2.1 Entomological study of ATSB
A Phase II entomological study (previously reported in this journal [16]) was undertaken in 14 villages in central Mali. The climate in this region is highly seasonal, with high rainfall in the rainy season (peaking in September) and very dry conditions in the dry season (December-March). Full details of the study and outcomes are reported elsewhere and are summarised here for completeness.
Fourteen villages were selected to participate in the study. In the first year of the study (April 2016 to May 2017), baseline entomological data were collected in all 14 villages. They were randomly sorted into two groups of seven, with one group designated as the intervention (ATSBs + standard of care) group and one as the control (standard of care) group. ATSBs were then deployed in the intervention villages in June 2017, and entomological data collected through to December 2017. To estimate the feeding rate on the ATSBs, 1-day tests using stained bait were carried out at monthly intervals in the control villages. As a means of estimating the bait-feeding rate, simple tests were carried out in which attractive sugar baits without toxic additives (ASBs) were temporarily introduced to villages where ATSBs were not used. These baits contained a harmless dye which allowed captured mosquitoes in the relevant villages to be separated into those which had fed on the ASBs and those which had not.
Mosquitoes were collected monthly in each village using Centre for Disease Control (CDC) UV light traps, Malaise traps and pyrethroid spray catch (PSC) inside houses. Here we use the data from CDC traps as a measure of mosquito density. In addition, human landing catch (HLC) measurements were carried out indoors and outdoors. A random sample of the captured mosquitoes were examined to determine the proportion containing viable sporozoites and therefore onwardly infectious; these data were combined with the number caught per human in HLC experiments to estimate the entomological inoculation rate (EIR).
2.2 Estimating the impact of ATSBs on mosquito density and EIR
To estimate the impact of the ATSBs on the two entomological endpoints – mosquito count and EIR – we formulated a non-linear model to capture the seasonal variation in outcomes in addition to the effect of the intervention whilst accounting for the village cluster-level variability. The non-linear model with mosquito count outcomes from the CDC light traps had convergence difficulties. To improve convergence, the mosquito counts were divided by 1,000. The resultant outcome, a continuous variable that captured the mosquito density (mosquito count per thousands), was then modelled by a normal distribution with its parameters captured by the model shown in Equation 1. We let Mij denote the mosquito population density in village i where i = 1, 2...14 (7 treatment and 7 control villages) at time t (indexing days as proportion of year in which count of mosquito outcome was obtained, this proportion being calculated by dividing the reported day of the year by 365). The mean of the normal distribution was defined by the term
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The fixed effect part of Equation 1 containing the term a sin(bt – c) is a trigonometric function that captures the seasonal variation in the mosquito population density where a, b, c, d are parameters to be estimated. The term R denotes the treatment effect coefficient for ATSB (the fractional decrease in population density) while δT is the predictor that identifies treatment assignment at village level (coded as 1 and 0 for treatment and control villages respectively). The terms ri and εij denote the random intercept that captures the correlation of mosquito population density at village level and the residual variability respectively. These are assumed to be normally distributed as ri ~ N(0,σr2) and εij ~ N(0,σe2) where σr2 and σe2 are variance components to be estimated.
The EIR is modelled in a similar manner (Equation 2). Due to the nature of the data, the time t was measured in months in which the EIR value was obtained. The months were coded as t= 1 to 7 representing the months from June to December.
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)
2.3 Estimating the excess mortality
Equation 3 expresses the rate of change of the mosquito catch M following the introduction of ATSBs. This expression, based on the approach taken by Marshall et al [8], is a simplified version of the more detailed mosquito population model (see section 2.4 and supplementary information), used here as a means of relating the function fitted to the observed data (Equation 1) to mosquito mortality parameters.
![](data:image/jpeg;base64,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Here MEQ is the equilibrium mosquito catch rate (which may be constant or vary seasonally). µBASE is the baseline mosquito birth and death rate in the absence of ATSBs (such that the catch rate will equal MEQ under control conditions), and µATSB is the excess mortality due to ATSBs. µBASE is given by the natural mosquito death rate µNAT added to any additional mortality due to vector control interventions present in both control and ATSB villages. This is discussed in more detail in section 3.2.
Experimental data suggest that the rate of death after ingestion of the toxin in the ATSB is so high as to be effectively instantaneous [8]. In this case, we expect µATSB to be equal to the bait feeding rate. From Equation 1, the average mosquito catch rate in the control and ATSB arms can be written as shown in Equations 4a-b.
![](data:image/jpeg;base64,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)
The expression for catch rate changes in terms of the bait feeding rate µATSB (Equation 3) can be re-arranged to express µATSB as a function of MEXP and MEQ:
![](data:image/jpeg;base64,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)
If the approximation MEQ = MCON is used (i.e. it is assumed that when µATSB = 0, the population remains at equilibrium levels) and Equations 4a-b used to substitute for MCON and MEXP, Equation 5c can be rewritten as follows to give an estimate of µATSB in terms of the estimated parameters a, b, c, d, R and the natural death rate:
![](data:image/jpeg;base64,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2.4 Estimating the impact of ATSBs on malaria prevalence and incidence
An existing detailed model [17–19] of malaria was used for simulations of the effects of ATSBs on malaria infection levels in human populations. In the model, individuals begin life susceptible to P.falciparum infection and are exposed to infectious bites at a rate that depends on local mosquito density and infectivity. Newborn infants passively acquire maternal immunity, which decays in the first 6 months of life. After exposure, individuals are susceptible to clinical disease and may progress through a range of infection categories (clinical infection, asymptomatic infection, subpatent infection, treated and prophylaxis). As they age, the risk of developing disease declines through natural acquisition of immunity, at a rate that depends on the rate of continued exposure. At older ages, parasitaemia levels fall so that a high proportion of asymptomatic infections become sub-microscopic. Full mosquito-population dynamics were included in the model to capture the effects of vector control in preventing transmission, killing adult female mosquitoes, and the resulting reduction in egg-laying. The model has previously been fitted to existing data on the relationship between rainfall, mosquito abundance, entomological inoculation rate (the rate at which people receive infectious bites), parasite prevalence and clinical disease incidence in order to establish parameter values. Full mathematical details of the model and a complete parameter list are included in the supplementary information.
The effect of ATSBs was included in the model by modifying the death rate of mosquitoes from µBASE to µBASE + µATSB as shown in the previous section. The initial conditions for a study were created by generating characteristics (proportions of humans in different infection categories, immunity levels, etc.) at steady state under particular levels of adult mosquito density, then after an extended period of time with particular seasonal variation in adult mosquito density. ATSBs were then introduced to modify the mosquito death rate, resulting in reduced mosquito populations due to direct death and reduced larval birth rate. As noted above, the population of infectious mosquitoes decreases more significantly than the overall population, due to increased death rates causing fewer infected mosquitoes to survive for the duration of the parasite incubation period. This in turn caused reductions in EIR which in turn reduced the number of new infections. Benchmark data values including malaria prevalence and clinical incidence were recorded at regular intervals and the results compared with the same data values under control conditions (where the mosquito death rate is simply equal to the natural value µNAT) to measure the effectiveness of ATSBs.