Mathematical model overview

PopGEM is a deterministic stage structured model and is fully described in appendices 1–5 in S1 File and conceptually shown in Fig 1. Briefly, PopGEM models the life cycle of mosquitoes in daily time-steps, incorporating both aquatic (eggs, larvae, pupae) and adult stages for males and females. The model considers that each mosquito can have a different level of IR, caused by resistance genes encoded at single loci, with two alleles per loci (either Susceptible (S) or Resistant (R)). For modelling mixture interventions, we extend the model to include a second gene, to allow for tracking IR to the second insecticide (see appendix 5). PopGEM models adult female mosquitoes that enter the feeding cycle starting with seeking a host, then they can find a host and feed on it, rest and lay eggs. Mosquitoes can bloodfeed on either animals or humans. Mosquitoes that prefer humans (anthropophagic) and feed indoors (endophagic) may be exposed to ITNs, depending on coverage. The impact of ITNs will depend on the ITN type and the genotype of the mosquito encountering the ITN as described in Fig 1 and Table 1.

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Table 1. Parameters in sensitivity analysis simulations.

https://doi.org/10.1371/journal.pcbi.1014612.t001

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Fig 1. Overview of the PopGEM (Population Genetics and Ecology in Mosquitoes) model.

The model simulates the developmental life cycle of mosquitoes, progressing from eggs to adults. The model tracks both male (blue) and female (red) mosquitoes that can mate when they reach the adult stage. Adult female mosquitoes transition to the blood-feeding cycle, either before or after mating. During this phase, females seek blood meals from vertebrate hosts, bloodfeed, rest, and lay eggs (if they managed to mate beforehand). Mosquitoes that are both anthropophilic (feed on humans) and endophagic (feed indoors) are exposed to ITNs dependent on coverage. Mosquito survival after ITN exposure depends on IR genotype. The model assumes resistance to each insecticide is encoded at single loci, with two alleles per loci (either Susceptible (S) or Resistant (R)). Mosquitoes can have three different genotypes: SS (light red, light blue), RS (red, blue), and RR (dark red, dark blue). The genotypes dictate ITN efficacy. Note that the killing effect of ITN for each genotype varies within a range in the analysis (see Table 1). For modelling NGM-ITNs, we extended the model to include a second gene, to allow for tracking IR to the second insecticide (see appendix 5).

https://doi.org/10.1371/journal.pcbi.1014612.g001

Unlike most resistance management models, which include an unspecified mechanism for fitness costs associated with IR [11,12,14,17], the fitness costs in PopGEM are directly attached to specific life-history traits, better representing how fitness costs impact real-world mosquito populations. However, given the expansive parameter space this can add (see section 5.8 of Appendix 5 in S1 File), we did not include fitness costs in the presented simulations. Considering fitness costs are most beneficial when considering the rotation strategy [10] which was not evaluated here, this omission does not impact the model conclusions.

We applied the model in three simulation sets to explore the deployment of three ITN types (agnostic to specific net brands). These ITN types are:

• Pyrethroid-only ITN (PYR-ITN): an ITN containing only a pyrethroid insecticide.
• Next-generation mixture ITN (NGM-ITN): a mixture ITN, containing both a pyrethroid and a single novel insecticide partner in mixture. We assume both insecticides are deployed at full-dose.
• Novel-ITN: a hypothetical ITN, containing only a single novel insecticide, the same that is used in the NGM-ITN. This allows for full quantification of any potential IRM benefit of the NGM-ITN.

PopGEM can account for ITN attrition and insecticide efficacy decay which is explored in Simulation Set 3; but is not included in Simulation Set 1 or 2.

Simulation Set 1: Impact of PYR-ITNs on IR and Malaria Vector Control

First, we investigated the impact of the evolution of IR considering PYR-ITN only deployments for comparison with previous studies [18,24,25]. This also allowed us to identify parameters driving the spread of IR and the ability to control vector populations via sensitivity analysis.

We compared three scenarios. We first ran a scenario without any interventions (worst case). Next, we ran two scenarios that included interventions with randomly sampled intervention coverage (Table 1), where the coverage was defined as the proportion of households using ITNs. In one simulation, IR was not included and allowed to spread (best case), whereas in the other, IR evolution was allowed. For the IR simulations, the initial genotype frequency was set under Hardy-Weinberg equilibrium (1 = R² + 2RS + S²) with inputs S=0·999999, R = 0·000001.

From these three scenarios (No Intervention, Intervention with no IR, Intervention with IR), we extracted the vectorial capacity (an entomological measure of transmission, see appendix 6 in S1 File), total adult female population size, and resistance allele frequency at 1-, 3-, 5- and 10-year time horizons. Based on these calculated vectorial capacities, we calculated the vector control loss (%) in the simulation where IR was allowed to evolve. Vector control loss measured the relative reduction in the PYR-ITNs capability to control the mosquito population (i.e., reduction in vectorial capacity) due to the spread of IR (see Equation S6.16 in S1 File). We reported the vector control loss in percentage at 1-, 3-, 5-, and 10-year time horizons. Fig 2 illustrates how changes in resistance allele frequency over time impact adult female mosquito population size and vectorial capacity, causing the progressive loss of vector control in the scenario where IR was allowed to evolve.

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Fig 2. An example of simulation outcomes for the three scenarios of PYR-ITNs: No intervention, intervention without IR, and intervention with IR.

For all panels, the black line is the no intervention comparison, the grey line is the intervention without IR, and the red line is the intervention with IR simulation. Within the IR scenarios, genotypes are further stratified by blue shades (SS = light blue, RS = blue, RR = dark blue) for the intervention with IR simulation. Left Panel: Change in the adult female mosquito population size over time across all genotypes. Centre panel: Changes in vectorial capacity over time. Right panel: Changes in vector control loss over time in the simulation where IR can evolve. This is a single simulation to demonstrate the underlying process, parameter values are therefore omitted to avoid overinterpretation of a single simulation run.

https://doi.org/10.1371/journal.pcbi.1014612.g002

For each scenario, we simulated an adult female population size between 10,000 and 1,000,000 depending on larval carrying capacity (see appendix 2 in S1 File). To perform the sensitivity analysis, Latin hypercube sampling [26] was used to generate 100,000 parameter sets (Table 1). Only populations which were viable in the absence of interventions were included in the analysis. Of the 100,000 parameter sets used, 90,637 gave viable populations (see Fig U in S1 File). The sensitivity analysis involved using plots of the parameter density distributions and partial rank correlation coefficients (PRCC) to understand how parameter values impacted vector control loss. The secondary analysis involved understanding the implication of the randomly sampled parameter values on the primary outcomes of malaria vectorial capacity and population size. The analysis was conducted in R, using the package epiR [27] for the PRCC.

Simulation Set 2: Impact of NGM-ITNs on IR and malaria vector control

NGM-ITNs may demonstrate their full potential (from an IRM perspective) only over long time horizons, which is impractical to measure in field trials. We compared the performance of NGM-ITNs against PYR-ITNs over a long evolutionary timeframe and allowed IR to both insecticides to increase over time dependent on the level of selection.

We assumed that the insecticides on the ITNs were deployed at the full recommended dose. In all simulations, we considered the novel insecticide resistance allele to be rare (frequency of 10^-6), while pyrethroid resistance allele was moderately frequent (frequency of 0·25), allowing the impact of IRM to be seen for both the novel and pyrethroid insecticides. We assume that the survival phenotype to the NGM-ITN is the product of the survival phenotypes to each individual insecticide.

PYR-ITNs costs have lower per unit costs than NGM-ITNs [28]. This highlights that achieving equivalent coverage with NGM-ITNs would require higher financial investment. To offset costs, there have long been concerns that manufacturers might reduce insecticide doses to reduce per net cost [15]. The alternative may be that donors procure fewer nets, leading to lowering coverage [15]. We accounted for the cost discrepancy by reducing the NGM-ITN coverage by 10%, 20% and 30% of the comparator pyrethroid-ITN coverage, as a reduced coverage may impact both malaria vector control and IRM. This is implemented by scaling the parameter (Table 1). We therefore ran six deployment scenarios: PYR-ITN, NGM-ITNs with no reduction, and 10%, 20% and 30% reduction in coverage of the comparator PYR-ITN coverage, and a Novel-ITN. The Novel-ITN (same coverage as PYR-ITN) was used to quantify the full IRM benefit of NGM-ITN.

For each deployment scenario, the same 20,000 parameter sets were used for each deployment type, enabling direct comparisons between the deployment scenarios (Table 1). Only simulations which gave viable populations in the absence of an intervention (defined as the adult female population size being between 10,000 and 1,000,000) were included in the analysis. Therefore, 19,108 (95·54%) of the simulation sets were included in the analysis. Each simulation was run for 15 years. The outcomes were the corresponding resistance allele frequencies to the pyrethroid and novel insecticide, adult female population size, and malaria vectorial capacity. The outcomes were compared across each deployment scenario.

Simulation Set 3: Impact of NGM-ITNs on IR and Malaria Vector Control with Net Retention and Insecticide Decay

Insecticide decay and ITN retention are two important considerations for both vector control and insecticide resistance evolution. We therefore replicate Simulation Set 2 using the exact same parameter inputs. The one exception is now including decaying insecticide efficacy and ITN retention when ITNs are deployed every three years. In brief, we assume ITNs are retained following a Weibull distribution [29], and similarly that insecticide efficacy also follows a Weibull distribution, with each insecticide having the same decay profile, which is detailed in the Intervention Module in Appendix 1 of the S1 File. Given that in these simulations we are looking at whether the inclusion of decay and retention alters the conclusions from Simulation Set 2, the exact parameterisation is not overly critical. We acknowledge that different ITN brands and different insecticides have different retentions and decays and these are often further location dependent. Rather than using the vectorial capacity at the end of each year (as in Simulation Set 2), we instead compare the yearly sums of the vectorial capacity due to the more complex resistance-transmission dynamics the inclusion of insecticide efficacy decay and ITN retention (Fig 5).

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Fig 3. Malaria vector control loss from IR evolution at different time horizons under PYR-ITNs deployments.

Each panel reports the distribution of vector control loss due to IR across all simulations (see parameter ranges in Table 1) at the specified time horizon from the 90730 simulations that gave a viable mosquito population (defined as the adult female population size being between 10,000 and 1,000,000 in the absence of interventions). Malaria vector control loss was calculated from equation S6.16 in S1 File). Note, while absolute times are reported, interpretation must consider these as considering short-term (1-3 years) and longer-term (10 years) trends, as precise timescale predictions of evolutionary models are not possible.

https://doi.org/10.1371/journal.pcbi.1014612.g003

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Fig 4. Partial Rank Correlation Coefficient of parameter value on the outcome (vector control loss) at four time horizons.

Partial Rank Correlation Coefficients (PRCCs) showing the influence of parameter values (see parameter ranges in Table 1) on vector control loss for a PYR-ITN across four time horizons (1, 3, 5, and 10 years). A positive bar (blue) indicates that increasing the parameter is associated with greater vector control loss, while a negative bar (pink) indicates a reduction in vector control loss. Bar length reflects the magnitude of each parameter’s effect on vector control loss, and error bars represent 95% confidence intervals.

https://doi.org/10.1371/journal.pcbi.1014612.g004

Results for Simulation Set 1: Impact of PYR-ITNs on IR and malaria vector control

Fig 3 illustrates how malaria vector control declined over time due to the IR evolution in PYR-ITN scenario across all simulations (see parameter ranges in Table 1). In the first year, the vector control loss was minimal as resistance gene frequencies remained low and most mosquitoes were still susceptible (and effectively controlled). Over time, as the frequency of resistance genes increased, mosquito survival against ITNs increased, resulting in the increased vector control loss. However, as the ITNs still had an impact on homozygote resistant (RR) mosquitoes, even when the resistance gene frequency reached high levels after 10 years, ITNs still contribute to vector control. Therefore, the vector control loss did not reach 100%. In opposition, in some simulations, vectorial capacity remained stable (less than 1% change) even after 10 years indicating the level of selection was not sufficient to cause the resistance allele to be frequent enough to yet compromise vector control in the time horizons evaluated.

To understand why, in some cases, the vector control loss was large, and in some other cases low, we investigated the influence of parameters on vector control loss (Fig 4), but note that due to population viability filtering this means some parameter values occur more frequently than expected in the analysis. At the 10-year mark, the male insecticide encounter rate had the largest impact on vector control loss. Higher rates of male insecticide encounter accelerated IR spread and consequently reduced vector control. Male mosquitoes are often overlooked in this context because they do not transmit P. falciparum, however, our simulations demonstrated that their exposure to insecticides significantly influences the spread of resistance genes, accelerating IR development and exacerbating vector control loss.

ITN coverage emerged as the most important factor in preventing vector control loss. While this may seem counterintuitive (since higher ITN coverage accelerated the spread of IR), however once IR had spread, higher ITN coverage led to overall better vector control because higher coverage better suppresses malaria transmission by exposing mosquitoes to more ITNs (that still have some impact). Thus, although insecticide pressure accelerated resistance, maintaining high ITN coverage remained a crucial strategy to sustain effective malaria control. Interestingly, the mosquitoes’ feeding behaviour also had a great impact on vector control loss. Highly anthropophilic species were associated with greater vector control loss, as they were more exposed to ITNs and therefore, any reduction in efficacy (due to resistance) was more noticeable. Similarly, highly endophagic species were associated with higher levels of vector control loss, since they were also more exposed to ITNs.

Results for Simulation Set 2: Impact of NGM-ITNs on IR and malaria vector control

We next examined the effects of NGM-ITNs on IRM and malaria vector control. Fig 5 presents a randomly selected simulation that illustrate the typical impact of the different scenarios on the spread of IR. Generally, deploying NGM-ITNs slowed the spread of pyrethroid resistance compared to deploying PYR-ITNs. Moreover, lower coverage of NGM-ITNs further reduced the spread of pyrethroid resistance. A similar pattern was seen for resistance to the novel insecticide, where deploying NGM-ITNs provided greater IRM benefits than deploying Novel-ITNs (since the pyrethroid still had a minor effect), and reducing the coverage of the NGM-ITNs increased this IRM benefit. Further sensitivity analysis is presented in appendix 7 in S1 File.

We compared the differences in vectorial capacity of the different types of ITNs at yearly intervals across all simulations (see parameter ranges in Table 1), where the strategy with the lowest vectorial capacity was declared winning (Fig 6). At equal coverage levels, NGM-ITNs consistently reduced vectorial capacity more than PYR-ITNs. Even when deployed at reduced coverage, NGM-ITNs generally outperformed PYR-ITNs. The benefit of NGM-ITNs at reduced coverage becomes more apparent over time as rising pyrethroid resistance reduces the effectiveness of PYR-ITNs. When comparing the different reduced coverage levels of NGM-ITNs, the higher coverage almost always provided stronger vector control than the lower coverages. However, in a small subset of simulations, lower coverages appeared in some simulations to provide better vector control than the higher coverage in long term. We suspected that lower coverage exerted less selection pressure for resistance, resulting in the slower development of IR, which allowed NGM-ITNs to maintain their effectiveness over a longer time-period, but this is offset by a reduced ability to control mosquito populations early in the simulations.

An operational question facing manufacturers is whether there is an advantage of mixing their novel chemistries with pyrethroids. Providing coverage is equal, the NGM-ITNs consistently outperform a Novel-ITN, as the pyrethroid can still have a minor mosquito killing effect. However, when NGM-ITN coverage is reduced, the Novel-ITN can becomes preferable in early years, but becomes less beneficial over time as resistance to the novel insecticide evolves more rapidly than when in a NGM-ITN.

We investigated in which conditions where NGM-ITNs with a 30% coverage reduction were more effective than PYR-ITNs (Fig 7). This happened in simulations where pyrethroid was still (mostly) effective at killing female resistant mosquitoes. However, over time, as the RR genotype became more prevalent in the population, the benefit of switching to NGM-ITN (despite being at lower coverages) increased. This supports the recommendation that NGM-ITNs should be used in areas of high pyrethroid resistance. PYR-ITNs were also better if females were not very endophagic or anthropophilic. If female mosquitoes are not very endophagic or anthropophilic, there is a need for more nets rather than fewer effective better nets. This is because mosquitoes would be unlikely to encounter an NGM-ITN at the reduced coverage, and therefore they would not be able to provide the improved protection to individuals or the wider community (through increased mosquito mortality and population suppression). Further sensitivity analysis is presented in appendix 7.

Results for simulation Set 3: Impact of NGM-ITNs on IR and malaria vector control with net retention and insecticide decay

Fig 8 shows the comparison accounting for ITN retention and the decay of insecticide efficacy between re-deployments. Overall, the same qualitative conclusions can be drawn as for Simulation Set 2. The example simulation in Fig 5 highlights how the inclusion of ITN retention and insecticide efficacy decay may marginally improve the IRM aspect as coverage lowers. Albeit decay in insecticide efficacy increases the survival probabilities of heterozygous and homozygous resistant individuals.

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Fig 5. An example simulation plots for the combined IRM and vector control of NGM-ITNs for Simulation Sets 2 and 3.

An example simulation is shown to give a representation of how the simulation performs for the three outcomes of pyrethroid resistance allele frequency (left panel), novel resistance allele frequency (centre panel), and vectorial capacity (right panel). This simulation was selected randomly, and we do not report here the randomly sampled parameter values used in the simulation to prevent over-interpretation. Within this simulation run, six simulations were conducted, one for each of the interventions. In all plots, the grey line is the PYR-ITN only run. The green line is NGM-ITN without coverage reduction (relative to the standard pyrethroid-only ITN coverage). The orange line (10% coverage reduction), purple line (20% coverage reduction), and pink line (30% coverage reduction) are the NGM-ITN simulations where coverage was reduced when compared to the standard PYR-ITN coverage. The blue line is the Novel-ITN, and was at the same coverage as to the standard PYR-ITN coverage. The simulations are replicated with the same input parameter values except without (top row) and with (bottom row) insecticide efficacy decay and ITN retention.

https://doi.org/10.1371/journal.pcbi.1014612.g005

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Fig 6. Comparative performance of the different ITN deployments over time.

The figure shows the percentage of simulations (see parameter range in Table 1) that had a lower vectorial capacity between the comparator strategies (PYR-ITN, NGM-ITN, and Novel-ITN) at yearly time points. A lower vectorial capacity is defined as being more effective, as there is less transmission. The panel descriptors describe which two deployment options are being compared. The colour scheme is the same as for Fig 5, where the bar colours are used to designate the winning strategy (lower vectorial capacity). For example, for the top left panel, this would be read as comparing NGM-ITN with 10% coverage reduction and NGM-ITN at 20% coverage reduction, where the orange bars indicate the percentage of simulations where the NGM-ITN with 10% coverage reduction winning (having a lower vectorial capacity), and the purple bars indicates this for the NGM-ITN at 20% coverage reduction won.

https://doi.org/10.1371/journal.pcbi.1014612.g006

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Fig 7. Parameter Distributions for Simulations where the NGM-ITN at 30% coverage reduction outperforms the PYR-ITN in reducing vectorial capacity.

This compares the parameter distributions for all simulations (black line). The coloured lines show simulations at each different time horizons at where the NGM-ITN with 30% coverage reduction outperformed the PYR-ITN. The NGM-ITN with 30% coverage reduction was chosen as the comparator because it highlights a moderate reduction in coverage. Where the coloured lines are above the black line this means the parameter values are over-represented (portions of the parameter space where NGM-ITNs with 30% coverage reduction outperform PYR-ITNs), and where the coloured lines are below the black line this means the parameter values are under-represented (portions of the parameter space where PYR-ITNs outperform NGM-ITNs with 30% coverage reduction).

https://doi.org/10.1371/journal.pcbi.1014612.g007

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Fig 8. Comparative performance of the different ITN deployments over time accounting for ITN retention and insecticide decay.

The figure shows the percentage of simulations (see parameter range in Table 1) that had a lower vectorial capacity between the comparator strategies (PYR-ITN, NGM-ITN, and Novel-ITN) at yearly time points. A lower vectorial capacity is defined as being more effective, as there is less transmission. The panel descriptors describe which two deployment options are being compared. The colour scheme is the same as for Fig 5, where the bar colours are used to designate the winning strategy (lower vectorial capacity). For example, for the top left panel, this would be read as comparing NGM-ITN with 10% coverage reduction and NGM-ITN at 20% coverage reduction, where the orange bars indicate the percentage of simulations where the NGM-ITN with 10% coverage reduction winning (having a lower vectorial capacity), and the purple bars indicates this for the NGM-ITN at 20% coverage reduction won.

https://doi.org/10.1371/journal.pcbi.1014612.g008

The dual benefit of NGM-ITNs for vector control and IRM

In our simulations, NGM-ITNs were more effective than PYR-ITNs not only because it is a superior intervention with a greater mosquito killing effect, but also because NGM-ITNs provide an IRM benefit that extends their impact over a longer timeframe. Trials evaluating NGM-ITNs may underestimate their value by not fully accounting for the additional long-term IRM benefits compared to PYR-ITNs. This is our key operational finding, which supports the WHO recommendation of using mixture ITNs [31].

The role of coverage and economic trade-offs in ITN deployment

Increasing ITN coverage is beneficial for controlling malaria transmission, however, increasing coverage inevitably comes at the expense of increased selection for IR. Nevertheless, our simulations highlight that maintaining high coverage of ITNs can also help mitigate the negative impact of IR on malaria vector control. ITNs reduce transmission in two ways. First, by providing a personal protective chemical and physical barrier reducing an individual’s likelihood of being bitten. Second, by providing community protection through mass killing, which reduces mosquito survival rates and population sizes. ITN users benefit from both personal protection and community protection, while non-users only benefit from community protection. As IR in the mosquito population increases there is a declining efficacy of ITNs. This, in turn, can lead to an increase in mosquito population size and mosquito survival, which reduces the overall community-level protective effect. To offset this effect, an increase in ITN coverage is needed. Killeen [32] argued that the mass effect of ITNs as a result of increased mortality rates in mosquitoes was of such critical importance that a decrease in coverage is justifiable if more lethal ITNs are distributed. Our simulations considering the deployment of NGM-ITNs were consistent with this argument.

One issue which NGM-ITNs have long since had is that both insecticides in NGM-ITNs must be deployed at their respective full-doses for their IRM efficacy to be highest [11,17,33]. There have long been concerns that to compensate for the increased costs of NGM-ITNs, the dose of each respective insecticide partner may be reduced [15]. However, reduced dose NGM-ITNs are less efficacious for IRM than a full dose NGM-ITNs [17,33]. Consequently, we expect reduced coverage (in the short term) to be an inevitability due to the limited budgets of national malaria control programmes and higher cost of NGM-ITNs. From a combined IRM and disease management perspective, if the increased cost of the mixtures must be offset, reducing coverage is the option to choose as this does not compromise IRM in the way that reducing dosing does [33] (and should further encourage manufacturers to develop full-dose mixtures). Due to the superior performance of NGM-ITNs versus PYR-ITNs in reducing transmission [7,8], this reduction in coverage may not compromise malaria control, while extending the “resistance lifespan” of the mixture, as reducing coverage inevitably reduces selection. Rather than compromising on the dosing of the NGM-ITNs (where the maximal IRM efficacy is obtained), the economic compromise, which may be better for both epidemiological outcomes and IRM, is to reduce the coverage of NGM-ITNs, and the magnitude of this reduction will be dependent on the transmission setting. These findings were further found to be robust when including insecticide efficacy decay and ITN retention.

Role of male mosquitoes

Although male mosquitoes are widely regarded as unimportant for malaria transmission, we identified their importance in accelerating the loss of malaria vector control due to increasing IR. Male mosquitoes are critical in the spread of resistance genes, as they provide half the genes for the next generation. Our knowledge of male mosquitoes is often severely limited [34], and there is little understanding of the insecticide selection pressures on adult male mosquitoes in the field. Models which have evaluated exclusively the impact of IRM strategies have shown that while selection on male mosquitoes accelerates the spread of IR [10], this is often considered a low issue (because models scale selection so males do not encounter insecticides as frequently as females). However, by reframing the evaluation of the impact of insecticide selection by interventions on vectorial capacity, we instead see that male mosquitoes increase in their importance. We can frame this by understanding that IR selection on male mosquitoes is inherently wasted, because male mosquitoes play no direct role in transmission, however, when considering resistance, they help propagate IR through the population. Further studies should better evaluate the exposure of male mosquitoes to insecticides and monitor the level of IR in male mosquitoes to address this knowledge gap.

Model limitations

As with any modelling study, there are some limitations which must be addressed. Each simulation had an upper limit on IR, and this may not be applicable to areas with intense levels of IR [35]. The three gene model version (see appendix 5 of the S1 File) would allow for the cumulative addition of resistance genes, which may be more suitable for dealing with higher resistance intensities. Seasonality and environmental conditions also impact mosquito population dynamics, however, to focus directly on the impact of resistance evolution we have not considered this. The potential for behavioural resistance to evolve was not considered, however behavioural resistance (whereby mosquitoes adapt to avoid interventions) would impact both insecticide selection pressure and transmission, and so is likely to have complicated interwoven dynamics. Finally, we used vectorial capacity as our measure of transmission. The advantage of this is the generalizability to multiple mosquito-borne disease systems (malaria, dengue, lymphatic filariasis), where resistance is also a key consideration. This comes with the benefit of not needing to additionally extend the model to directly include malaria transmission and the human malaria lifecycle. However, we expect IR to have interactions with transmission intensity and the immunity of the population to malaria (as seen with malaria drug resistance [36]). By reporting vectorial capacity, we have negated these complications to better aid model results communication, but understand this may lead to underestimation of epidemiological benefits of IRM.