The model estimates people keep and use ITNs for considerably less than 3 years. Across all regions in all six countries studied, the population-weighted mean duration of ITN access, herein referred to as ITN retention time, was 26.8 months (95% CrI: 26.7, 26.9). Retention times were estimated to vary notably between and within countries (Figure 1), with median estimates ranging from 14.8 months (95% CrI: 14.5, 15.1) in rural Tete, Mozambique, to 41.5 months (95% CrI: 40.7, 42.2) in rural Ségou, Mali, with only 23 of 146 (15.8%) regions estimated to have a mean retention time greater than 3 years. The mean durations of ITN use similarly varied notably both subnationally and between countries and were estimated to be consistently lower than mean retention times (Figure 1), with a population-weighted mean across all regions of 21.0 months (95% CrI: 20.9, 21.0). The mean duration that ITNs remain in use was also estimated to be shortest in rural Tete with a median estimate of 12.0 months (95% CrI: 11.8, 12.3). Meanwhile, the longest mean duration of use was in urban Est, Burkina Faso (Figure 5—figure supplement 1A) at 37.8 months (95% CrI: 34.9, 40.6), which was the only region (0.7%) with a median estimate greater than 3 years. Caution is needed when comparing retention times between countries, due to differences in the timings of surveys relative to mass campaigns, but these are likely to be minimised over subnational scales within a country. While no systematic differences in the durations of use or access were estimated between urban and rural regions in Senegal, differences were observed in some other countries, such as in Ghana, where values were estimated to be broadly lower in urban settings (Figure 5—figure supplement 2A). For most regions, the gap between use and access was estimated to widen over time following mass campaigns, indicating people stop using ITNs substantially before they stop owning them, so that use given access is not constant but typically wanes as ITNs age (Figure 2A).

Figure 1

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Access and use of ITNs are estimated to have varied substantially over time, both within and between countries (Figure 2A, Figure 2—figure supplement 1A). Inferring changes over time from observational data alone can give misleading results. For example, in rural Centre-Nord in Burkina Faso, DHS survey data suggests a sustained decrease in use between 2014 and 2022 (Figure 2A); however, the model which considered the timings of mass campaigns and routine ITN distribution estimates that overall ITN use immediately following mass campaigns increased over this period. The observed decrease in use and access across many regions in Burkina Faso may therefore be a by-product of DHS surveys being conducted at progressively later dates relative to the most recent campaign; this does not necessarily indicate an underlying trend in decreasing use or access over longer timescales. This highlights the potential limitations of making direct comparisons between different surveys, which may be conducted at different intervals since the preceding campaign (Figure 2A). This waxing and waning dynamics in use over time is also observed in P. falciparum prevalence (Figure 2B). In many countries peak ITN use and access following mass campaigns has increased over time; for example in rural Thiès in Senegal, the overall use immediately following the first 2009 mass campaign was estimated to reach 18%, yet peak levels of use above 80% were estimated to be achieved following all mass campaigns since 2016 (Figure 2—figure supplement 1A). Similar trends can be seen in the context of access (dotted lines, Figure 2A and Figure 2—figure supplement 1A).

Mean ITN use over the 3 years following a campaign is estimated to be modest, with a population-weighted mean of 45.4% (95% CrI: 45.2, 45.5) across all regions studied. Overall access to an ITN was estimated to be greater over the 3-year period, with 58.1% (95% CrI: 58.0, 58.2) of people having access to an ITN, on average. The population-weighted mean use given access across all regions was estimated to be 75.7% (95% CrI: 75.5, 76.0). While no regions were estimated to have a mean use or access greater than 80% over either the 3- or 2-year periods following a mass campaign, in the context of use given access, 46% of subnational regions had median estimates greater than 80% over a 3-year period following a mass campaign, increasing to 70% of regions when only the first 2 years were considered (Figure 3, Figure 3—figure supplements 1–3). Nevertheless, some regional differences are observable, with southern Malawi having a low overall ITN use despite the region having a similar level of access to the rest of the country. Across all regions, mass campaigns are estimated to increase ITN use in their immediate aftermath to greater than 80% in 76.8% of regions (bottom row, Figure 3, Figure 3—figure supplements 1–3), with considerable variability within and between countries. For example, for rural areas in Burkina Faso, the northern Sahel region is predicted to never achieve ITN use above 80%, whereas use is predicted to be maintained above 80% for 6 months following a mass campaign in the south-western region of Cascades.

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The contribution of ITNs from continuous channels also differed between and within countries; for example, in rural regions of Thiès (Figure 2—figure supplement 1) the use of ITNs from continuous channels was estimated to be 15.8% (95% CrI: 14.7, 17.0) at the end of 2024, in comparison to 4.1% (95% CrI: 3.8, 4.5) in Sédhiou. Differences in the use of continuously distributed ITNs were also notable between countries, with 19.8% (95% CI: 17.4, 22.2) of person-nights of ITN use (one person using an ITN for one night) across Burkina Faso estimated to be attributable to continuously distributed ITNs over a 3-year period, compared to Malawi at 61.2% (95% CI: 58.3, 64.1) (Figure 2—figure supplement 2B).

There is considerable variability in observed mean access and use within a region, with notable uncertainty between communities, as indicated by the high uncertainty around the probability an individual randomly selected from the region will use an ITN (Figure 1A). The effect of this is illustrated by rural Thiès and Ziguinchor, which both have a mean overall ITN use of 58% when averaged over 3 years following the last mass campaign. Though the average is the same across both regions, more people in rural areas of Ziguinchor either have a very low or very high probability of using an ITN, indicating greater inequity in ITN use in rural areas of Ziguinchor than in Thiès (Figure 4). A similar trend is also apparent in the context of access and in other settings (Figure 4—figure supplements 1 and 2).

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The framework can identify regions of low ITN use and make suggestions about how this could be improved (Figure 5A, B). ITNs will be most effective in areas where people have access to nets for a long period of time and are more likely to use them (quadrant 1, Figure 5B). In areas where people keep ITNs but have low use given access (quadrant 2, Figure 5B) NMPs may wish to consider social and behaviour change (SBC) interventions such as ‘hang-up’ campaigns. Conversely, in areas with lower ITN retention times but high use given access (quadrant 4, Figure 5B) NMPs may wish to consider more regular mass campaigns to improve equality of access between different regions. Both of these policy changes may be warranted in regions with both low retention and use given access to improve overall ITN use (quadrant 3, Figure 5B). Results varied by country (Figure 5—figure supplements 1–5).

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The statistical model can be used to predict the increase in use caused by increasing the frequency of mass campaigns from 3 to 2 years, assuming the contribution of continuous distribution channels and the decay in use given access following mass campaigns remains the same. Increases in access are estimated to be modest, with percentage-point population-weighted mean increases across all settings of 8.15% (95% CrI: 8.13, 8.17), from 58.1% (95% CrI: 58.0, 58.2) to 66.3% (95% CrI: 66.2, 66.4). Greater increases are predicted to be seen for ITN use, with the population-weighted mean use across all settings increasing from 45.4% (95% CrI: 45.3, 45.5) to 53.9% (95% CrI: 53.7, 54.1), an increase of 8.50% (95% CrI: 8.47, 8.54). An increase in use given access is also projected, with the population-weighted mean increasing by 4.13% (95% CrI: 4.07, 4.20) in absolute terms from 75.7% (95% CrI: 75.5, 76.0) to 79.9% (95% CrI: 79.6, 80.2). Subnational variation is also predicted in changes of access, use and use given access following adoption of biennial mass campaigns (Figure 3 and corresponding Figure 3—figure supplements 1–3).

Policy-makers may wish to optimise ITN distribution to maximise epidemiological impact. We generate estimates of clinical cases under different distribution strategies by simulating halting mass campaigns or changing the campaign interval from 3 to 2 years. Fifty-eight percent of ITNs distributed in sub-Saharan Africa in 2023 were reported to have been pyrethroid-PBO nets (World Health Organization, 2024c); we therefore estimate changes in clinical cases for alternative strategies compared to the current triennial pyrethroid-PBO campaigns with supplementary continuous distribution, with triennial pyrethroid-chlorfenapyr strategies as a comparator also presented (Figure 6—figure supplement 1).

The number of clinical cases averted by the different strategies varies substantially, both within (Figure 5C and Figure 5—figure supplements 1–5, panel C) and between countries (Figure 6). For example, in Mali switching from a triennial to biennial pyrethroid-PBO mass campaign is estimated to avert fewer than 50 additional cases per 1000 people in Gao, but over 100 in Sikasso (Figure 5C.vi). The benefit of the different strategies is projected to differ in each setting, though broad trends are observable. Generally, fewer cases are projected to be averted under triennial pyrethroid-chlofenapyr campaigns than with biennial pyrethroid-PBO distribution, with 74.6% of regions having fewer clinical cases predicted when you increase the campaign frequency than when the net class is changed (Figure 6—figure supplement 2F vs H and regions with negative y-axis values in Figure 6—figure supplement 1F). Triennial distribution of pyrethroid-chlorfenapyr ITNs was predicted to avert more cases than biennial distribution of pyrethroid-only ITNs for 94.3% of regions (Figure 6—figure supplement 2H vs C and regions with positive y-axis values in Figure 6—figure supplement 1C). This was more consistent for policy decision-making than the differences between triennial pyrethroid-PBO distribution and biennial pyrethroid-only distribution, with distributing pyrethroid-PBO ITNs averting more cases in 65.6% of regions (Figure 6—figure supplement 2E vs C and regions with positive y-axis values in Figure 6C).

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It is unlikely that bespoke simulation modelling will be available for all policy decisions, but the models can indicate trends that can support subnational tailoring of ITNs. The models indicate current clinical incidence is the best predictor of the number of cases averted for the different strategies. For example, for both pyrethroid-PBO (Figure 6F) and pyrethroid-chlofenapyr ITNs (Figure 6—figure supplement 1I), the projected additional cases averted by switching to biennial distribution is estimated to gradually increase as clinical cases increase up to approximately 300 mean annual clinical cases per 1000 people, though above this point trends are less obvious. Similar trends are seen in countries with a broad range of transmission intensities, such as Mali (Figure 5C.vi) and Mozambique (Figure 5—figure supplement 4B.vi), though it is less clear in countries where are no low transmission regions, such as in Burkina Faso (e.g. Figure 5—figure supplement 1C.vi). Similar trends can be observed by using all-age malaria prevalence as an indicator to select regions which will have the greatest benefit of greater investment in ITNs (Figure 6—figure supplement 3). Selecting areas to target using the level of pyrethroid resistance is less reliable (Figure 6—figure supplement 4), in part because there is little variability within countries and differences between countries are confounded by transmission intensity in this analysis. Surprisingly, there was no discernible association between either ITN retention times or the mean duration that nets remain in use on the impact of increasing campaign frequencies (Figure 6—figure supplements 5F and 6F). This is because ITNs have a bigger epidemiological impact in areas where they are used for longer, though policy-makers may wish to consider equity in disease burden in their tailoring process which is not considered here. There were, however, clearer relationships that indicated more cases may be averted following a switch from pyrethroid-PBO to pyrethroid-chlofenapyr triennial distribution in regions with greater mean access, use, and use given access (Figure 6—figure supplements 7–9H), though these associations are weaker than those seen for clinical cases or prevalence.

The cessation of mass campaigns is projected to lead to notable resurgences in clinical cases in many regions; an additional 150–300 clinical cases per 1000 people are estimated for moderate to high transmission intensity regions (those with more than 150 mean annual clinical cases per 1000 people under triennial pyrethroid-PBO distribution strategies). It has been suggested that the potential increase in cases caused by halting mass campaigns could be mitigated by concurrently switching to using pyrethroid-chlofenapyr ITNs in continuous distribution channels (Figure 6G vs D). This modelling exercise indicates such mitigation is unlikely, with only 1 of the 146 regions showing a reduction of cases when switching from combined continuous distribution and triennial mass campaigns with pyrethroid-PBO to continuous distribution alone with pyrethroid-chlorfenapyr. This was for the capital city of Mali, Bamako (Figure 5C.vii), which has moderately low transmission, while Mali was estimated to distribute more ITNs through continuous channels than most other countries considered in this analysis (Figure 2—figure supplement 2).

The majority of data were sourced from Demographic and Health Surveys (DHS) and Malaria Indicator Surveys (MIS) (ICF, 2025). AIDS Indicator Surveys (AIDS) were also included where additional malaria questions were included (ICF, 2025). Subsequent references to DHS surveys refer to all surveys included. Data on the number of ITNs distributed nationally were also sourced from The Alliance for Malaria Prevention, 2024.

Here, we assume each ITN is used every night for a continuous period after receipt (duration of use), but may remain accessible for a different length of time following receipt (duration of access/retention time). It is important to distinguish between people who have access to an ITN but do not sleep beneath it and those who do not have access to one. We generate subnational estimates of both the population mean duration of use and retention time and assume these are constant over time. Single estimates of both these quantities are estimated separately for rural and urban areas of each region to allow the identification of systematic differences between locations that could allow the geographical targeting of resources.

Retrospective analyses were conducted from 2008, to align with the introduction of mass distribution campaigns until 2024. Analyses were conducted at an administrative-one level stratified by urban and rural settings, as recorded in survey responses. To account for inconsistencies in administrative-one naming conventions, such as alternative French and English spelling, best efforts were made to unify recorded administrative-one entries with the naming conventions recorded by GADM v4.0 (Global Administrative Areas, 2021). Note that while administrative-one is referred to as a region in Senegal, for example, terminology differs between countries; here, the units of analysis are consistently referred to as (subnational) regions. The initial inclusion criteria were restricted to countries where at least three DHS/MIS surveys had been conducted between 2010 and 2022. This was to ensure there were sufficient data for all countries after mass campaigns had been established. Ten countries initially met this criteria: Burkina Faso, Ghana, Liberia, Malawi, Mali, Mozambique, Nigeria, Senegal, Tanzania, and Uganda.

All mass campaigns were assumed to be conducted nationally, although their timings were not restricted to occur in synchrony across subnational regions. Instead, the timing of each mass campaign was allowed to vary subnationally within time intervals that were defined at a national level. Due to this assumption, Liberia was excluded from our analysis due to rolling campaigns being conducted between 2008 and 2012 (Koenker et al., 2019a). We also excluded Nigeria where mass campaigns follow different distribution schedules between states (Koenker et al., 2019a). Tanzania was also excluded as a mixture of annual school-based distributions and 5-yearly mass campaigns are conducted within different subnational regions (Koenker et al., 2023a). We finally excluded Uganda since there have been notable changes to its administrative-one level boundaries over the assessed period; this has resulted in significant discrepancies between the administrative-one level regions recorded in DHS surveys and the naming conventions used in GADM v4.0. Although Ghana was included in all analyses, the sub-division of the regions of Brong-Ahafo, Northern and Volta in 2019 was not accounted for in the retrospective analyses of historical use and access; the new regions were however accounted for in the transmission dynamics models for future projections. For Malawi, we conducted retrospective analyses of use and access at an administrative-one level (termed regions in the country); however, as data we sourced for other covariates, such as rainfall patterns and non-ITN interventions, were stratified at an administrative-two level (districts) for Malawi (Winskill, 2024b), we excluded the country from the transmission dynamics analyses. These other covariates were stratified at the administrative-one level for all other countries (Winskill, 2024b).

All subsequent analyses described are conducted independently for use and access and were conducted in R (v4.3.2, R Development Core Team, 2023). The code for models used in this study can be found at https://github.com/andrewcglover/itn_campaigns/tree/elife-2025 (copy archived at Glover, 2026). Unless otherwise stated, median central estimates are quoted in the main text.

Due to the sparsity and irregularity of DHS and MIS surveys, we were unable to investigate seasonal fluctuations in either access or use; we therefore assume that nets provide access or are used continuously over some period of time. Although seasonal differences are not identifiable under our model, overdispersion in individual-level use and access may partially absorb unexplained variation between observations, including variation arising from unmodelled seasonal differences (Equation 7). However, this does not allow us to quantify seasonal variation in ITN use or access. If ITN use were systematically higher during high-transmission rainy seasons, our assumption of continuous use may underestimate the protective impact of ITNs during these periods. We do not assume these periods are equal, and so differentiate between the duration of time that a net is slept under (duration of use) and the period for which it provides access before being discarded or repurposed (retention time). Using a Bayesian hierarchical model fitted to pooled ITN age distribution data across DHS surveys, we separately generated initial subnational estimates of the mean duration of use and mean retention times of ITNs from DHS survey data using the age distributions of ITNs in surveyed households. When inferring mean retention times under our hierarchical model, we implicitly assume ITNs are only distributed to individuals without them; this is a necessary methodological step, but is relaxed later in our analysis. Although the methodology is applied analogously in the context of use, the remainder of this section focuses on access.

Under the assumption that nets are lost at a constant rate, the long-term age distribution of nets providing access follows an exponential distribution, allowing retention times to be inferred from observed net ages. The hierarchical structure pools information across regional, national, and continental spatial scales to reduce bias arising from survey timing relative to mass campaigns, particularly in regions with sparse survey data. Region-specific mean retention times were modelled with country-level random effects, and country-level means were in turn modelled with a continent-level random effect. Right-censoring of reported net ages at 36 months and survey sampling weights were explicitly accounted for in the likelihood when fitting the model in Stan via the R interface RStan (v2.32.6, Stan Development Team, 2024). Full specification of the hierarchical model and prior distributions are provided in Appendix 2.

We then sought to estimate the timings of mass campaigns in different regions. We use annual estimates of the number of ITNs delivered nationally from the AMP Net Mapping Project (The Alliance for Malaria Prevention, 2024) to estimate time intervals within which each mass campaign was likely to occur for each country. We do however allow for the timings of campaigns to vary subnationally within these intervals. For each region, the timing of each mass campaign is estimated probabilistically by constructing distributions over plausible months using DHS data on the ages of ITNs recorded in surveys. As time elapses since a mass campaign, ITNs are less likely to be recorded in DHS surveys. Our initial ITN retention estimates help correct for this bias (see Appendix 3.1 Estimating subnational timings for further details). We can then probabilistically infer the timing of the previous campaign (${\varphi }_j$) relative to some time $t_j$ in a given region (see Appendix 3.2 Time since the most recent campaign for further details), noting that in contrast to Appendix 3.2 Estimating subnational timings, we do not explicitly indicate subscript $i$ notation to indicate the region of interest for notational ease. In turn, this allows us to infer the time since the previous campaign ($m_j$) relative to all calendar times considered in our model:

We then utilise the following discrete-time model of the proportion of the population with access ($p_j$) for a given region at some time $t_j$ in the observed survey period:

where superscripts 0 and $t$ are used for notational purposes and do not indicate exponentiation. An in-depth explanation of the model can be found in Appendix 4.1 Core model structure, but in brief, we firstly assume access can be attributable to ITNs received from campaign ($c_j$) or continuous distribution ($d_j$) channels (Equation 2). Secondly, we use $q^0$ to denote the proportion of the population with access to an ITN from a campaign relative to access to any ITN immediately post-campaign, which is assumed to be the same following all campaigns for a given region (Equation 3); the relative proportion with access to an ITN from continuous distribution channels at these times is therefore given by $1-q^0$ (Equation 4). Thirdly, we assume logistic-type growth in access achieved immediately following each subsequent campaign, denoted by $p_j^0$; this growth is characterised by the parameters ${\beta }_j^0$ and ${\beta }_j^t$ (inverse-logit function in Equation 5), and is bounded by an upper limit, $\psi$. We therefore also implicitly assume logistic-type growth in access to ITNs from continuous channels over time ($p_j^0$ in Equation 4) and ITNs distributed through campaigns over time ($p_j^0$ in Equation 3). Finally, we assume access to campaign nets decays following mass campaigns (exponential term in Equation 3); the rate of this decay is governed by the decay parameter, λ, which is related to the mean retention time (${\mathrm{\Lambda }}^{-1}$) such that:

where retention times are assumed to be the same for all nets irrespective of their distribution channel. In contrast to the earlier hierarchical model, the discrete-time model and subsequent intervention impact projections assume random allocation of ITNs in deriving the updated estimates of mean retention time (Equation 6). Under this assumption, at the point of distribution, an individual already with access to an ITN has the same probability of receiving a new ITN as an individual currently without access. Further details on how retention times are inferred from the approximation in Equation 6 can be found in Appendix 4.4 ITN retention under random allocation.

We do however use our regional posterior estimates of mean ITN retention times from our previous hierarchical model (which assumed ITNs are only distributed to those without access) as informative priors for mean retention times under random allocation to aid parameter identifiability. Either non-informative or regularising priors are used for other region-specific parameters (see Appendix 4.2 Prior distributions for further details).

When fitting our model in Stan with the R interface CmdStanR (v0.7.1, Gabry et al., 2024), we accounted for the potential of individual-level access (and indeed use, in that context) to vary subregionally; for example, between different wards or districts. Indeed, examination of the raw data (e.g. Figure 2—figure supplement 1A) indicates substantial variability in the recorded proportions of use and access in adjacent months. This may reflect substantial subregional variability, and there are likely other covariates that our model does not account for that will create additional variability in the probability of access (and use) within an administrative-one unit at any given point in time. Our discrete-time model thus far describes the proportion of the population with access ($p_j$ in Equation 2). However, we also consider the probability of individuals having access at each time $t_j$, which is denoted by ${\tilde{p}}_j$. We do not assume the probability of access is the same for all individuals in a region at a given point in time. Instead, we assume the probability any given individual has access to an ITN at time $t_j$ can be described by a Beta distribution:

Under this assumption, the mean probability of access across all individuals at a given time is equal to the overall proportion of the population with access. Meanwhile, for a given proportion of the population with access, the overdispersion parameter, denoted by ${\alpha }^0$, is approximately inversely proportional to the variance in the probability of individual-level access. This overdispersion parameter, which is fitted for each region and assumed to remain constant for each over time, therefore controls the estimated level of subregional heterogeneity in access. DHS data on the total number of surveyed individuals by month, in addition to the number with access to ITNs from different sources, are accounted for in our likelihood specification for region-specific access over time and the relative contribution towards this from campaign and continuous distribution channels. Further details can be found in Appendix 4.3 Likelihood specification.

With the exception of panels B and C, respectively, in Figures 2 and 5 (and associated Figure Supplements), Figures 1–5 are generated using predictive posterior estimates from our discrete time model. Current mean estimates under triennial (or biennial) campaigns (Figure 3) are inferred from Equations 2–5 over a 3- (or 2-) year period had a hypothetical campaign been conducted in every region at the start of January 2025, using posterior parameter estimates for December 2024 (the end of the period of included surveys). Estimates of the proportion of the population with different probabilities of access (and use) are then inferred from this using Equation 7 (Figure 4). This provides a measure of equity in use and access of nets within a region which will have important policy implications for distribution strategies.

The future scenarios considered were no future ITN distribution, continuous distribution in isolation, in addition to biennial and triennial campaigns with supplementary continuous distribution. Distribution of pyrethroid-PBO ITNs is assumed in all regions prior to December 2024. Distribution of different ITN classes (pyrethroid-only, pyrethroid-PBO, or pyrethroid-chlorfenapyr) is simulated from January 2025 onwards for each distribution strategy. Biennial and triennial distribution strategies are, respectively, simulated to commence either 2 or 3 years following the median estimate of the last estimated campaign prior to 2025. For strategies with campaigns, clinical cases are recorded over a 6-year interval commencing on the first simulated campaign after December 2024. Clinical case estimates for continuous-only distribution and no future distribution are recorded over a 6-year period commencing on the mid-point between the start of the recorded 6-year biennial and triennial scenarios, should these differ for a region. For each subnational region, 100 stochastic realisations were simulated for a population of 100,000 individuals, and cases averted were calculated relative to the baseline scenario with no future ITN distribution. For each realisation, parameters are drawn from our joint posterior distribution of fitted parameters from our discrete-time model of use, however ongoing logistic growth in use of ITNs from continuous channels and immediately following campaigns is not assumed beyond December 2024. Future campaigns, whether conducted every 2 or 3 years, are therefore assumed to achieve a consistent initial level of use. Since epidemiological dynamics are only dependent on whether ITNs are ultimately used, our simulations are agnostic of our access estimates. For each realisation and distribution event, parameter draws are also made from previously generated posterior distributions of the probability of repellency and mortality at different pyrethroid-resistance levels; these were fitted to data from systematic reviews of experimental hut trials across Africa (Sherrard-Smith et al., 2022; Churcher et al., 2024). Region-specific uncertainty in ITN efficacy, use, retention, and the relative contributions of continuous and campaign channels is therefore propagated through to our estimates of cases averted.

Regional differences in transmission intensities are accounted by calibration of historical baseline estimates of the entomological inoculation rate (EIR) prior to the introduction of any interventions. Baseline EIR estimates were calibrated by fitting our modelled annual mean P. falciparum prevalence in children between the ages of 2 and 10 (PfPR₂₋₁₀) to those estimated by the Malaria Atlas Project, which were compiled with the site (v0.2.2) R package (Winskill, 2024b; Figure 2B). Forecasted increases in pyrethroid resistance were incorporated, while coverage of other interventions (including IRS, SMC, drug treatment, and vaccination) was assumed to be maintained at 2024 levels in each region; these were estimated using the site (v0.2.2) R package (Winskill, 2024b) package.

Future projections were generated using malariasimulation (v1.6.0) (Charles et al., 2024), an individual-based malaria transmission model that incorporates typical seasonal patterns in transmission. The transmission dynamics model, which incorporates typical seasonal patterns in each region, is broadly able to reproduce the observed changes in PfPR_6−59mo, as estimated by DHS surveys, providing some confidence in the resulting epidemiological predictions. However, while the model captures typical seasonal dynamics, it does not account for inter-annual variation or specific weather events. These factors may have contributed to larger deviations from DHS PfPR_6−59mo point estimates at certain times; estimates that themselves often have wide 95% credible intervals (Figure 2B). Full details of model calibration, ITN efficacy parameters, and simulation procedures are provided in Appendix 5.

The methods used here can be divided into four main steps. Firstly, the mean durations of use and access (retention time) are initially estimated from a hierarchical model fitted to the pooled age distributions of ITNs that were used or provided access (Appendix 1—figure 1A, with further details in Appendix 2). ITN use is inferred from DHS data (ICF, 2025) on whether individuals slept under an ITN the previous night. While all individuals who used an ITN are assumed to have access, when fewer than two individuals used an ITN, that ITN is assumed to be able to provide access to up to two individuals in total within a household. Under this assumption, when ITNs in a household can provide access to more individuals than the number of users, access is assigned at random to non-users within each household under our framework. DHS data were obtained throughout with the RDHS R package (v0.8.4) (Watson et al., 2019).

Secondly, the timings of campaigns are estimated at a monthly resolution for each subnational region (Appendix 1—figure 1B, with further details in Appendix 3). This step utilises annual ITN deliveries by country from the (The Alliance for Malaria Prevention, 2024) Net Mapping Project and the monthly empirical distribution of delivery dates from DHS surveys (ICF, 2025). Initial estimates of retention times are used to correct for sampling bias due to older ITNs being less likely to be observed in DHS surveys.

Thirdly, inferred use and access of ITNs from different channels from DHS surveys are used to fit discrete-time models of historical use and access for each subnational region (Appendix 1—figure 1C, with further details in Appendix 4). This utilises previously generated estimates of when campaigns occurred in each region. ITN retention estimates are re-fitted during this process, with previously generated estimates used as informative priors.

Finally, clinical case estimates are generated for different ITN distribution strategies using our estimates of the mean duration of use, the level of use achieved immediately following a campaign, and the relative contribution to use from campaign and continuous distribution channels for each subnational region (Appendix 1—figure 1D, with further details in appendix 5). Simulations are parameterised for different ITN types using estimates of the probability of repellency and mortality (Churcher et al., 2024; Sherrard-Smith et al., 2022) for region-specific estimates of pyrethroid resistance from the site R package (v0.2.2) (Winskill, 2024b). Simulations also account for other region-specific characteristics, including demography, seasonality, and non-ITN interventions using the site package. Historical estimates of ITN use and region-specific characteristics from the site package are used alongside mean annual PfPR estimates from the Malaria Atlas Project, also compiled by site, to calibrate historical entomological inoculation rates (EIR) prior to the introduction of interventions using the cali R package (v1.0.8) (Winskill, 2024a). Clinical case projections are then estimated using the individual-based transmission dynamics model malariasimulation (v1.6.0) (Charles et al., 2024) for different future ITN distribution strategies.

Appendix 1—figure 1

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Additionally, in relation to uncertainty estimates, credible intervals are shown for all subnational quantities that are directly estimated in our models. National and continental values are reported as population-weighted summaries of the median subnational estimates generated from the discrete-time models (Appendix 4) and therefore do not correspond to explicitly estimated model parameters, so credible intervals are not shown for these aggregated estimates.

Throughout this study, we assume that a net $l$ in given region $i$ is used continuously each night over some period of time, ${\rho }_{il}^u$, but may provide access for a different period, ${\rho }_i^a$. We also assume that nets in region $i$ cease to be used and are disposed of by households at constant, but not necessarily equal, rates ${\gamma }_i^u$ and ${\gamma }_i^a$, respectively, such that:

where $x=u$ and $x=a$ in the contexts of use and access, respectively. Unless otherwise stated, both use and access are treated as proportions of the population throughout. The expected mean duration of use and access (the retention time) of nets are assumed to be $1/{\gamma }_i^u$ and $1/{\gamma }_i^a$, respectively. Here in Section 2 Initial estimation of ITN retention times, ITNs are assumed to be distributed without replacement (i.e. only individuals without an ITN would receive one), though this is relaxed later when fitting our historical estimates of use and access (Appendix 4), and when simulating future impact projections (Appendix 5). However, throughout this study, the durations of use and retention time are always estimates of how long an individual continues to use or have access to a net in the absence of future replacement; estimates of these are therefore reflective of behaviour or ITN durability and not distribution patterns themselves.

The remainder of Section 2 Initial estimation of ITN retention time is presented for inference of the mean duration of access, or retention time. Aside from subsetting the data for nets that are used, instead of those that provided access, the methodology is otherwise identical for inferring the mean duration of use and is repeated independently in that context. We therefore drop superscript notation previously used to explicitly indicate access-specific parameters.

For clarity, the notation used in this appendix is summarised at the end in Appendix 1—table 2.

2.2. Bayesian hierarchical model

Given Equation 9, provided a mass campaign strategy is suitably long-established where a large number of surveys have been conducted over time, the mean retention time can be estimated from the mean of an exponential distribution fitted to the empirical age distribution of ITNs that provided access across all recorded DHS surveys. Additionally, the limit behaviour in Equation 10 can be shown to hold both when surveys are conducted randomly or at regular intervals $\mathrm{\Delta }s$, provided that $\mathrm{\Delta }s\ne \mathrm{\Delta }t$ (Appendix 2—figure 1). Although these methods are presented in the context of access, they are repeated independently for use.

Appendix 2—figure 1

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In the case where $\mathrm{\Delta }s=\mathrm{\Delta }t$, the rate parameter in Equation 9 will lead to biased estimates for the decay rate; if surveys are consistently conducted soon after a mass campaign, the empirical age distribution will be biased towards younger nets, such that the fitted rate parameter for the distribution in Equation 9 would overestimate the true decay rate; the converse would hold true when surveys are consistently conducted immediately prior to a mass campaign. Given the frequency of DHS surveys can vary significantly between countries, for countries with fewer surveys, there is an increased risk this may lead to biased estimates in decay rates. For example, if surveys are systematically conducted immediately after a mass distribution campaign, this will lead to overestimates in the decay rates. Therefore, to attempt to reduce this risk of bias, we use a hierarchical model to pool information over larger spatial scales with the following positive-truncated normal (${\text{N}}_{>0}$) prior distributions:

Region-level prior:

(11) ${\displaystyle {\displaystyle {\displaystyle {\gamma }_i^{-1}\sim {\text{N}}_{>0}\left({\gamma }_{\zeta (i)}^{-1},{\sigma }_{\zeta (i)}^2\right)}}}$

Country-level hyperpriors:

(12) ${\displaystyle {\displaystyle {\displaystyle {\gamma }_{\zeta (i)}^{-1}\sim {\text{N}}_{>0}\left({\gamma }_0^{-1},{\sigma }_0^2\right)}}}$

(13) ${\displaystyle {\displaystyle {\displaystyle {\sigma }_{\zeta (i)}\sim {\text{N}}_{>0}\left({\chi }_0,{\omega }_0^2\right)}}}$

Continent-level hyperhyperpriors:

(14) ${\displaystyle {\displaystyle {\displaystyle {\gamma }_0^{-1}\sim {\text{N}}_{>0}\left(24,{12}^2\right)}}}$

(15) ${\displaystyle {\displaystyle {\displaystyle {\sigma }_0\sim {\text{N}}_{>0}\left(1,1\right)}}}$

(16) ${\displaystyle {\displaystyle {\displaystyle {\chi }_0\sim {\text{N}}_{>0}\left(1,1\right)}}}$

(17) ${\displaystyle {\displaystyle {\displaystyle {\omega }_0\sim {\text{N}}_{>0}\left(1,1\right)}}}$

Under our hierarchical model, there is a country-level random effect on the region-specific mean ITN retention time (${\gamma }_i^{-1}$, Equation 11). There is then a continent-level random effect on the country-specific mean ITN retention time (${\gamma }_{\zeta (i)}^{-1}$, Equation 12), where $\zeta (i)$ is the country of region $i$. Standard deviations are modelled in an analogous manner using a hierarchical structure (Equation 13).

We then used a weakly informative hyperhyperprior for the continent-wide mean retention time estimate (${\gamma }_0^{-1}$, Equation 14), with a mean and standard deviation of 24 and 12 months, respectively. A prior mean of 24 months broadly reflects findings from previous studies (Bhatt et al., 2015; Bertozzi-Villa et al., 2021), yet Equation 14 cautiously imposes a prior belief there is a 95% probability the continent-wide mean is between 3.9 and 47.6 months.

The between-country standard deviation in mean ITN retention time (${\sigma }_0$, Equation 15) is then assumed a priori to have a mean and standard deviation of 1 month. Since the central 95% range of a ${\text{N}}_{>0}(1,1)$ distribution is [0.08, 3.03], conditional on values of ${\sigma }_0$ near the upper tail of this prior would allow roughly 95% of country-level means to lie within approximately 6 months of the continental mean a priori. This is broadly in line with previous estimates by Bhatt et al., 2015 who estimated 85% (n=40) of sub-Saharan African countries had a median retention time between 1.5 and 2.5 years; the smooth-compact loss function assumed in that study leads to similar mean and median estimates. Imposing a marginally tighter inter-country variance than previous studies is nevertheless intentional. This is because the derivation that the age distribution of ITNs when pooled across surveys tends to the same distribution as the duration of continuous access assumes periodic distribution of ITNs is long-standing and that a sufficiently large number of surveys have been conducted without inherent bias in their timings relative to mass campaigns. While mass campaigns have been conducted for roughly an order of magnitude greater than expected ITN retention times, in countries where more Malaria Indicator Surveys (MIS), which are often conducted 6 months after a campaign, than other DHS surveys that are not timed in relation to campaigns, this may create an inherent bias that overestimates the decay rate of ITN use (and access). Assuming a random effect a priori with a slightly smaller variance than indicated in previous studies helps to mitigate bias arising from survey timings for data-sparse countries.

The mean (${\chi }_0$, Equation 16) and standard deviation (${\omega }_0$, Equation 17) of the inter-regional standard deviation of mean ITN retention times within each country (${\sigma }_{\zeta }$) are also assumed a priori to have means and standard deviations of 1 month. Here ${\chi }_0$ and ${\omega }_0$, respectively, govern the magnitude and variability of within-country heterogeneity in mean ITN retention times. Given the upper bound of the 95% range of these hyperhyperprior distributions is approximately 3 months, this would correspond to inter-regional standard deviations up to approximately 9 months in extreme cases where ${\sigma }_{\zeta }$ has values around ${\chi }_0+2{\omega }_0$. Conditional on such values, 95% of regional mean retention times would lie within approximately $\pm 2{\sigma }_{\zeta }\approx \pm 18$ months of the country mean. Although the hyperhyperpriors (which govern inter-regional variability) assumed in Equations 16 and 17 are the same as the hyperprior (which governs between-country variability) assumed in Equation (15), the model structure assumes random effects of greater magnitude between regions than between countries. As discussed, we have assumed a marginally narrower prior belief in inter-country variability than findings from previous studies (Bhatt et al., 2015; Bertozzi-Villa et al., 2021) to minimise the risk of survey timing biasing our estimates. Since DHS surveys and mass campaigns are often conducted at similar timings within a country, these biases are likely to be conserved across regions, allowing for greater scope to assume greater inter-regional variability a priori.

Under our assumption that nets are discarded at a constant rate within each subnational region $i$, the age, ${\alpha }_{il}$, of each net $l$ is modelled as exponentially distributed with rate ${\gamma }_i$. However, as DHS surveys do not record ages of nets greater than 36 months, but report them as being older than this threshold, we therefore treat these observations as right-censored at 36.5 months (due to whole-month rounding), giving a likelihood:

(18) ${\displaystyle {\displaystyle {\displaystyle \pi \left({\alpha }_{il}\mid {\gamma }_i\right)=\{\begin{array}{ll}f\left({\alpha }_{il};{\gamma }_i\right)& \text{, if}{\alpha }_{il}\le 36\\ 1-F\left(36.5;{\gamma }_i\right)& \text{, otherwise}\end{array}}}}$

where $f(\alpha ;\gamma )$ and $F(\alpha ;\gamma )$ are Exponential density and cumulative distribution functions, respectively.

To correct for non-random probabilities of households being sampled in DHS surveys, we also conduct the fitting process using pseudo-counts, $M_{ir}$, of the number of nets of a given age $\alpha =r$ in region $i$, where:

(19) ${\displaystyle M_{ir}=\left[\sum _{l=1}^{N_{ir}}{w}_{il}\right]}$

given $N_{ir}$ is the surveyed number of nets of age $r$ in region $i$, $w_{il}$ is the household survey weight for net $l$, while [·] denotes a standard rounding function. As DHS surveys have a stratified sampling design each household has a unique probability of being sampled within each region $i$. To account for these non-random probabilities of households being surveyed, each net $l$ that is recorded has an associated household weighting, $w_{il}$. The DHS also scales these weightings by a factor of 10⁶; our notation here of $w_{il}$ corrects for this scaling, and is therefore equal to the reported DHS household weightings divided by 10⁶.

After fitting our model in Stan with the R interface RStan (v2.32.6, Stan Development Team, 2024), we generated 1000 samples from each of the four MCMC chains after a burn-in period of 1000 iterations. This simulated 4,000 draws from the posterior distributions of the mean duration of use and retention time at subnational, national, and continental scales.

Our subnational posterior estimates of the mean duration of use and retention time are then used in Section C in estimating the timing of mass campaigns. They are subsequently used as informative priors and are re-fitted to observed use and access data in Section D. This subsequent re-fitting process aids in reducing potential biases arising from the relative timings of surveys and campaigns as discussed above, and further reduces the influence of prior assumptions made in the hierarchical model described in Equations 11–13.

It should also be highlighted that while we have assumed an exponential loss function for the duration of use and access, other studies, including those by Bhatt et al., 2015 and Bertozzi-Villa et al., 2021, have utilised an ‘S-shaped’ smooth-compact loss function. This was originally developed for the net procurement planning tool, NetCALC (available at: http://www.networksmalaria.org/networks/netcalc) (Paintain et al., 2013). This functional form was fitted to net age distribution data ($n>2500$ nets) across 12 surveys in Uganda prior to 2013 and was selected on the basis that the pooled observed age density peaked around 2 years and was sixfold greater than the density for newly distributed nets (Supplementary file 2, figure 2 in Paintain et al., 2013). Meanwhile for this study, discounting peaks at 12, 24, and 36 months (due to whole year rounding), the empirical age distribution broadly appears to be monotonically decreasing from month 6 onwards when pooled across all DHS surveys and countries included in this study (Appendix 2—figure 2a). However, the slight peak at month 6, which is twofold greater than at month 0, may be an artifact of MIS surveys often being conducted 6 months post-campaign, which would bias the sampled data to include more nets of this age. In light of potential survey artifacts and the largely monotonic decrease in net age, there was limited evidence against the use of an assumed exponential loss function from the data used in this study.

Appendix 2—figure 2

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The model presented in this section describes how we estimated historical trends in access. Aside from fitting the model to the number of individuals who used nets, $u_{ij}$, instead of those who had access, $a_{ij}$, in region $i$ at time $t_j$, the methodology is otherwise identical to how we estimated historical trends in use.