Inference for entomological semi-field experiments: Fitting a mathematical model assessing personal and community protection of vector-control interventions

The effectiveness of vector-control tools is often assessed by experiments as a reduction in mosquito landings using human landing catches (HLCs). However, HLCs alone only quantify a single characteristic and therefore do not provide information on the overall impacts of the intervention product. Using data from a recent semi-field study which used time-stratified HLCs, aspiration of non-landing mosquitoes, and blood feeding, we suggest a Bayesian inference approach for fitting such data to a stochastic model. This model considers both personal protection, through a reduction in biting, and community protection, from mosquito mortality and disarming (prolonged inhibition of blood feeding). Parameter estimates are then used to predict the reduction of vectorial capacity induced by etofenpox-treated clothing, picaridin topical repellents, transfluthrin spatial repellents and metofluthrin spatial repellents, as well as combined interventions for Plasmodium falciparum malaria in Anopleles minimus. Overall, all interventions had both personal and community effects, preventing biting and killing or disarming mosquitoes. This led to large estimated reductions in the vectorial capacity, with substantial impact even at low coverage. As the interventions aged, fewer mosquitoes were killed; however the impact of some interventions changed from killing to disarming mosquitoes. Overall, this inference method allows for additional modes of action, rather than just reduction in biting, to be parameterised and highlights the tools assessed as promising malaria interventions.

mosquito that dies postprandially (after biting) may transmit malaria to the host on which 48 it fed. If a mosquito is repelled it remains in the host seeking stage and may bite another 49 host during the current feeding cycle. There will be community protection from preprandial 50 and postprandial killing and disarming, since these end points prevent the mosquito biting 51 other members of the community during the current (and future if the mosquito is killed) 52 feeding cycle, unlike repellency. 53 Denz et al. [10] developed models and parameterisation methods to estimate the effect 54 of spatial repellents and odour-baited traps on the rate at which mosquitoes fed on humans 55 based on only HLC data from a semi-field study [24]. Although model allowed differentiation 56 between repellency, preprandial mortality and disarming, data allowing for parameterisation 57 of the magnitude of these effects was not available. It was assumed that all the reduction in 58 HLCs was due to preprandial killing or disarming. the study also modelled and parameterised 59 postprandial killing based on the proportion of mosquitoes caught by HLC which died within 60 24 hours. Results from these models were then used to inform a previously published model 61 for vectorial capacity [7], estimating the potential impact of these interventions. Their results 62 showed that the distinction disarming and preprandial mortality can have large impacts on 63 estimates of reduction in vectorial capacity. 64 In this study, we use data from semi-field experiments extended to include aspiration of survived until the next days feeding period, and therefore would have died before feeding on 126 a human and potentially transmitting malaria. 127 During round one of the experiments (2020-2021) relatively low levels of blood feed-128 ing were recorded during many of the control experiments. The World Health Organisa-129 tion (WHO) guidelines for efficacy testing of spatial repellents suggest that 50% of control 130 mosquitoes should land and 25% should feed [39]. These behaviours are desired in the con-131 trol as a change in these behaviours is needed to measure the effect of the active ingredient.

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A lack of these behaviours may be due to an error in the rearing process or damage by 133 HLC volunteers during capture. WHO guidelines on ITN evaluation suggest 50% of control 134 mosquitoes should feed [40]. This is because mosquitoes that blood feed are more likely to 135 survive. Since we also want to measure postprandial mortality here, we have combined these 136 guidelines and introduced a 50% threshold for landing and feeding. This was included in the 137 Standard Operating Procedure in round two of the experiments. For consistency, we only 138 consider data which meets this criteria for both rounds of this study. Table S1 describes how 139 many experiments met this specification for each intervention and year.  or be killed or disarmed (DM ), with probabilities P A (t), P H (t) and P DM (t), respectively.

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It is assumed that these probabilities are independent of how long the mosquito has been 157 in state A and mosquitoes leave state A following an exponential distribution. We assume 158 that the probabilities that a mosquito moves to state H or DM within a short time can 159 be approximated linearly in time with constant rates α H and α DM , respectively. Here we 160 consider the time step duration (t) to be one hour.

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Each time step the probability that a mosquito remains in state A is 162 P A (t) = exp(−(α H + α DM )t). (1) respectively. Therefore, the probabilities that a mosquito moves to state H and DM are bites a protected human on day k is given by where a, b ∈ R and σ a , σ b ∈ R + are defined in Table 3. The mean rates are the expected respectively. 243 We consider ϕ a and ϕ b , with elements ϕ a,k , ϕ b,k ∈ R, describing how a and b deviate 244 nightly from the mean according to the scale of the standard deviation, that is  logistically distributed parameter, Z, the nightly probability of the event is given as where z, ϕ z k ∈ R and σ z ∈ R + are hyperparameters. Specifically, z is the mean of logit(Z k ), 255 σ z is the standard deviation of logit(Z k ) and ϕ z,k is the normalized deviation of logit(Z k ) 256 from the mean on night k.

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The mean probability over all nights is calculated as  respectively. Here, in Equation 10, we assume that in the absence of interventions (control 277 arm), the probability of feeding for resting and HLC mosquitoes is the same. This is because 278 many control experiments had low counts of resting mosquitoes. 3.3.2 Host-availability and preprandial mortality or disarming rates 280 We denote the 15-minute intervals in which HLC data is collected ast, witht = t/4. The

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probability that a mosquito remains in state A for the first i 15-minute intervals, and then 282 enters state H during the following j 15-minute intervals is given by ity that a mosquito is a HLC in the i th 15-minute HLC interval, for i = 1, 2, . . . , 18, p Hi . For

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For the subsequent hours we assume that HLCs in the first 15-minute interval are a proxy 287 for the HLCs which would have occurred during the last 15-minute interval of the prior 288 hour as well as the first 15-minute interval of the current hour (in which they were caught).

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The probability that a mosquito is still in state A at the end of the 6-hour experiment 292 (6 1-hour time steps) is the probability the mosquito is still host seeking (p A = P A (1) 6 ).

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However, in the datasetsx A will include disarmed mosquitoes. Therefore, if we consider the 294 the true probability a mosquito remains host seeking is p A × (1 − P D A ). Rearranging for the 295 probability a mosquito is captured resting and survives 24 hours, denoted p A † , gives The probability that a mosquito is killed preprandially or is disarmed is p DM = P DM (6).

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Combining for a vector of the probability a mosquito is a HLC each 15-minute interval, 299 resting, and killed or disarmed during the experiment we get To quantify the effect of an intervention, we calculate the relative reduction of the vectorial 328 capacity when an intervention is utilised in a population compared to when it is not. This  Table 4 gives the median estimates and 95% confidence intervals (CIs) for the relative re-  This suggests the response effects to the active ingredients is dose-dependent.

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The median predicted probability a HLC mosquito was disarmed (P D H ) was between 0.12 382 and 0.91 for intervention-arms. Since the median value for all interventions is larger than 0, 383 if blood feeding was not considered, the reduction in biting would have been underestimated.

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The median predicted probability that a resting mosquito was disarmed (P D A ) was between 385 0.04 and 0.57 for intervention-arms. This indicates that disarming in HLCs in more common 386 than resting mosquitoes, however if there are a larger number of resting mosquitoes, the 387 total number of disarmed resting mosquitoes may still be larger. If blood feeding was not 388 considered, these mosquitoes would be considered as repelled and would therefore search for 389 a blood meal elsewhere, which is not the case for disarmed mosquitoes. HLCs are assumed to be a proxy for biting, however the reduction in blood feeding is evidence    Figure 1: The Anopheles feeding cycle. Mosquitoes emerge at the start of the cycle, the host-seeking stage. From here they will either die, sugar feed or encounter a host. If they encounter a host they may die before feeding, be disarmed (inhibited from blood feeding) or feed. If they feed malaria transmission may occur to the host or mosquito. After feeding the mosquito dies or rests while their eggs develop. Then, they will search for a site for oviposition. If they survive this search they will lay the eggs and either die or return to the host-seeking stage and begin the cycle again.   Table 2. Boxes with a dashed outline represent a possible end-point for mosquitoes. Dashed lines represent were resting and HLC mosquitoes are reclassified as disarmed based off blood-feeding data.
Figure 3: Relative reduction in vectorial capacity for Anopheles minimus due to each intervention for a range of coverage levels. Etofenprox-treated clothing was trailed as new and 20 days old (aged). TransPassive was trialed as new and 30 days old (aged). In round one EtoCivilian type A was used, whereas in round two type B was used. Figure 4: Median estimated values for each intervention of (Top) Relative reduction in the host availability rate for mosquitoes encountering a protected human compared to an unprotected human (π) and the increase in the rate of preprandial killing or disarming for a protected human compared to the host availability rate of an unprotected human(κ), (Middle) The contributions to κ from disarming (κ×ω) and preprandial mortality (κ×(1− ω)), (Bottom) π and the increase in postprandial mortality of protected humans compared to unprotected humans (ξ). 31 Table 1: Data generated from semi-field studies used in the statistical inference.

Definition Denotation
Number of HLC mosquitoes during the 18 15-minute intervals HLCs were performed (first three 15-minute intervals, of each hour, for 6 hours).
x H Total number of HLC mosquitoes over the 6 hours of HLCs which fed when offered a blood meal. The number of mosquitoes knocked-down at the end of the 6 hours of HLCs or resting at the end of the 6 hours of HLCs which did not survive for 24 hours.
x DM The number of mosquitoes knocked-down at the end of the 6 hours of HLCs which recovered within 24 hours.x DM Frequency data set generated each experiment, given as D = {x H1 , x H2 , . . . , x H18 ,x A , x DM }. α DM Rate host-seeking mosquitoes killed or disarmed (hour −1 ) P F,k Probability a mosquito feeds night k P F A ,k Probability a resting mosquito feeds night k P F H ,k Probability a HLC mosquito feeds night k P D,k Probability a mosquito from the intervention experiment is disarmed on night k P D A ,k Probability a resting mosquito from the intervention experiment is disarmed on night k P D H ,k Probability a HLC mosquito from the intervention experiment is disarmed on night k π Relative reduction in the host-availability rate for mosquitoes encountering a human protected by the intervention compared to a unprotected (control) human κ Increase in the rate of preprandial mortality or disarming due to an intervention relative to the rate of HLCs in the control ξ Increased probability of death after a mosquito has fed on a human protected by the intervention P M,k Probability of mortality after a mosquito bites a human ω Proportion of mosquitoes disarmed of all mosquitoes either killed preprandially or disarmed Table 4: Estimated median values and 95% confidence intervals (CIs) of the intervention parameters. π: Relative reduction in the host availability rate for mosquitoes encountering a protected human compared to an unprotected human. κ: Increase in the rate of preprandial killing or disarming for a protected human compared to the host availability rate of an unprotected human. ξ: Increase in the probability of postprandial mortality if a human is protected by the intervention. ω: Proportion of mosquitoes disarmed out of all mosquitoes either killed preprandially or disarmed by the intervention.