## Transmission modelling to investigate potential epidemiological impact at the population level

The *malaria simulation* model (48) was adjusted to include a potential mechanism of action that replicates the installation of ITS. This *Plasmodium falciparum* transmission model has been described fully (63, 64) and the house-screen updated code is publicly available (https://github.com/mrc-ide/malariasimulation; housing branch, accessed 29 March 2024).

The vector model is compartmental and deterministic, tracking different species of mosquito from eggs through to adults. Only adult females are tracked after emergence from pupae, and the sex ratio at emergence is assumed 50:50 following (65). The mosquito carrying capacity is assumed to track rainfall patterns locally (64). Adult mosquitoes seek hosts after emerging, can oviposit after successfully feeding and their mortality rate, prior to interventions are assumed as indicated in Table S2 for the species included in our simulation exercise (*An. arabiensis* and *An. funestus*). The proportion of bites taken on humans are estimated following (66, 67). The probability that bites are attempted indoors or in bed in the absence of indoor interventions is estimated following (31). Life expectancy, foraging and blood feeding rates are taken from Griffin et al. (2010) (68).

In the transmission model, the probability of a mosquito of a given species *v* biting host *i* during a single blood feeding attempt is defined as \(y_{i}^{v}\); the probability of the mosquito biting and surviving the feeding attempt is\(w_{i}^{v}\), and the probability that she is deterred without feeding is\(z_{i}^{v}\). Given these probabilities exclude natural vector mortality with no protection, these probabilities are \(y_{i}^{v}=w_{i}^{v}=1\) and \(z_{i}^{v}=0\). Not all mosquitoes feed successfully when entering a house so\(y_{i}^{v}\),\(w_{i}^{v}\) and \(z_{i}^{v}\)must take account of the potential repeating behaviour of female mosquitoes foraging prior to introducing insecticides.

Following Le Menach et al. (2007) (69) and Griffin et al. (2010) (68), we add the potential impact from barriers to the model equations tracking the probable outcomes of a female vector feeding attempt through her oviposition cycle. During a single feeding attempt on either animals or humans, a mosquito will feed successfully with probability \({W^v}\) such that:

\({W^v}=1 - Q_{0}^{v}+Q_{0}^{v}\sum\limits_{i} {{\pi _i}w_{i}^{v}}\) , [Equation 7]

Where the last term in the equation is the probability that she will be deterred without feeding (\({Z^v}\)):

\({Z^v}=Q_{0}^{v}\sum\limits_{i} {{\pi _i}z_{i}^{v}}\) , [Equation 8]

Here, \(Q_{0}^{v}\) represents anthropophagy which is defined in the model as the proportion of bites taken on humans by species when interventions are absent (Table S2). Similarly, denotes the proportion of bites that person *i* receives, without interventions present. Protection due to house screening and ITNs, both depend on the proportion of bites that are taken when a person is protected by these interventions, and this depends on human sleeping patterns and mosquito activity. In the model, we define the proportion of bites taken indoors as *φ**I* and the proportion of bites taken in bed as *φ**B.* Assumed values for these probabilities are shown in Table S2 for *An. arabiensis* and *An. funestus* mosquitoes.

When a mosquito attempts to enter a house, she can do so successfully (feeding and surviving, *s*), be killed (*d*) or be forced to repeat her search (*r*). Here, we denote the success, death or repetition due to house screening as *s**h*, *d**h* and *r**h* respectively, following the notation from (Griffin et al 2010) (68), [a superscript *v* could be included for species but we leave this out for simplicity]. Similarly, *s**n*, *d**n* and *r**n* show the corresponding outcomes with ITNs. Figure 4 demonstrates this pathway as depicted previously for ITNs by Griffin et al. (2010) (68) with the addition of some form of house screening which induces a mortality effect (*d**h*), and the removal of IRS impacts consistent with the SFS study design. The house screening is the first commodity that may be experienced by the indoor biting mosquito, where we assume that she may be deterred, killed or feed successfully. A mosquito that attempts to bite humans in bed may encounter an ITN where she may again be deterred, killed or feed successfully. If she survives (regardless of whether she was deterred or was able to feed), she must then exit the house passing the house screen (assuming that the screening completely covers all entry points) a second time, where she may again be deterred, killed or exit the house. We assume that if she is deterred during her second encounter with the house screen, she moves back into the house space, where she will be killed (assuming 100% kill from the screen) given she will encounter the screen on her attempt to exit.

The r*h*, *d**h* and r*h* terms are therefore included at both stages of the pathway, entering and exiting the building.

In the absence of house screening, both *r**h* and *d**h* are set to 0, and *s**h* is set to 1, which means that mosquitoes cannot be trapped inside the house. Similarly, in the absence of ITNs, *r**n* and *d**n* are 0, while *s**n* is 1.

**Figure 4**. **A schematic showing the modelled decision tree pathways for mosquito repetition, biting and survival, in a household with housing screen (see subscript** **h****) and where people may be sleeping under ITNs (see subscript** **n****).** We assume that a proportion of bites are taken outside (blue background; where there are no protective interventions), a proportion are attempted indoors but not on sleeping humans (green background; where they may encounter a house screen resulting in deterrence *r**h*, killing *d**h* or survival and a successful bite *s**h*) and a proportion are attempted on a sleeping human in bed (yellow background; where in addition to a house screen, they may additionally encounter an ITN, which again may result in deterrence *r**n*, killing before they are able to bite *d**n*, or successful biting *s**n*). Following a successful bite or repulsion by an ITN, a mosquito then must attempt to exit the house, passing again through the house screen, where she may again be deterred, killed or pass through safely having fed. This time, mosquitoes are deterred back into the house (assuming ITS offer complete screening), where we make the assumption that they will eventually die. Bites occur at the positions on arrows marked with a red line. Symbol *φ**I*: Proportion in mosquitoes attempting to bite humans indoors in the absence of interventions; *φ**B*: Proportion of mosquitoes attempting to bite humans in bed in the absence of interventions.

Given this structure, it is possible to estimate the probability of a mosquito of a given species being deterred, biting or successfully feeding depending on the combination of interventions in action. We adjust the (Griffin et al 2010) (68) probabilities to include the effects from house screening, (while removing the impact of IRS), and define the probability of surviving a successful feeding (*w**i*) as:

\(1-{\phi }_{I}+\left({\phi }_{B}{s}_{n}{s}_{h}^{2}\right)+({\phi }_{I}-{\phi }_{B}){s}_{h}^{2}\) [Equation 9]

Similarly, we introduce the potential impacts from housing to the probability of biting (*y**i*) such that:

\(1-{\phi }_{I}+\left({\phi }_{B}{s}_{n}{s}_{h}\right)+({\phi }_{I}-{\phi }_{B}){s}_{h}\) [Equation 10]

And the probability of repeating (*z**i*) as:

\({\phi }_{B}{{s}_{h}}^{2}{r}_{n}+{\phi }_{I}{r}_{h}\) [Equation 11]

This mechanism allows us to set a fraction of a population to receive some form of protection from the housing adaptations, to simulate that the household changes reduce the entrance of mosquitoes by a defined quantity, and that some mosquitoes will be killed on contact with the screens.

In this contribution, the SFS data are used to quantify the effect from the ITS. In previous work, meta-analyses of experimental hut trials have been used to quantify the entomological impact of ITNs by taking the estimates for mosquitoes killed, fed or deterred (numbers in exit traps) in a given treated hut, and weighting these estimates by the deterrence estimate that is a comparison between mosquitoes caught within the untreated control hut and the treated hut (70) to generate parameter values for the model (63, 71). Combining the data in this way allows an estimate of the model parameter values for *s**n0*, *r**n0*, and *d**n0* that, respectively, represent the probabilities of mosquitoes successfully feeding, repeating or being killed when an ITN is present, works optimally (subscript 0 indicative of the net having been implemented on this day as a new product), and these values sum to 1 (63, 68, 71).

With the SFS data (see Supplementary data 1), we have estimates for the necessary model parameters for the ITN at 1 year, and for the ITS both new, and after 1 year. To choose representative model parameters, only the recaptured mosquitoes are considered. For each data point (daily count of mosquitoes given species and treatment), we determine the parameter estimates following the pathways in Fig. 4. This means that, the mosquitoes recovered in the SFS data that are outside of the hut, fed and alive, out of the total recaptured, represent those who have passed into and out of the house in the screening treatment group. These are thus, *s**h**2*, so we must take the square-root to estimate *s**h* for the model parameter. The corresponding proportion of mosquitoes who have been forced to repeat their feeding attempt *r**h* can be estimated by the mosquitoes counted outside and alive, but unfed out of the total recaptured. Then, *d**h* *= 1 – s**h* *- r**h*.

In the year-old ITN treatment, the proportion of mosquitoes that were recovered dead (either indoors or outdoors and either fed or unfed) represents the parameter *d**n,t = 365 days*, where *t* can indicate optimal performance for newly applied netting (*t* = 0), or year-old performance (*t* = 365 days) as appropriate. The parameter *r**n,t = 365 days* is calculated as the proportion of mosquitoes who are recaptured outside and alive out of the total recaptured during the SFS. The corresponding estimate for *s**n,t = 365* is calculated as 1 – *r**n*,*t = 365 days* – *d**n,t = 365 days*.

Importantly, in the model, we need the estimates for these parameters at time 0, that is, the induced outcomes from products when they are newly introduced and working optimally. It is also necessary to estimate the durability of the products and make an assumption on how rapidly these impacts decay after three years use. This represents a critical unknown for both the pyrethroid PBO ITN and ITS products, and this is being addressed for the former in ongoing work [57]. Previously, a mean duration of mortality inducing impact has been estimated by Griffin et al. (2010) [69] from Mahama et al (2007) [73] for pyrethroid-only ITNs using washed ITNs, and the same logic applied for pyrethroid-PBO ITNs (71). This assumes that the killing effect from ITNs will decrease at a constant rate *γ**n.*.

The impacts from implementing ITNs are projected to changes so that:

$${r}_{n}=\left({r}_{n0}-{r}_{nm}\right){exp}^{-t{\gamma }_{n}}+{r}_{nm}$$

$${d}_{n}={d}_{n0}{exp}^{-t{\gamma }_{n}}$$

$${s}_{n}=1-{r}_{n}-{d}_{n}$$

Applying these rates of decay to the data from the SFS, and back-calculating for the pyrethroid-PBO ITN entomological impact at time 0 returns higher mortality estimates than the meta-analysis (Table 2).

In the absence of further information for durability of the ITS, we explore a reasonable range in the mean duration of the product mortality inducing impact that would return mortality estimates after 365 days within the range of the SFS results. A minimum deterrence impact is set for both ITNs (*r**mn*) and screens (*r**mh*). For ITNs, this estimate is assumed to be 0.24 (Griffin et al. 2010). For the screens, we cap this at 0.25 indicating a 25% reduction in entry assuming it is unlikely that the barrier will be lost even as insecticide potency wanes and it is assumed to be less likely that holes will accumulate as rapidly in the screen netting than the ITN netting. We mirror the structure for waning efficacy from ITNs into the mechanism of action for ITS such that:

$${r}_{h}=\left({r}_{h0}-{r}_{hm}\right){exp}^{-t{\gamma }_{h}}+{r}_{hm}$$

$${d}_{h}={d}_{h0}{exp}^{-t{\gamma }_{h}}$$

$${s}_{h}=1-{r}_{h}-{d}_{h}$$

In addition, we include simulations that use pyrethroid-PBO ITN parameters developed via the statistical framework and validated against gold standard randomised control trial data for testing the epidemiological impact from these interventions (63). In the review work preceding the validation exercise (70), associations between entomological impact and the level of phenotypic resistance in *Anopheles* populations were statistically determined allowing the resistance-level specific parameterisation of impacts on mosquitoes from ITNs within the transmission model. Values aligning with the resistance status of the species *An. arabiensis* and *An. funestus* tested within the SFS are used here for the model simulation exercise.

Table 2

Transmission model parameter ranges describing entomological impact from the pyrethroid-PBO ITN, and ITS as estimated from a systematic review of experimental hut trials (70) and modified for modelling and validated against RCTs (63), using the SFS data. Parameters shown are required to simulate the potential epidemiological impacts from these interventions.

Parameter value and description | Parameter ranges simulated |

| Description | *An. arabiensis* outcomes: assuming 3–46% of mosquitoes are killed on exposure to discriminating dose of pyrethroid at tube bioassay testing | *An. funestus* outcomes: assuming 10–78% of mosquitoes are killed exposure to discriminating dose of pyrethroid at tube bioassay testing |

Pyrethroid PBO ITNs meta-analysis parameters | Median, 10th − 90th percentiles |

*r**n0* | Deterrence outcome from pyrethroid-PBO ITN working optimally immediately after deployment | 0.500 (0.567–0.471) | 0.467 (0.551–0.444) |

*d**n0* | Mortality inducing effect from pyrethroid-PBO ITN working optimally immediately after deployment | 0.454 (0.261–0.504) | 0.500 (0.365–0.541) |

*γ**n* | Mean duration of mortality effect from pyrethroid-PBO ITN when working optimally | 808 (378–998) days | 995 (582–1277) days |

Pyrethroid PBO ITNs semi-field system estimated parameters | Median, 25th – 75th percentiles |

*r**n0* | Deterrence outcome from pyrethroid-PBO ITN working optimally immediately after deployment | 0.28 (0.46–0.24) | 0.27 (0.34–0.24) |

*d**n0* | Mortality inducing effect from pyrethroid-PBO ITN working optimally | 0.57 (0.48–0.57) | 0.72 (0.63–0.75) |

*γ**n* | Inferred mean duration of mortality impact from pyrethroid-PBO ITN when working optimally | 1392 (1016–1472) days | 1419 (1257 – 1472) days |

ITS | Median, 25th – 75th percentiles |

*r**h0* | Deterrence outcome from ITS working optimally immediately after deployment | 0.13 (0.04–0.25) | 0.04 (0.00–0.13) |

*d**h0* | Mortality inducing from ITS working optimally immediately after deployment (SFS data) | 0.72 (0.59–0.82) | 0.91 (0.80–0.95) |

*γ**h* | Mean duration of mortality effect from pyrethroid-PBO ITN when working optimally, inferred from SFS data | 774 (467–1795) days | 1284 (774–2101) days |

## Scenario analysis

We use the adjusted transmission model to simulate a set of theoretical intervention scenarios. To manage feasibility in the number of simulations run, and to specifically explore the comparison between pyrethroid-PBO ITNs and ITS, for all simulations, we use the median model parameters that have been fitted previously for malaria simulation (48, 68, 72, 73), except for the values indicated in Table 2. This is a limitation as we do not express full uncertainty, but this serves our purpose to illustrate potential impact from ITS, and comparable impact with pyrethroid-PBO ITNs. For the set up, we use a theoretical setting with malaria prevalence in children of 6 to 59 months of age reaching about 60% during the peak season, with a single transmission season profile. In all simulations, treatment of clinically ill patients is implemented so that 45% of people receive artemisinin combination therapy (ACT) when needed, a further 15% receive non-ACT treatment. It is assumed that 50% of mosquitoes have the *An. arabiensis-*like bionomics and 50% have the *An. funestus-*like bionomics (Table S2) and corresponding impacts from the ITN or ITS interventions (Table 2) given the range in resistance expressed during WHO tube bioassay testing (Table S1) as determined by Nash et al. (2021) (70) and validated in Sherrard-Smith et al. (2022) (63). Adherence to ITN use is also simulated to wane over time (22) so that by three years, half as many people are using the original net. Each simulation is run for 15 years. The first six years generate a relative equilibrium before we switch on comparative scenarios (in Fig. 6, this is year 0). Pyrethroid-PBO ITNs are implemented every 3 years from the start, depending on the scenario explored, ITS is also implemented on 3-year cycles from year 0 (Fig. 6). It is assumed for both that the interventions are deployed overnight and to the target proportion of the population, who immediately replace old nets with the newly distributed ones and gain the benefit from their impact. In reality, it will take longer to provide a community with ITS, but the longer-term gains should level out for this theoretical exploration of epidemiological impacts.

To consider the potential impact, of each intervention class (pyrethroid-PBO ITNs or ITS), a counterfactual simulation is also run where ITNs are distributed in year − 6 and − 3 but then no longer deployed. Older nets may still circulate in the population but will have a far lower efficacy given that insecticide would have waned, and use fallen to a low level. To estimate reductions in prevalence, the average prevalence in children of 6–59 months of age, 5–15 years and for all-ages, over years 0–3 for the treatment simulation (*C**T*) are compared to the corresponding estimate from the counterfactual simulation (*C**C*). To estimate cases averted, the same age groups are considered across 3 years to generate an estimated number of cases averted per 1,000 population. That is:

$$Epidemiological Impact= \frac{\left({C}_{C}-{C}_{T}\right)}{{C}_{c}}$$

Where *C* can indicate prevalence or cases as required.

The pyrethroid-PBO ITNs – parameterised using the meta-analysis approach (63, 70) or using the directly comparable approach by generating parameters from the SFS data, and ITS products are simulated as stand-alone or combined interventions (Fig. 6). Code is provided as Supplementary Material 2.

Next, to consider the potential of this novel product, a simple sensitivity analysis is performed on the population ITS coverage and product durability (the mean duration of the mortality inducing impact). The counterfactual is the use of pyrethroid-PBO ITNs, parameterised as per the meta-analysis (63, 70), distributed every three years to 60% of the population on deployment. Here, we simulate the median estimated impact from the ITS given increasing cover from 0 to 80% of the community, and for a product that has a mean duration of one year through to five years.