Decay Model for Long-Lasted Insecticide-Treated Nets (LLINs)

Originally published: December 2012
Assessed as up-to-date: September 2013

We have looked for information on how long long-lasting insecticide-treated nets (LLINs) can be expected to stay functional (and in use) after a distribution. Unfortunately, the information we've found is limited (in terms of having relatively little empirical data behind it) and ambiguous (in that the analysis we've seen is not precise about the model it is using).

We first discuss the most common "decay model" we've used, then discuss the limited empirical evidence we've seen on what the best model is.

Decay model

Alliance for Malaria Prevention 2011 lays out a model for estimating the number of LLINs still in use after distributions:

We have seen the same model used or recommended in multiple other sources including an Alliance for Malaria Prevention presentation,2 an empirical analysis discussed below3 and a spreadsheet from the African Leaders Malaria Alliance estimating LLIN coverage gaps.4

Unfortunately, it is difficult to use this model to infer the "useful life" of an LLIN because the model is specified only year-by-year; for example, it would assume the same number of LLINs still in use based on a distribution 1 month ago or 12 months ago. The only work we have seen that gives a more specific model is a presentation made on behalf of the Malaria Consortium, and the model here seems to imply a much longer LLIN life.5

If we assume that an LLIN has a 92% chance of being in use at a given point in the first year after distribution, this implies that for each LLIN delivered, an average of 0.92 LLIN-years of use are obtained in the first year. Assuming 0.92 LLIN-years of use in the first year, 0.8 in the second year and 0.5 in the third year would yield an overall average of 2.22 years of use per LLIN. This is substantially less than the "official life" of an LLIN.6 As discussed below, we believe this makes sense because the decay function is intended to account for wastage of all kinds, including loss/failed delivery of LLINs, improper use resulting in disrepair, etc.

Empirical analysis

We have located three reviews of how long LLINs last in the field: a presentation by World Health Organization staff members,7 , a section of a broad paper on LLIN distribution strategies,8 and the WHO's World Malaria Report from 2009.9 We discuss each in turn.

Otten and Lines presentation

World Health Organization staff members Otten and Lines compared the number of nets delivered to data from national-level household surveys in order to ascertain the discrepancy between "how many LLINs are distributed by manufacturers" and "how many LLINs are actually owned by households," using data from 2008-2009.10 While the results are reported in a presentation and not a scholarly paper, it was fully transparent about its data sources and methods and we were able to perform a confirming spot-check on how it was generating its estimates.

The key figures compare:11

• The number of ITNs owned by households, estimated based on (a) the number of ITNs owned per household (from national Demographic and Health Surveys12 ); (b) the number of people per household (from the same surveys); (c) the total number of people (using United Nations population estimates).13
• The number of LLINs distributed, according to manufacturers.
• The number of LLINs distributed, according to National Malaria Control Programs.
• The expected discrepancies based on the authors' model, which we assume to be the same model discussed in the previous section based on the fact that the authors refer to it as "8%-20%-50%."14

Weighting countries by the number of nets reported to be distributed by manufacturers, the average ratio of reported nets to the number implied by the decay model across the seven included countries is 95%.15 However, this relatively high level of overall predictive success obscures large deviations from the model.

First, there are many more old nets, and many fewer young nets, than the 8%-20%-50% model would imply. Across the seven countries, 18% of nets are reported by their owners to be more than three years old, even though the 8%-20%-50% model implies that 0% of nets are still in use after three years.16 Conversely, there are only 75% as many reported nets under three years old as the 8%-20%-50% model implies there should be.17 Because we do not have data more than three years back on the number of nets distributed or the age breakdown of nets that are more than three years old, we cannot estimate a revised empirical figure for the average lifespan of a net that accounts for the survival of some nets beyond three years. Given that the presence of fewer new nets and more old nets than predicted seem to roughly cancel out (i.e. overall reported net ownerships rates map pretty closely to the decay model's predictions), it is not clear which direction the effect of an empirical revision to the decay model on the estimated average lifespan of a net would point.

Second, the overall high-level agreement with the decay model obscures quite a bit of variation at the country level:

• The model's prediction is relatively accurate for Kenya and Senegal.
• For Uganda, the number of ITNs found in surveys exceeds the number delivered over the last three years. It's possible (our speculation) that this is a function of ITNs lasting longer than anticipated, of delivery data failing to capture all ITNs delivered, or of survey respondents' exaggerating their ownership of ITNs.
• For Liberia and Sao Tome and Principe, decay appears substantially worse than what the decay model and manufacturer data would predict (there are fewer than half as many ITNs in ownership as the model would predict), and National Malaria Control Program data is not available. We speculate that this may be a function of problematic national control programs.
• For Sierra Leone and Rwanda, substantially fewer ITNs were found than the decay model and delivery data would predict (less than half as many for Sierra Leone; about 75% in Rwanda).

Overall, the decay model overestimates coverage for four countries (two of which may have problematic National Malaria Control Programs), underestimates coverage for one, and is roughly accurate for two. Given the many uncertainties in extrapolating from delivered to owned ITNs, we find these figures reasonably close.

Note that this analysis straightforwardly compares ITNs found in household surveys to ITNs originally delivered by control programs; therefore, its decay model is implicitly accounting for anything that would cause ITNs to no longer be present in the household, including loss/failed delivery of LLINs, improper use resulting in disrepair, etc. On the other hand, the net distribution figures rely on self-reported data by a subset of net manufacturers and Ministries of Health. To the extent that the surveyed manufacturers and the Ministries of Health are underestimating actual net distributions (through, e.g., market exchanges), the level of decay will be underestimated.

Kilian et al. 2010

Kilian et al. 2010 is broad review of papers on several topics relevant to LLIN distributions. Regarding how long LLINs remain in use in the field, it states:

The table referred to above (Table 1 in Kilian et al. 2010) appears to us to show similar loss rates,19 but we are not confident that we're correctly interpreting the table, and changes in these figures may be partly a function of population growth. Kilian et al. 2010 states that the observed figures fit with a model that is similar to the one used in the previous section (though Kilian's models imply longer average net life):

World Malaria Report 2009

The 2009 World Malaria Report states that:

To the extent that survey results on the proportion of households with at least one ITN are a reliable reflection of the lifespan of a net, the data from these four countries would generally suggest that the 8%-20%-50% model is too conservative (i.e. that bednets last longer than the decay model expects).

Synthesis

In general, the evidence we have reviewed seems to indicate that the standard decay model offers a reasonable predictive model for the number of nets that are in use following a distribution. The Kilian et al. 2010 and World Malaria Report 2009 data might appear to suggest that the standard decay model is too conservative (i.e. it assumes nets decay faster than they do), but we would guess that these results are misleading. Because households may be able to obtain nets from sources other than large campaigns (e.g. through the marketplace or an NGO), or may take especially good care of their final remaining net, simply observing how the proportion of households with at least one ITN changes over time following a campaign is likely to lead to an underestimate of the decay of campaign nets.

The standard decay model performs relatively well in using manufacturer data to predict current reported bednet ownership rates, though the decay model appears to overestimate the proportion of new nets in use and underestimate the proportion of old nets in use. The decay model's overestimate of the number of new nets that are owned may be a result of several factors, including failed distributions or a situation in which nets that are delivered by a manufacturer during one period are not actually distributed to people until substantially later. (This latter scenario appears fairly likely in the case of Sierra Leone, in which individuals reported far more one-year-old and far fewer two-year-old bednets than the decay model predicted.22 ) It is also possible that people are simply misreporting the age of their bednets.

If manufacturers and Ministries of Health are reporting the distribution of fewer bednets than are actually in circulation, then the apparent coherence with the decay model may be unwarranted, and bednets may decay faster than expected.

Bottom line

We believe that the "8%-20%-50%" model is the most widely used and most reasonable approximation available at the moment for capturing the extent to which LLINs remain in use in the years following distribution, accounting for any factors that might cause LLINs to be discarded or additional LLINs to be purchased. It implies an average of 2.22 years of use for each LLIN distributed. Data and analysis on this topic appears extremely thin; we have little sense for how long LLINs last in practice.

Sources

• 1

  Alliance for Malaria Prevention 2011, Pg 3-12.

• 2

  Buj presentation.

• 3

  Otten and Lines presentation.

• 4

  African Leaders Malaria Alliance 2011. Column W.

• 5

  Kilian presentation, Pg 9. Note that even for the model with less-long-lasting nets, it appears that ~95% of nets remain in use after a full year (more after less than a year); ~80% remain in use after two full years (more between 1-2 years); ~50% remain in use after three full years (more between 2-3 years); and some nets remain in use after three years.

• 6

  Quotes regarding Sumitomo's Olyset Net, the main net used by Against Malaria Foundation:

  • "Sumitomo Chemical's Olyset Net uses the latest research and technology to achieve a breakthrough in the global fight against malaria. Permethrin is incorporated inside the Olyset fibres to create a bed net guaranteed to last at least five years.* It is tear-proof, wash-proof, and never requires treatment." Sumitomo Chemical, "Olyset Net."
  • " Background: Insecticide-treated nets represent currently a key malaria control strategy, but low insecticide re-treatment rates remain problematic. Olyset™ nets are currently one of two longlasting insecticidal nets recommended by WHO. An assessment was carried out of the effect of Olyset™ nets after seven years of use in rural Tanzania.

    Methods: A survey of Olyset™ nets was conducted in two Tanzanian villages to examine their insecticide dosage, bioassay efficacy and desirability compared with ordinary polyester nets.

    Results: Of 103 randomly selected nets distributed in 1994 to 1995, 100 could be traced. Most nets were in a condition likely to offer protection against mosquito biting. Villagers appreciated mainly the durability of Olyset™ nets and insecticide persistence. People disliked the small size of these nets and the light blue colour and preferred a smaller mesh size, features that can easily be modified. At equal price, 51% said they would prefer to buy an Olyset™ net and 49% opted for an ordinary polyester net. The average permethrin content was 33%-41% of the initial insecticide dose of 20,000 mg/Kg. Bioassay results indicated high knock-down rates at 60 minutes, but the mosquito mortality after 24 hours was rather low (mean: 34%). No significant correlation was found between bioassay results and insecticide concentration in and on the net.

    Conclusions: Olyset™ nets are popular, durable and with a much longer insecticide persistence than ordinary polyester nets. Hence, Olyset™ nets are one of the best choices for ITN programmes in rural malaria-endemic areas." Tami et al. 2004.

• 7

  Otten and Lines presentation.

• 8

  Kilian et al. 2010.

• 9

  World Malaria Report 2009.

• 10

  Otten and Lines presentation.

• 11

  Otten and Lines presentation, Pg 11.

• 12

  Measure DHS website, homepage.

• 13

  Otten and Lines presentation, Pgs 4-5.

• 14

  Otten and Lines presentation, Pg 18. Using the model described in the previous section also allows us to replicate their calculations correctly.

• 15

  GiveWell, Otten and Lines Bednet Data, Sheet1, Column K.

• 16

  GiveWell, Otten and Lines Bednet Data, Sheet1, Column N.

• 17

  GiveWell, Otten and Lines Bednet Data, Sheet1, Column M.

• 18

  Kilian et al. 2010. Pg 11.

• 19

  The "ITN %" figures for the 4th through 6th rows, which focus on one-time ("campaign") distributions rather than continuous distributions, show:

  • Togo, national: 62.5% in 2004, 40.2% in 2006, which represents a decrease of 36% over two years. Nets were distributed sometime between the 2003 and 2004 surveys. A 36% loss between the first and third years after distribution is slightly less than the 8%-20%-50% model suggests (47% expected loss from going from 92% to 50%).
  • Sofala, Mozambique, provincial: 47.6% in 2005, 21.7% in 2007. The campaign happened sometime between the 2003 and 2005 survey. Conservatively assuming the campaign was conducted within a year of the 2005 survey, the 8%-20%-50% model would again suggest 47% expected loss between 2005 and 2007, compared to the observed 54% loss.
  • Manika, Mozambique, provincial: 51.5% in 2005, 36.9% in 2007. Again conservatively assuming that the campaign occurred closer to the 2005 survey than the 2003 survey, the model would suggest a 47% loss, compared to the observed 28% loss.

  All of these figures represent the proportion of households with at least one ITN. These figures do not rebut the possibility that families may have lost additional bednets at higher rates but continued to own at least one (e.g. if they took better care of the final remaining bednet after losing previous ones), and the figures include bednets acquired through means other than the studied campaigns. Campaign timing is inferred from the changes in reported level of net ownership.

• 20

  Kilian et al. 2010. Pgs 12-13.

• 21

  World Malaria Report 2009. Pg 17.

• 22

  Otten and Lines presentation. Pg 13.