Predicting the impact of outdoor vector control interventions on malaria transmission intensity from semi-field studies

Background Semi-field experiments with human landing catch (HLC) measure as the outcome are an important step in the development of novel vector control interventions against outdoor transmission of malaria since they provide good estimates of personal protection. However, it is often infeasible to determine whether the reduction in HLC counts is due to mosquito mortality or repellency, especially considering that spatial repellents based on volatile pyrethroids might induce both. Due to the vastly different impact of repellency and mortality on transmission, the community-level impact of spatial repellents can not be estimated from such semi-field experiments. Methods We present a new stochastic model that is able to estimate for any product inhibiting outdoor biting, its repelling effect versus its killing and disarming (preventing host-seeking until the next night) effects, based only on time-stratified HLC data from controlled semi-field experiments. For parameter inference, a Bayesian hierarchical model is used to account for nightly variation of semi-field experimental conditions. We estimate the impact of the products on the vectorial capacity of the given Anopheles species using an existing mathematical model. With this methodology, we analysed data from recent semi-field studies in Kenya and Tanzania on the impact of transfluthrin-treated eave ribbons, the odour-baited Suna trap and their combination (push–pull system) on HLC of Anopheles arabiensis in the peridomestic area. Results Complementing previous analyses of personal protection, we found that the transfluthrin-treated eave ribbons act mainly by killing or disarming mosquitoes. Depending on the actual ratio of disarming versus killing, the vectorial capacity of An. arabiensis is reduced by 41 to 96% at 70% coverage with the transfluthrin-treated eave ribbons and by 38 to 82% at the same coverage with the push–pull system, under the assumption of a similar impact on biting indoors compared to outdoors. Conclusions The results of this analysis of semi-field data suggest that transfluthrin-treated eave ribbons are a promising tool against malaria transmission by An. arabiensis in the peridomestic area, since they provide both personal and community protection. Our modelling framework can estimate the community-level impact of any tool intervening during the mosquito host-seeking state using data from only semi-field experiments with time-stratified HLC.


A Elaboration of Continuous Markov chain model for host seeking behaviour
We assumed that for short times h the probabilities P H (h), P T (h), P M (h) can be approximated linearly in time with constant rates α H k , α T k and µ k , respectively, and that P A is the complementary probability of the sum of the other probabilities. This uniquely defines a a time-homogeneous, continuous-time Markov chain X(t) on the finite state space {A, H, T, M } ([1], Theorem 5.2.7, or [2], section VI.6). X(t) is characterised by the infinitesimal generator matrix and the initial probability distribution P [X(0) = A] = 1. The transition probability function P(t) = (P i,j (t)) i,j is a matrix giving the probability P i,j (t) of a transition from state i to j after time t for any i, j ∈ {A, H, T, M}. The transition probability function for our model satisfies with probabilities P A (t) = e −(αH k +αT k +µ k )t ) P H (t) = (1 − e −(αH k +αT k +µ k )t ) αH k αH k +αT k +µ k P T (t) = (1 − e −(αH k +αT k +µ k )t ) αT k αH k +αT k +µ k P M (t) = (1 − e −(αH k +αT k +µ k )t ) µ k αH k +αT k +µ k , (A. 4) for staying in 'A', moving from 'A' to 'H', moving from 'A' to 'T' and moving from 'A' to 'M', respectively, within time t.

B Non-central version of Hierarchical Bayesian model for semi-field experiments over multiple nights
We explicitly give the parameterisation and equations for the non-central version of Hierarchical Bayesian model for semi-field experiments over multiple nights. symbol description C R identifier for control arm in spatial repellent experiment I R identifier for intervention arm in spatial repellent experiment C T identifier for control arm in trap experiment I T identifier for intervention arm in trap experiment C P identifier for control arm in push-pull experiment I P identifier for intervention arm in push-pull experiment To avoid parameter correlation originating from the hierarchical model structure [3], we transform (9) to the non-central equivalent for all k ∈ {1, ..., 16}. Equation (11) still holds; equation (10) then becomes and equation (12)

C Parameter inference for semi-field model
For this section we use the notation presented in Table 1.
C.1 Intermediate, night-unspecific parameters for semifield model  Figures 7 and 8 show the inference on the intervention effect parameters by use of the semi-field model matching control and intervention. Running a no-data fit, i.e. replacing all log-likelihood functions that take data as input with 1, should approximately output the priors specified for each parameter if the prior distributions are independent of each other. The no-data fit of the intervention parameters π and ρ did not follow the specified log-normal prior distributions but were much flatter while having the same support. The no-data fit of the scale parameters for the nightly variation, σ a , σ b and σ m , did not follow the specified Half-Cauchy prior distributions, but were more concentrated around 0 while having the same support. This is surprising since the model was written in a non-centered way so that all parameters that stan samples are independent. We don't have an explanation for this behaviour. We checked that posteriors were not affected by this by running the model also with much larger scale parameters for the priors. Hence, this has no impact on the parameter inference based on data or on any other result presented in the main text. For the trap experiments, the posteriors for control and treatment human availability rate as well as the posteriors for control and treatment mortality rate lie exactly on top of each other for the matched fit since we parameterise the trap exclusively by the relative availability ρ. Figures 13, 14 and 15 show the inference on the parameters capturing the nightly variation (normalised) of the rates on the log-scale in the semi-field model without matching control and intervention for the repellent, trap and push-pull experiments, respectively. Note that the deviation of the log-rates from the mean of the log-rates is normalised here, so neither the magnitude of the deviation from the mean nor the width of the credible intervals can be compared between different rates or different experiments.   push-pull experiments, respectively. . These plots were generated with the function 'pairs' in R [4]. These plots are suitable to detect unwanted parameter correlations and identifiability problems. All independent parameters of the model were investigated, but the normalised nightly variations are not shown here. Figures 19  and 21 show negative correlation between the parameters for repelling effect (π) and killing effect (κ). This is not surprising as increasing π and increasing κ both lower the probability to encounter a host, and only the time pattern of the HLC counts over 4 HLC periods can reveal the differential contribution of the two effects. However, this does not constitute an identifiability problem since the correlation is limited to a reasonably small region of the parameter space, i.e. the posterior sample doesn't stretch over the whole parameter space. In Figures 20 and 21 the posterior sample for parameter σ b is very widespread and seems to be truncated at 0. This is due to the very low number of accidental trap catches in the control experiments, while σ b is the standard deviation of the log of the corresponding probability.    . These plots are suitable to detect unwanted parameter correlations and identifiability problems. All independent parameters, except for the normalised nightly variations, are shown, while the latter were also investigated. generated with function 'pairs' in R [4].

E Inhibition of host-seeking behaviour for multiple days
To model inhibition of host-seeking behaviour for multiple days we send mosquitoes that encountered a shadow host around the feeding cycle without actually feeding, by setting all proportions to 1, except for the proportion P Ci to move to resting state and the proportion P Di to survive the resting state. Note that this is only possible for a number of days being a multiple of the fixed number of days required to move from state B back to state A with the current model [5].   Figure 29