Heterogeneity of use, access and retention of insecticide-treated nets: implications for subnational tailoring to maximise malaria control

  1. Andrew C Glover
  2. Hannah Koenker
  3. El Hadji Amadou Niang
  4. Kate Kolaczinski
  5. Thomas S Churcher

  • Curated by eLife

    eLife logo

    eLife Assessment

    This paper provides a novel and valuable method improve the accuracy of predictions of the impact of insecticide-treated net (ITN)-based strategies for malaria control and elimination by using sub-national estimates of the duration of ITN access and use over time from cross-sectional survey data and annual country ITNs received. The authors propose a sophisticated methodological framework that accounts for many sources of uncertainty, providing compelling evidence.

Reviewed by

Read the full article

Discuss this preprint

Start a discussion What are Sciety discussions?

Listed in

Log in to save this article

Abstract

Insecticide-treated nets (ITNs) are the most impactful and cost-effective control tool against malaria. ITNs are primarily distributed through triennial mass campaigns across Africa, though overall ITN use remains modest in many areas as most ITNs do not last three years. In times of funding constraints and a lack of economic alternative antimalarial interventions it is unclear whether disease control could be best improved by distributing more effective ITNs (e.g. dual active-ingredient ITNs) and/or deploying nets more frequently. There are increased calls to improve allocation of resources through sub-national tailoring of interventions, though benefits will depend on how long people use ITNs and how this varies between subnational regions. However, subnational variation in ITN retention and the duration that ITNs remain in use have not previously been quantified. Here we estimate subnational differences in ITN use, access and retention for six countries, Burkina Faso, Ghana, Malawi, Mali, Mozambique and Senegal. These estimates are used to calibrate a Plasmodium falciparum transmission dynamics model to generate sub-national estimates of ITN use and cases averted under different ITN distribution strategies. On average, people use their ITNs for 21 months, though this varies substantially between subnational regions from 12 to 38 months. Shifting from triennial to biennial campaigns is predicted to lead to mean population use across all regions increasing from 41.7% to 49.6%. No regions of the 146 investigated were estimated to maintain use over 80% even under biennial distribution, though switching to dual active-ingredient ITNs would likely avert more cases under present distribution frequencies. Our results highlight that although transmission intensity remains an important factor for subnational tailoring of malaria control interventions, other factors, such as ITN use given access, meaningfully influence optimal deployment strategies. The framework highlights how routinely collected data can aid policymakers in tailoring disease control programmes at subnational levels.

Article activity feed

  1. eLife

    eLife Assessment

    This paper provides a novel and valuable method improve the accuracy of predictions of the impact of insecticide-treated net (ITN)-based strategies for malaria control and elimination by using sub-national estimates of the duration of ITN access and use over time from cross-sectional survey data and annual country ITNs received. The authors propose a sophisticated methodological framework that accounts for many sources of uncertainty, providing compelling evidence.

  2. eLife

    Reviewer #1 (Public review):

    This paper aims to improve the accuracy of predictions of the impact of ITN strategies by developing a method to estimate duration of ITN access and use over time on a subnational scale from cross-sectional survey data and the numbers ITNs received annually. The subnational estimates are then input into a mathematical model to predict clinical cases under different ITN distribution strategies.

    Strengths:

    The approach is novel and addresses a useful and timely topic. It makes use of available routine data, and has considered all of the relevant components of ITN distributions.

    The authors have made revisions, particularly to the methods, appendices and title - leaving the paper easier to follow, and with a clear, consistent aim. The assumptions are clearly stated.

    Weaknesses:

    The weaknesses are shared with other models of a similar complexity - it is not easy for a casual reader to fully understand the model or the implications of the assumptions which were required to be made. That routine data is used is good for availability, but data quality may be an issue in some places.

  3. eLife

    Reviewer #2 (Public review):

    Summary:

    The authors design a custom Bayesian model to estimate the probabilities of access, use and use given access of insecticide-treated nets in six African countries, providing sub-national estimates and inferring the average duration of ITN use and access. An individual-based model was employed to simulate malaria epidemics and estimate the effectiveness of different ITN distribution strategies. The study finds that the mean probability of use or access did not reach 80% (a universal coverage formerly targeted by WHO) for any of the regions even for biennial campaigns, demonstrates that switching from triennial to biennial distribution campaigns increases population use by 7.9%, and evaluates the impact of employing more efficient ITNs on P. falciparum prevalence.

    Strengths:

    The authors developed a data-driven model that accounts for data collection imperfections and sources of uncertainty while differentiating between ITN use and access. They developed a methodology to infer the timing of mass campaign from publicly available data instead of assuming fixed dates. The probability of use given access allows determining the regions where ITN distribution is least effective. This work can help better inform future interventions by identifying regions where increasing mass campaign frequency or employing better ITNs are most effective. Finally, in addition to insights on ITN access and use for the six countries analyzed, the paper contributes with a methodological framework that can likely be extended to other countries.

    Weaknesses:

    Since the models employed are rather complex, the methodology description may be hard to follow for some readers. In addition, the models assume many hypotheses, including exponential decay of ITN use/access and narrow prior distributions. It is worth noting that, in the revised version of the manuscript, the authors justified the choice of exponential decay and narrow prior distributions, and made a significant effort to clarify the methodology and the model equations.

    Comments on revised version:

    I appreciate the improvements made to the text. The methodology description is much clearer now. I have no further suggestions.

  4. eLife

    Author response:

    The following is the authors’ response to the original reviews.

    Public Reviews:

    Reviewer #1 (Public review):

    Summary:

    This paper provides a novel method to improve the accuracy of predictions of the impact of ITN strategies, by using sub-national estimates of the duration of ITN access and use over time from cross-sectional survey data and annual country ITNs received.

    Strengths:

    The approach is novel, makes use of available data, and has considered all of the relevant components of ITN distributions.

    Weaknesses:

    (W1.1) The main message of the paper was not very clear, and did not seem to fit the title. The title focuses on sub-national tailoring of ITN, but the abstract did not feature results directly about SNT. It was not very clear what the main result of the paper was - there are several ITN observations in the results and discussion. Most did not seem to be directly about SNT, but rather sub-national differences in use and access were accounted for in the analyses. It was not clear if the same conclusions would be reached without accounting for sub-national differences, but the estimates and predictions could be expected to be more accurate.

    Thank-you for highlighting this. We agree the title could be improved to better reflect the main messages of the paper and have now updated it to “Heterogeneity of use, access and retention of insecticide-treated nets: implications for subnational tailoring to maximise malaria control”. All parameters are estimated at a subnational level; this is not always the case a national level. We therefore do not have national-level models without subnational differences that our results could be compared to.

    (W1.2) Some of the results seemed to me to be apparent even without a modelling exercise (eg high coverage could not be maintained between campaigns, use would be higher with 2-yearly distributions rather than 3-yearly) or were not in themselves new insights (eg estimates of the duration of use). It would be helpful to clearly state what the novel results are in the abstract, the first paragraph of the discussion and the conclusions, and to make sure that the title is consistent.

    It is our understanding assessments on ITN coverage are often made from infrequent surveys, for example from MIS. These are typically conducted six months postcampaign and may miss notable reductions in use and access beyond this. Comparisons on ITN use and access are also frequently made directly between DHS surveys, which can be misleading in isolation if the time between campaigns and surveys is not considered. We have tried to highlight this more clearly in relation to Burkina Faso with the following text:

    “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.”

    We do believe modelling exercises, such as the methodology presented here, can help generate improved estimates of ITN use and access over time than estimates from surveys alone, which can be biased by the relative timings of campaigns. It is also our understanding previous studies have generated national estimates of ITN retention. We are not aware of any previous studies that have estimated the duration ITNs continue to be used for, which is arguably of greater epidemiological importance than retention time. To best knowledge, these have also not been estimated at subnational scales previously.

    We acknowledge the novelty of some results were not clearly presented previously and are grateful to the reviewer for highlighting this. We have now highlighted some of the novel findings more clearly in the abstract, with the following text:

    “However, subnational variation in ITN retention and the duration that ITNs remain in use have not previously been quantified.”

    “Our results highlight that although transmission intensity remains an important factor for subnational tailoring of malaria control interventions, other factors, such as ITN use given access, meaningfully influence optimal deployment strategies.”.

    We have also highlighted the novelty and relevance of our findings more clearly in the first paragraph discussion, with the following text:

    “Funding constraints have also increased the need for consideration of subnational tailoring, with many recommendations being made on the basis of transmission intensity in the World Health Organisation (2025) Subnational Tailoring Reference Manual. However, a key uncertainty in assessing the potential impact of different ITN interventions has been how long nets remain in use rather than how long they are retained, and how this varies between regions. Here, to our best knowledge, we present the first estimates of subnational variation in ITN retention and the duration that ITNs remain in use, and also quantify for the first time how ITN use, access and retention vary between subnational regions across multiple African countries. Our work supports the change in guidance to optimal coverage as it highlights ITN interventions have notable differences in impact between settings, and that distributing fewer but more effective ITNs, particularly pyrethroid-chlorphenapyr products, is likely to be more impactful than maximising long-term coverage through increased campaign frequencies with pyrethroid-only ITNs. Our work also broadly supports World Health Organisation (2025) recommendations for subnational tailoring, particularly the consideration of deprioritisation of ITN distribution in very low transmission settings. However, our results provide new indications that deprioritisation of areas with higher ITN use given access may lead to greater resurgences in cases, highlighting that subnational tailoring decisions could be optimised further by considering additional factors to transmission intensity alone.”

    The novelty and relevance of our results are also now highlighted in the following text, which has been incorporated into the concluding paragraph:

    “In conclusion, the work indicates that universal coverage targets of 80% are unlikely to be consistently met due to waning overall ITN use in the intervening years between triennial mass campaigns. Improved coverage can be achieved through more frequent biennial distributions, though this is unlikely to be feasible at scale given the current funding landscape. Indeed, when resources are constrained, deprioritisation of ITN mass campaigns in certain settings is being increasingly considered through subnational tailoring of malaria control interventions. Our work highlights that the relationship between transmission intensity (whether measured in terms of prevalence or clinical cases) and intervention impact is non-linear, and notable resurgences in cases may follow when campaigns are deprioritised in all but very low transmission settings. This broadly supports WHO subnational tailoring guidance, which suggests consideration of deprioritising distribution of ITNs in regions with PfPR2-10 < 1% (World Health Organization, 2025). However, while the World Health Organization (2025) Subnational Tailoring Reference Manual proposes that the withdrawal of ITNs in favour of indoor residual spraying should be considered in areas with low ITN use, here we estimate that ITN use alone appears to be a notably poorer predictor of the impact of ceasing mass campaigns than use given access. Our findings suggest that regions with higher use given access may experience disproportionately greater resurgences in cases following deprioritisation. This implies that regions with low use given access may warrant consideration for cessation of ITN distribution, rather than decisions being based solely on low overall ITN use irrespective of whether communities have sufficient ITN access. However, subnational differences in ITN use, access and retention are key knowledge gaps in many settings, and when estimated from infrequent surveys they are highly sensitive to bias arising from the timing of surveys relative to when campaigns were conducted. To our knowledge, this study is the first to estimate subnational variation in ITN retention and the first to estimate the duration that ITNs remain in use, which is of greater epidemiological relevance than retention time. It also provides a novel framework to correct for biases in estimates of ITN use and access arising from when campaigns were conducted. Although campaigns have historically aided increasing ITN use and access over time, we estimate the mean duration of ITN use is consistently shorter than mean retention times in all regions. This raises questions about whether punctuated distribution of ITNs through campaigns is the optimal mechanism for maximising their effectiveness and cost-effectiveness. Maximising the cost-effectiveness of interventions has become increasingly pertinent in the current funding context, and consideration of alternative distribution strategies, such as increased distribution through continuous distribution channels, including school- or community-based distribution, may be warranted. Frameworks such as the one presented here, which take into account the potential for impact from different net types and the high variability of ITN duration and use, could support NMP decision making on how best to maximise impact from available funds. Whilst such frameworks may be a useful tool, local knowledge of factors impacting ITN access and use as well as operational decision making will be paramount for NMP-led tailoring of subnational strategies.”

    (W1.3) On L236, the link to SNT is stated: "the models indicate trends that can support subnational tailoring of ITNs". They could indeed, but SNT itself is not done in this paper. It seems to be about improving sub-national predictions of the impact of single ITN strategies, by taking into account sub-national variation in access and use duration. This is useful, and the model developed has novel aspects.

    Thank-you for highlighting this. We hope our updated title and response to W1.12 below help address this. Where relevant we have also framed our findings in relation to the World Health Organization’s Subnational tailoring of malaria strategies and interventions: refence manual which was published following our original submission; examples of this are highlighted in our response above to W1.2.

    (W1.4) Individual countries may have records on when nets were distributed to the regions rather than needing to use the annual country number of nets together with the DHS data. It could be helpful to say what the analysis steps would be in that case.

    We have now added the following text of appendix 3.2 to clarify how the methodology could be adapted:

    “In contexts where national malaria programmes or other stakeholders have knowledge of the timings of mass campaigns (i.e. when there is no uncertainty in ɸij), the methodology can be adapted by deterministically evaluating the time since the last campaign (equation S18) for each time point.”

    (W1.5) There were several assumptions that needed to be made in building the model. There is some validation of the timing of the distributions (L633 "verified where possible through discussion with interested parties nationally and internationally") and the fit of estimated access and use to survey data, and agreement between predictions of prevalence and MAP estimates. It would be helpful to say which assumptions are important for the results (and would be key knowledge gaps) and which would not make a difference. It might be possible to validate the net timing model using a country where net distributions are known reasonably well.

    Thank-you for raising this. We acknowledge that to investigate which assumptions are less likely to make a meaningful difference, we would ideally have conducted a full sensitivity analysis on these. This however would be challenging, since many of these are structural assumptions rather than numerical ones (for example, the assumption of an exponential decay in use and access) which would require the entire methodology to be adapted to conduct a sensitivity analysis. We did validate our estimated campaign timings against some known subnational campaign timings for Senegal. However, we could not source data on when all campaigns were conducted for all regions of Senegal to the nearest month to be able to conduct validation against this. We were also not able to source other use and access data from separate data sources to the DHS to be able to validate our discrete-time models of historical use and access. PfPR2-10 estimates are however fitted to equivalent MAP estimates. These were validated against DHS estimates of PfPR6-59mo, which were not used at any stage to fit our models. We have made slight changes to the original wording in relation to this at the end of appendix 5.2.

    (W1.6) What was assumed about what happens to old nets after a mass campaign was not clear. This assumption is likely to affect the predictions of access for the biennial distributions.

    To generate our initial estimates of the mean duration of use and retention time with our hierarchical model, we assume nets are only distributed to individuals who do not already have ITNs (appendix 2). This initial step is necessary for our methodology, but is relaxed later under our discrete-time model where we assume ITNs are distributed at random such that individuals with an ITN are equally likely to receive a new ITN (and replace their existing one) following a mass campaign (appendix 4). Much of the aforementioned sections has been rewritten and we hope this is now clearer.

    (W1.7) L312 and elsewhere: That use given access declines with net age is plausible. However, I wondered if this could be partly a consequence of the assumptions in the model (eg the two exponential decays for access and use, the possible assumption that new nets displace the current ones when there is a mass campaign).

    Declining use given access as nets age is not affected by model assumptions. Due to being fitted independently of each other, there are no constraints that would prevent a faster decay in access than use. Had the data supported this, this would have led to use given access increasing over time since the last campaign. The data did not support this. Further clarification that use and access are fitted independently of each other is has now been provided in the following text:

    “All subsequent analyses described are conducted independently for use and access”

    (W1.8) The Methods section on Estimating historical use and access seemed to be aimed at readers familiar with formulae, but I think it could lose other interested readers. It could be useful to explain a little more about what is happening at each step and also why.

    Thank-you for highlighting this. We have re-written this section in the main manuscript, now named ‘Historical use, access and retention times’, where we now only highlight key equations and provide a high-level overview of the methodological steps. We have sought to provide clearer explanations here behind the rationale for each step to ensure maximum accessibility for interested readers. The original wording was used as a basis for the newly provided series of appendices which provide further technical detail; this wording has also been heavily re-drafted to improve clarity of each step.

    (W1.9) The model was fitted to MAP estimates of PfPR2-10, which themselves come from a model. It may be that there is different uncertainty in the MAP estimates for different regions. I couldn't see this on the graph, but maybe the uncertainty is small. Was this taken into account in the fitting?

    We only used median MAP estimates of PfPR2-10 to calibrate the baseline EIR for each region in our model. We have clarified our rationale in appendix 5.2:

    “Since the relationship between baseline EIR and PfPR2-10 here is specific to malaria simulation, MAP uncertainty estimates were not propagated through to our estimates in baseline EIR since these would not faithfully represent its true uncertainty.”

    (W1.10) Was uncertainty from each estimated component integrated into the other components?

    Thank-you for highlighting this as this indicates we had failed to clearly indicate this. To confirm, we propagate uncertainty in each component through to our estimates of cases averted. New text has been provided to clarify this in the following text:

    “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.”

    Further details are also provided in the preceding text of the same paragraph. The central 95% credible intervals of cases averted shown in figures 5.C and 6 and associated figure supplements are reflective of this uncertainty.

    (W1.11) Eyeballing Figure 2 (Burkina Faso), there is a general pattern of decline in all the regions, some differences between the regions and some differences in how well the model fits between the regions. If possible, it could be helpful to say how much better the fit was when using regionspecific compared to countrywide parameter values for access and use, and how different the results would be.

    In the “Universal coverage: was it achievable under triennial mass campaigns” results section, we have now provided further emphasis that the observed decrease from DHS data may be driven by surveys being conducted progressively later in relation to the last campaign:

    “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.”

    In the case of Burkina Faso (figure 2.A), aside from months when very small numbers of individuals were surveys where either 0% or 100% use or access was reported, no other data lie outside our 95% credible interval for any region.

    We are unable to generate comparisons with countrywide parameters as these are not generated when fitting our discrete-time model, even though they are a by-product of the initial hierarchical model used to generate initial estimates of region-specific ITN retention, which was a necessary methodological step. We hope the extensive revision of the text in the methods and appendices helps to improve the clarity on this. Where national estimates are provided, these are population-weighted means of the subnational median posterior estimates. New text is included in appendix 1 to clarify this:

    “National and continental values are reported as population-weighted summaries of the median subnational estimates generated from the discrete-time models”

    (W1.12) The question of moving from a campaign every three to every two years may not be the most pertinent question in the current funding landscape. I realise that a paper is in development for a long time, but it would be helpful to comment on what else the model could be used for when fewer rather than more nets are likely to be available.

    We acknowledge the funding landscape has changed substantially, but we still believe this work has important implications in the current context. We have emphasised this further in the following text:

    “If budget constraints necessitate the deprioritisation of campaigns, our results highlight that this should be avoided, if possible, in regions with moderate to high transmission intensity, particularly those with mean annual incidence exceeding 100– 150 clinical cases per 1,000 people. Shortening campaign intervals from three to two years in moderate- and high-transmission regions is projected to avert more cases than the additional cases that may arise from ceasing campaigns in some lower-transmission settings. Additionally, although pyrethroid–chlorfenapyr ITNs are more costly, the additional cases projected to be averted by them relative to pyrethroid-only and pyrethroid–PBO ITNs are substantial. In certain national contexts it may be more cost-effective for biennial pyrethroid-chlorfenapyr campaigns to be conducted in fewer subnational regions even under reduced budgets. However, more thorough economic analyses will be needed to understand this fully. Moreover, as ITNs remain one of the most cost-effective malaria control interventions, improving the impact of them could still be more cost-effective than the introduction of new untested interventions (Topazian et al., 2023; Schmit et al., 2024).”

    We have also related some of our findings to the WHO Subnational Tailoring Reference Manual (as highlighted in W1.2), which we hope better relates our findings to the current context.

    Reviewer #2 (Public review):

    Summary:

    The authors design a custom Bayesian model to estimate the probabilities of access, use and use given access of insecticide-treated nets in six African countries, providing sub-national estimates and inferring the average duration of ITN use and access. An individual-based model was employed to simulate malaria epidemics and estimate the effectiveness of different ITN distribution strategies. The study finds that the mean probability of use or access did not reach 80% (a universal coverage formely targeted by WHO) for any of the regions, even for biennial campaigns, demonstrates that switching from triennial to biennial distribution campaigns increases population use by 7.9%, and evaluates the impact of employing more efficient ITNs on P. falciparum prevalence.

    Strengths:

    The authors developed a data-driven model that accounts for data collection imperfections and sources of uncertainty while differentiating between ITN use and access. They developed a methodology to infer the timing of a mass campaign from publicly available data instead of assuming fixed dates. The probability of use given access allows for determining the regions where ITN distribution is least effective. This work can help better inform future interventions by identifying regions where increasing mass campaign frequency or employing better ITNs are most effective. Finally, in addition to insights on ITN access and use for the six countries analyzed, the paper contributes a methodological framework that can likely be extended to other countries.

    Weaknesses:

    Since the models employed are rather complex, the description of the methodology may be hard to follow for most readers. In addition, the models assume many hypotheses, including:

    (W2.1) Exponential decay of ITN use/access.

    We do acknowledge different modelling studies have typically assumed either an exponential decay or an “S-shaped” smooth-compact loss function, with many of these studies having been validated against cluster-randomised trial data for both functional forms. We believe the ITN age distribution data across the DHS surveys inspected provides reasonable evidence to support the use of an Exponential decay function here. We have now included a proof (appendix 2.1) demonstrating an exponentially distributed ITN age distribution will be yielded for an exponential decay function with the same rate parameter; this is true under periodic ITN distribution and becomes an approximation for a finite number of surveys. We now also included additional text (appendix 2.2) highlighting the empirical ITN age distributions appear to support our exponential decay assumption.

    (W2.2) The decay rates for the probability of the ITN repelling and killing a mosquito are the same.

    Although the same decay rate parameter (\gamma_N) is present in our expressions for the probability of repellency and mortality (equations (53) and (54)), the half-life of the latter is shorter, since repellency is assumed to decay towards a constant value. These structural forms are not unique to this paper but are shared among all malaria simulation-based studies with ITN interventions. This decay rate parameter has been estimated in previous studies (Sherrard-Smith et al., 2022; Churcher et al., 2024), and we carry through uncertainty estimates from those previous studies into the work presented here; additional text has been added to clarify this:

    “Uncertainty in ITN repellency and mortality parameters (equation (53) and (54)) is also propagated forward to this study by simulating random draws from previous posterior distributions (Sherrard-Smith et al., 2022; Churcher et al., 2024) across each distribution event and realisation.”

    (W2.3) Given a time instant, all individuals in the same administrative unit and have the same probability of using a net;

    Our discrete-time model estimates the proportion of the population with use and access at each time instant. We purposefully do not conflate this with the probability of use and access, which can vary between individuals within the same subnational unit of analysis (urban and rural regions of each administrative-one area). We are grateful this point has been raised as it indicates we had not communicated this sufficiently clearly before. We hope the extensive re-draft of the ‘Historical use, access and retention times’ methods section has helped address this, in particular in the following text preceeding equation (7):

    “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 tj can be described by a Beta distribution”

    (W2.4) ITN use/access decay models do not depend on the distribution strategy (e.g. bienal vs trienal distribution).

    We may not have fully understood this point, but in terms of our historical models of use and access, assumptions are not imposed on the frequency of previous campaigns. Instead, historical campaign timings are estimated from data from DHS surveys and the AMP Net Mapping Project (now detailed in appendix 3.1); historical estimated intervals could be either two or three years (or indeed any interval) as informed by this data. In terms of the duration of use and retention time, these are estimates how long a net would continue to be used, or provide access, if an individual were not to replace it at earlier date; these estimates are therefore independent of campaign intervals, and we have now added addition text to provide additional clarity:

    “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.”

    We do acknowledge under our approach, use immediately following a campaign is agnostic of campaign frequency; however, given an absence of data on how use changes following a switch from triennial to biennial campaigns, we believe this was a reasonably conservative assumption. Further confirmation is now provided in the following text, with additional preceding context:

    “Future campaigns, whether conducted every two or three years, are therefore assumed to achieve a consistent initial level of use.”

    (W2.5) The Bayesian model assumes some narrow prior distributions.

    Thank-you for highlighting this. We acknowledge the need for further justification for the choice of priors. We have provided this in depth for the hierarchical model of the mean duration of use and access (in appendix 2.2). Further justification for the choice of priors for the discrete-time model are also now provided in appendix 4.2).

    The impact of these hypotheses on the estimated parameters is not explored in the paper, and no sensitivity analyses are performed, although some limitations are discussed.

    We fully acknowledge we had not conducted sensitivity analyses for many of our assumptions, and we have now tried to provide better justification for our assumptions. The assumptions most likely to influence inference are structural components of the modelling framework rather than scalar parameters that can be varied independently in a conventional sensitivity analysis. Many of the assumptions highlighted above are structural, such as the assumption of an exponential decay (W2.1). In the case of our assumption of exponential decay, multiple elements of the methodology are restricted by this (for example, when correcting for biases that arise from nets being lost between campaigns and survey times when estimating the timing of campaigns in appendix 3.1). Investigating the sensitivity of this assumption over an assumed smooth compact function would require extensive adaptation of the methodology that would be beyond the scope of this paper. Some other assumptions, such the assumption of the same decay rate parameter for repellency and mortality (W2.2) have been estimated in the previous studies referenced and have been validated against cluster-randomised, controlled trials. We nevertheless recognise our justification of some assumptions could have been expanded upon previously, and we hope the changes highlighted above go towards addressing this.

    Recommendations for the authors:

    Reviewer #1 (Recommendations for the authors):

    (R1.1) I looked for the reference WHO 2024b for the recent optimal allocation guideline, but there were just three WHO 2024 references in the bibliography. In addition, what exactly the 80% rule applies to is not clear - this could be explained so it is clearer what result to compare to it (or explain that the rule itself is not clear).

    We have used the eLife LaTeX/BibTex template for citations throughout and acknowledge this doesn’t show letter suffixes in the reference list for multiple author-year entries. We unsure of how to address this given this is generated by the official template, though we note that when citations are clicked on in the document, the relevant citation is then shown at the top of the page on the web version.

    (R1.2) L24 'estimated', but this seems more like a prediction. The words 'estimated' and 'predicted' should be carefully used throughout when combining statistical and mechanistic modelling.

    This has now been changed.

    (R1.3) The point estimates should always have measures of uncertainty.

    The rationale for the omission of credible intervals for some point estimates has now been clarified in the manuscript (appendix 1). The following text has been added:

    “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.”

    (R1.4) It would be helpful to justify the choice of ADM1 as the geographical unit.

    We have clarified the rationale for this on the following text:

    “Here, (subnational) regions are defined as the first administrative unit below the country level and are further divided into rural and urban areas to align with DHS stratification”

    (R1.5) The terminology was slightly confusing: in some places, it sounded as if regions were the sub-national regions, in others as if they were different things (eg L74, L105). L45 'and' seems odd here.

    ‘Region’ is used interchangeably with ‘subnational region’ at points in the paper to aid the flow of the text. We hope the use of paratheses around (subnational) in the updated text quoted above (and on the following text) helps provide clarity:

    “here, the units of analysis are consistently referred to as (subnational) regions”

    (R1.6) Spurious accuracy in some estimates, e.g. L52.

    This was a result cited from Bertozzi-Villa et al. (2021) for which uncertainty estimates were not available. We hope the response to R1.3 above helps clarify the rationale for omitting credible intervals for some estimates generated here.

    (R1.7) L68 'lose' instead of 'loose'.

    Now corrected.

    (R1.8) L534. I suspect that the model was actually fitted in Stan via the R interface rstan.

    Language adjusted accordingly.

    (R1.9) L633 'through' rather than 'though'.

    This section has been heavily redrafted and we have checked for typos.

    Reviewer #2 (Recommendations for the authors):

    The paper is well-written and presents an important contribution to better aid interventions. The proposed models are reasonable, but because of their complexity, even readers who work with epidemic modelling might have issues understanding the methodology.

    We thank the reviewer for highlighting that the methodology may be difficult to follow. The methods section has now been substantially rewritten to provide a clearer conceptual description of the modelling framework, with detailed model specification and derivations moved to the appendices. We hope this restructuring will allow readers to follow the modelling approach at a high level in the main text with technical details contained in the appendices.

    To improve the clarity of the methods section, I suggest:

    (R2.1) Include a list of symbols with the meaning of each variable defined in the text.

    Definitions for symbols are now also shown in appendix 1 – tables 1-5.

    (R2.2) Include a centralized full description of each model, clearly stating the priors and likelihood (similarly to a Stan code).

    There are two models that are fitted with Stan (the hierarchical retention model and discrete-time use/access model). To improve clarity for the hierarchical model, priors are now presented in a single block (equations 11 – 17) in appendix 2.2, with the likelihood (equation 18). For the discrete-time model, we have split the presentation of the priors (equations 37 – 42) and the likelihood expressions (equations 43 – 45) into different subsections (respectively appendices 4.2 and 4.3).

    (R2.3) If needed, include additional data preprocessing in the form of an algorithm.

    Although we have not included an algorithm outlining the preprocessing steps, we have ensured sufficient detail has been provided to facilitate replicability. For example, in appendix 1, we now outline how use and access are inferred from DHS data:

    “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, the ITN is assumed to be able to provide access at random to up to two individuals in a household.”

    (R2.4) Mention the main hypotheses and limitations of the model in the main text.

    We have ensured key assumptions of the model are stated in the re-written ‘Historical use, access and retention times’ methods subsection; for example, in the following 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.”

    (R2.5) Including a flowchart or diagram that provides an overview of the proposed framework could be helpful.

    We have now included a flowchart of methodological steps in appendix 1 – figure 1.

    (R2.6) Line 89: Define NMP before presenting the acronym.

    We have ensured this is defined in the first instance on line 39.

    (R2.7) Equation (1): Explain why you chose the Exponential distribution (e.g. constant hazard), as this is one of the main hypotheses of the model.

    As highlighted in our response to W2.1, we have now included justification of this assumption in the final paragraph of appendix 2.2.

    (R2.8) Equation (2): Although Equation (2) passes a clear message of how alpha_i^x is distributed, I wonder if it is mathematically correct to express the limit this way, since the argument of the limit is a random variable. Maybe the limit should be applied to gamma_i^x instead.

    Thank-you for highlighting this. We acknowledge the limit behaviour was expressed in a short-hand manner that is not strictly mathematically correct. Indeed, the limit should be applied to the decay rate parameter gamma (now shown in equation 10). In appendix 2.1, we have now provided a proof demonstrating the rate parameter of the pooled ITN age distribution should tend to the same decay rate as the assumed exponential loss function.

    (R2.9) I think the difference between pho_i^x (Equation (1)) and alpha_i^x (Equation (2)) is not very clear in the text.

    In the context of access, rho_{i(l)} and alpha_{i(l)} are respectively the duration an ITN l is retained for and its age at the time of a survey. We hope the redrafted appendices make this clearer, in addition to the inclusion of the new parameter tables in appendix 1.

    (R2.10) Line 479: Typo (and or).

    Updated wording is now contained in appendix 2.

    (R2.11) Line 711: Typo (The limit is equal to infinity).

    This has now been corrected.

    (R2.12) Equation (15): I could not understand this equation. What is rho(s) and rho(s \in I), where I is one of the intervals mentioned in this equation?

    Rho(tau_ik) was introduced as simplified notation for the probability density of the timing of campaign k in region i (tau_ik) but we acknowledge this was not explained clearly. We also acknowledge this equation presented a lot of concepts at once. The equation attempted to describe the probability density of the last campaign in region i relative to time t_j, denoted phi_ij. We no longer make use of this previously notation (rho) for the probability density. This equation has been updated to equation (30), with incremental explanation of its construction now provided on lines in appendix 3.2.

    (R2.13) Line 642: What is t?

    The use of $t_j \ni t$ was previously used to indicate that the discrete time point t_j lies within continuous time t. We acknowledge this was a non-standard use of notation and was not clearly explained. This section (now in appendix 4) has been rewritten without this notation. The use of t and t_j to denote continuous time and discrete time points respectively is now defined in the core notation table (appendix 1 – table 1).

    (R2.14) The proposed model has narrow hyperhyperpriors because of convergence issues. Are the estimated parameters sensitive to the choice of hyperhyperpriors?

    We acknowledge limited justification was previously provided for the choice of hyperhyperpriors. We have now provided additional justification within appendix 2.2.

    (R2.15) Since the proposed Bayesian models are relatively complex, it might be useful to provide convergence diagnostic plots in the supplement.

    Convergence diagnostics were inspected using the ShinyStan packagxe. Chains showed satisfactory convergence based on standard diagnostics. We have not included diagnostic plots due to the large number of parameters in the fitted models. Under the hierarchical model (appendix 2) for ITN use, 146 region-specific parameters (one for each region), 12 country-level hyperparameters (two for each country), and four hyperhyperparameters were estimated. Under the discrete-time model (appendix 4), a further 876 parameters (six for each region) were estimated. In total, 1,038 parameters were fitted for the ITN use models. The same number of parameters were estimated for the ITN access models, giving a total of 2,076 estimated parameters.

  5. Version published to 10.7554/elife.108745.2 on eLife
  6. Version published to 10.7554/elife.108745 on eLife
  7. eLife

    eLife Assessment

    This paper describes a useful Bayesian model to estimate the probabilities of access, use, and use given access of insecticide-treated bed nets (ITNs), by using sub-national cross-sectional survey data and the annual number of ITNs received at the country level. The authors provide convincing evidence to support their modeling approach, which could be enhanced by more validation and exploration of model assumptions.

  8. eLife

    Reviewer #1 (Public review):

    Summary:

    This paper provides a novel method to improve the accuracy of predictions of the impact of ITN strategies, by using sub-national estimates of the duration of ITN access and use over time from cross-sectional survey data and annual country ITNs received.

    Strengths:

    The approach is novel, makes use of available data, and has considered all of the relevant components of ITN distributions.

    Weaknesses:

    (1) The main message of the paper was not very clear, and did not seem to fit the title. The title focuses on sub-national tailoring of ITN, but the abstract did not feature results directly about SNT. It was not very clear what the main result of the paper was - there are several ITN observations in the results and discussion. Most did not seem to be directly about SNT, but rather sub-national differences in use and access were accounted for in the analyses. It was not clear if the same conclusions would be reached without accounting for sub-national differences, but the estimates and predictions could be expected to be more accurate.

    (2) Some of the results seemed to me to be apparent even without a modelling exercise (eg high coverage could not be maintained between campaigns, use would be higher with 2-yearly distributions rather than 3-yearly) or were not in themselves new insights (eg estimates of the duration of use). It would be helpful to clearly state what the novel results are in the abstract, the first paragraph of the discussion and the conclusions, and to make sure that the title is consistent.

    (3) On L236, the link to SNT is stated: "the models indicate trends that can support sub-national tailoring of ITNs". They could indeed, but SNT itself is not done in this paper. It seems to be about improving sub-national predictions of the impact of single ITN strategies, by taking into account sub-national variation in access and use duration. This is useful, and the model developed has novel aspects.

    (4) Individual countries may have records on when nets were distributed to the regions rather than needing to use the annual country number of nets together with the DHS data. It could be helpful to say what the analysis steps would be in that case.

    (5) There were several assumptions that needed to be made in building the model. There is some validation of the timing of the distributions (L633 "verified where possible through discussion with interested parties nationally and internationally") and the fit of estimated access and use to survey data, and agreement between predictions of prevalence and MAP estimates. It would be helpful to say which assumptions are important for the results (and would be key knowledge gaps) and which would not make a difference. It might be possible to validate the net timing model using a country where net distributions are known reasonably well.

    (6) What was assumed about what happens to old nets after a mass campaign was not clear. This assumption is likely to affect the predictions of access for the biennial distributions.

    (7) L312 and elsewhere: That use given access declines with net age is plausible. However, I wondered if this could be partly a consequence of the assumptions in the model (eg the two exponential decays for access and use, the possible assumption that new nets displace the current ones when there is a mass campaign).

    (8) The Methods section on Estimating historical use and access seemed to be aimed at readers familiar with formulae, but I think it could lose other interested readers. It could be useful to explain a little more about what is happening at each step and also why.

    (9) The model was fitted to MAP estimates of PfPR2-10, which themselves come from a model. It may be that there is different uncertainty in the MAP estimates for different regions. I couldn't see this on the graph, but maybe the uncertainty is small. Was this taken into account in the fitting?

    (10) Was uncertainty from each estimated component integrated into the other components?

    (11) Eyeballing Figure 2 (Burkina Faso), there is a general pattern of decline in all the regions, some differences between the regions and some differences in how well the model fits between the regions. If possible, it could be helpful to say how much better the fit was when using region-specific compared to countrywide parameter values for access and use, and how different the results would be.

    (12) The question of moving from a campaign every three to every two years may not be the most pertinent question in the current funding landscape. I realise that a paper is in development for a long time, but it would be helpful to comment on what else the model could be used for when fewer rather than more nets are likely to be available.

  9. eLife

    Reviewer #2 (Public review):

    Summary:

    The authors design a custom Bayesian model to estimate the probabilities of access, use and use given access of insecticide-treated nets in six African countries, providing sub-national estimates and inferring the average duration of ITN use and access. An individual-based model was employed to simulate malaria epidemics and estimate the effectiveness of different ITN distribution strategies. The study finds that the mean probability of use or access did not reach 80% (a universal coverage formely targeted by WHO) for any of the regions, even for biennial campaigns, demonstrates that switching from triennial to biennial distribution campaigns increases population use by 7.9%, and evaluates the impact of employing more efficient ITNs on P. falciparum prevalence.

    Strengths:

    The authors developed a data-driven model that accounts for data collection imperfections and sources of uncertainty while differentiating between ITN use and access. They developed a methodology to infer the timing of a mass campaign from publicly available data instead of assuming fixed dates. The probability of use given access allows for determining the regions where ITN distribution is least effective. This work can help better inform future interventions by identifying regions where increasing mass campaign frequency or employing better ITNs are most effective. Finally, in addition to insights on ITN access and use for the six countries analyzed, the paper contributes a methodological framework that can likely be extended to other countries.

    Weaknesses:

    Since the models employed are rather complex, the description of the methodology may be hard to follow for most readers. In addition, the models assume many hypotheses, including:

    (1) Exponential decay of ITN use/access.

    (2) The decay rates for the probability of the ITN repelling and killing a mosquito are the same.

    (3) Given a time instant, all individuals in the same administrative unit and have the same probability of using a net;

    (4) ITN use/access decay models do not depend on the distribution strategy (e.g. bienal vs trienal distribution).

    (5) The Bayesian model assumes some narrow prior distributions.

    The impact of these hypotheses on the estimated parameters is not explored in the paper, and no sensitivity analyses are performed, although some limitations are discussed.

  10. eLife

    Author response:

    We would like to thank both reviewers for taking the time to review the manuscript in detail. Your comments have been extremely useful and constructive. A revised version of the manuscript will seek to address the weaknesses raised, clarifying the reasons for the assumptions made, the impact they have and how they influence the policy implication of the work. We will clarify the language to differentiate the work from the standard sub-national tailoring which is typically conducted to support National Malaria Programmes and emphasise why our mechanistic model can provide greater information than simple summary statistics.

  11. Version published to 10.7554/elife.108745.1 on eLife
  12. Version published to 10.1101/2025.08.27.25334550 on medRxiv