2.1 Entomological study of ATSB
A Phase II entomological study (previously reported in this journal ) 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
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.
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 , 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.
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 . 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.
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:
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:
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.