyrethroid-PBO distribution.
Points show median estimates of the change in clinical cases following a switch from triennial pyrethroid-PBO distribution to alternative strategies against all-age PfPR under the triennial pyrethroid-PBO strategy. Figure features otherwise remain unchanged from Figure 6.
Change in cases vs pyrethroid resistance.
Points show median estimates of the change in clinical cases following a switch from triennial pyrethroid-PBO distribution to alternative strategies against pyrethroid resistance. Figure features otherwise remain unchanged from Figure 6.
Change in cases vs duration of use.
Points show median estimates of the change in clinical cases following a switch from triennial pyrethroid-PBO distribution to alternative strategies against mean duration of use. Figure features otherwise remain unchanged from Figure 6.
Change in cases vs retention time.
Points show median estimates of the change in clinical cases following a switch from triennial pyrethroid-PBO distribution to alternative strategies against mean retention time. Figure features otherwise remain unchanged from Figure 6.
Change in cases vs use.
Points show median estimates of the change in clinical cases following a switch from triennial pyrethroid-PBO distribution to alternative strategies against mean use over any triennial distribution strategy. Figure features otherwise remain unchanged from Figure 6.
Change in cases vs access.
Points show median estimates of the change in clinical cases following a switch from triennial pyrethroid-PBO distribution to alternative strategies against mean access over any triennial distribution strategy. Figure features otherwise remain unchanged from Figure 6.
Change in cases vs use given access.
Points show median estimates of the change in clinical cases following a switch from triennial pyrethroid-PBO distribution to alternative strategies against mean use given access over any triennial distribution strategy. Figure features otherwise remain unchanged from Figure 6.
Flowchart of methods.
Data inputs and methodological steps are, respectively, summarised in orange and blue. 1DHS data (ICF, 2025) were sourced using the RDHS R package (v0.8.4) (Watson et al., 2019). 2Annual estimates of the number of ITNs delivered by country were obtained from the (The Alliance for Malaria Prevention, 2024) Net Mapping Project. 3Region-specific characteristics were sourced from the site R package (v0.2.2) (Winskill, 2024b). 4Parameter values that describe the probability of repellency and mortality as different ITN types age were sourced from Sherrard-Smith et al., 2022; Churcher et al., 2024 conditioned on annual pyrethroid (Pyr) resistance estimates for each subnational region from site. 5Mean annual PfPR2−10 Malaria Atlas Project estimates were sourced from the site R package (v0.2.2) (Winskill, 2024b); 6these were used to calibrate baseline entomological inoculation rates (EIR) with the cali (v1.0.8) R package (Winskill, 2024a) given historical ITN and non-ITN interventions, with coverage estimates of the latter sourced from site. 7Case projections were simulated for different ITN distribution strategies (D) using the malariasimulation R package (v1.6.0) (Charles et al., 2024) following characterisation of subnational differences in ITN use, access, and retention (A–C).
An illustration of the number of nets, , in a region over time with continuous replenishment of routinely distributed nets, , where nets are distributed every years through regular mass campaigns (solid black lines).
The contribution towards the total number of nets from routine distribution and previous mass campaigns are shown by the dashed and dotted blue lines, respectively. The timing of DHS surveys are shown by the red vertical dashed lines for both regular (left) and irregular (right) surveying.
Posterior predictive distributions (red) from the hierarchical model for the age of a used net in months if one is sampled randomly over time and across either sub-Saharan Africa (A), or within an exemplar country (B) or subnational region (C).
The shaded regions indicate 95% credible intervals, while the blue lines indicate the normalised empirical densities; these were generated from the pseudo-counts as described in Equation 19. The peaks at 12, 24, and 36 months in the empirical densities are believed to be artifacts from the survey data due to individuals rounding reported ITN ages to the nearest whole year.
Estimates of mass campaign timings in the subnational Est region in Burkina Faso.
Letting region be the Est region of Burkina Faso, (a) shows the empirical,, and smoothened,, annual numbers of nets delivered nationally are shown by the solid blue line (as reported by the Alliance of Malaria Prevention, AMP) and shaded region. The local minima of , which define the midpoints between net delivery dates are shown by the vertical black lines in (a) and (d) and indicate the assumed periods when mass campaigns are allowed to have occurred. The density proportional to the number of nets received subnationally by month, , is shown in red (b). The weighted version of this density, , to account for older nets being under-represented in DHS surveys is shown in yellow (c). The composite density, , and its smoothened counterpart, , which are constructed from the stepwise densities in (a) and (c) are shown by the green line and shaded region in (d). The densities, , are subsetted from by the black lines. These are treated as approximations of the probability of a mass campaign occurring in each month, and the expected value for the timing of each mass campaign are shown by the black triangles.
Tables
Core notation used throughout the main text and all appendices.
| Symbol | Definition |
|---|---|
| Subnational region index. | |
| Time point index. | |
| Mass campaign index. | |
| ITN or individual index, depending on context. | |
| Continuous time variable. | |
| Discrete time point corresponding to month . | |
| Country to which region belongs. | |
| Proportion of the population with ITN access in region at time . | |
| Proportion of the population with ITN use in region at time . | |
| Timing of the mass campaign in region . | |
| Timing of the most recent mass campaign in region before time . | |
| Number of months since the most recent mass campaign in region at time . | |
| Proportion of the population with ITN use or access in region at time . | |
| Component of attributable to campaign-distributed ITNs. | |
| Component of attributable to continuously distributed ITNs. | |
| Immediate post-campaign level of ITN use or access in region at time . | |
| Proportion of ITN use or access attributable to campaign-distributed ITNs in region at time . | |
| Proportion of immediate post-campaign ITN use or access attributable to campaign-distributed ITNs in region . | |
| Upper asymptote for in region . | |
| Region-specific intercept parameter governing the logistic-type trajectory in immediate post-campaign use or access. | |
| Region-specific slope parameter governing the logistic-type trajectory in immediate post-campaign use or access over calendar time. | |
| Region-specific exponential decay rate for the campaign-derived component of ITN use or access. | |
| Mean duration of ITN use or access (retention time) in region under the assumption of non-random allocation of ITNs. | |
| Mean duration of ITN use or access (retention time) in region under the assumption of random allocation of ITNs. | |
| Individual-level probability of ITN use or access in region at time . | |
| Region-specific overdispersion parameter governing heterogeneity in the individual-level probability . | |
| Age distribution of ITNs providing use or access in region . | |
| Age of ITN in region at the point of observation. | |
| DHS household survey weight for ITN in region , rescaled to remove the DHS factor of 106. |
Additional notation used in Appendix 2 beyond the core notation defined in Appendix 1—table 1.
| Symbol | Definition |
|---|---|
| Superscript indicating whether a quantity refers to ITN use () or access (). | |
| The duration ITN in region continues to be used or provide access. | |
| Mean duration ITNs in region continue to be used or provide access. | |
| Time-dependent replenishment process through which nets providing use or access are distributed at time . | |
| Long-run mean replenishment rate of nets providing use or access. | |
| Time horizon over which the long-run average replenishment rate is defined. | |
| Time period of the periodic equilibrium replenishment process. | |
| Interval between surveys when surveys are assumed to occur at regular intervals. | |
| Specific ITN age value used in the derivation of the pooled age density. | |
| Small age interval width used when considering ITNs with ages in . | |
| Vector of observed ITN ages () pooled across a finite number of surveys. | |
| Empirical estimate of the exponential decay rate obtained by fitting the pooled ITN age distribution. | |
| Country-specific mean ITN retention time for the country containing region . | |
| Country-specific standard deviation governing between-region variation in mean ITN retention times within country . | |
| Continent-level mean ITN retention time in the hierarchical model. | |
| Between-country standard deviation in mean ITN retention time. | |
| Hyperhyperprior mean for the country-level standard deviations . | |
| Hyperhyperprior standard deviation for the country-level standard deviations . | |
| Observed age of ITN in region in the hierarchical likelihood. | |
| Pseudo-count of the number of ITNs of age in region , after applying DHS household survey weights and rounding. | |
| Number of surveyed ITNs of age in region . |
Additional notation used in Appendix 3 beyond the core notation defined in Appendix 1—table 1.
| Symbol | Definition |
|---|---|
| Annual number of ITNs delivered to country at time . | |
| Smoothened distribution of annual ITN deliveries to country at time . | |
| Normalised density of the month in which ITNs recorded in DHS surveys in region were received. | |
| Survey date of ITN in region , measured in months. | |
| Weighted density of the month in which ITNs in region were received, after correcting for the under-representation of older ITNs in DHS surveys. | |
| Posterior mean estimate from the hierarchical model of the mean duration of access (retention time) in region under the assumption of non-random allocation of ITNs. | |
| Composite density for region constructed from and the national annual-delivery density . | |
| Smoothened version of the composite density for region . | |
| Normalised density for the timing of the mass campaign in region . | |
| Mean estimate of the timing of the mass campaign in region . | |
| Assigned standard deviation for the timing of mass campaign in region , taking values 1, 2, or 3 months to represent low, medium, or high uncertainty. | |
| Unit point mass at . |
Additional notation used in Appendix 4 beyond the core notation defined in Appendix 1—table 1.
| Symbol | Definition |
|---|---|
| Total number of surveyed individuals in region at time . | |
| Continuous-time analogue of . | |
| Continuous-time analogue of . | |
| Continuous-time analogue of . | |
| Continuous-time analogue of . | |
| Continuous-time analogue of . | |
| Posterior mean of the mean ITN retention time in region , used to parameterise the prior on . | |
| Posterior variance of the mean ITN retention time in region , used to parameterise the prior on . | |
| Standardised survey time corresponding to time . | |
| Mean survey time used to standardise . | |
| Standard deviation of survey times used to standardise . | |
| Intercept parameter on the standardised time scale. | |
| Slope parameter on the standardised time scale. | |
| Number of ITNs in region at time recorded or imputed as originating from campaigns. | |
| Indicator variable for whether ITN in region originated from a campaign () or continuous distribution (). | |
| Indicator variable denoting that the source of ITN in region was missing in the DHS data and was therefore imputed probabilistically. | |
| Observed proportion of ITNs providing access in region that were recorded as originating from campaigns. | |
| Proportion of the population using continuously distributed ITNs at the start of a month in the random-allocation approximation. | |
| Proportion of the population using continuously distributed ITNs immediately before the start of the next month. | |
| Proportion of the population that must receive ITNs through continuous distribution at the start of the next month under random allocation. | |
| Proportion of the population using ITNs immediately following an arbitrary mass campaign in the random-allocation approximation. | |
| Approximate exponential-decay solution for population ITN use as a function of time since the most recent campaign. |
Additional notation used in Appendix 5 beyond the core notation defined in Appendix 1—table 1.
| Symbol | Definition |
|---|---|
| Region-specific over-reporting parameter applied to ITN use in region . | |
| True value of PfPR6−59mo at time in region . | |
| Decay rate governing loss of ITN insecticidal efficacy with ITN age. | |
| Probability that a mosquito is repelled by an ITN of age α, conditional on a feeding attempt. | |
| Probability that a mosquito is killed by an ITN of age α, conditional on a feeding attempt. | |
| Probability that a mosquito successfully feeds in the presence of an ITN of age α, conditional on a feeding attempt. | |
| Probability that a mosquito is repelled by a new ITN. | |
| Probability that a mosquito is killed by a new ITN. | |
| Long-term probability of repellency from the physical barrier of the ITN alone. | |
| Central estimate of the timing of the last mass campaign before 2025. | |
| Interval between future mass campaigns. | |
| Timing of the first future mass campaign. | |
| Number of individuals testing positive for malaria in the calibration dataset. | |
| Number of individuals testing negative for malaria in the calibration dataset. | |
| Total number of individuals in the calibration dataset contributing positive test outcomes. | |
| Total number of individuals in the calibration dataset contributing negative test outcomes. | |
| DHS household survey weight for child in region at time , rescaled to remove the DHS factor of 106. |