Predicting the public health impact of a malaria transmission-blocking vaccine

Transmission-blocking vaccines that interrupt malaria transmission from humans to mosquitoes are being tested in early clinical trials. The activity of such a vaccine is commonly evaluated using membrane-feeding assays. Understanding the field efficacy of such a vaccine requires knowledge of how heavily infected wild, naturally blood-fed mosquitoes are, as this indicates how difficult it will be to block transmission. Here we use data on naturally infected mosquitoes collected in Burkina Faso to translate the laboratory-estimated activity into an estimated activity in the field. A transmission dynamics model is then utilised to predict a transmission-blocking vaccine’s public health impact alongside existing interventions. The model suggests that school-aged children are an attractive population to target for vaccination. Benefits of vaccination are distributed across the population, averting the greatest number of cases in younger children. Utilising a transmission-blocking vaccine alongside existing interventions could have a substantial impact against malaria.


Supplementary
: Data of malaria prevalence and oocyst counts in naturally infected mosquitoes in Longo (Burkina Faso). Panel A: prevalence data (black dots indicate the proportion, error bars showing the 95% CI) collected at the end of each time period of mosquito collection. These data were used to set the transmission intensity (determined by the value of the entomological inoculation rate, here set to 195 infectious bites per person per year) in the malaria transmission model, utilising data on ITN coverage and levels of insecticide resistance observed in the region. The black curve shows model-estimated prevalence by microscopy over time. The four time periods during which mosquitoes were collected are indicated by the horizontal black lines on this panel. No oocyst-positive mosquitoes were found in the first collection period, due to a combination of a lower malaria prevalence in humans, and a smaller mosquito population present in the study site during the dry season. Panels B, C, and D display the distribution of oocyst counts observed in infected mosquitoes (red bars) in collection periods 2, 3, and 4 and predicted by the best-fit model (turquoise bars). The model was fitted by attributing distinct distributions of oocyst counts for the four infectious states in the model (summarised in Figure 3D and shown in full in Figure S3). The data (red) is compared to the best-fit model (turquoise). Panels C and D are also shown in Figure 3 (panels B and C, respectively) in the main text, but are included again here for the convenience of the reader.  Figure 3: Oocyst counts associated with each of the four infectious states. The bestfit distributions (coloured lines) for the oocyst counts associated with each of the four infectious states in the transmission model. The states (as indicated on each panel) are untreated symptomatic disease (D); treated symptomatic disease (T); asymptomatic infection (A); submicroscopic asymptomatic infection (U) (colours as per Figure 3 and Supplementary Fig. 1). These distributions are summarised in their cumulative form in Figure 3D in the main text. The black line (which is the same curve in each panel) gives the probability (scale on the right-hand axis) of a vaccine with a TRA of 90% successively blocking an infection that, in the absence of vaccine-derived antibodies would have produced a given number of oocysts. For this value of the TRA, the TBA for each state is included on the panel.
Supplementary Figure 4: Impact of a malaria vaccine at differing transmission intensities. Additional results for the modelling scenarios outlined in Figure 7 in which additional malaria cases are averted by utilising a malaria vaccine (80% coverage of the specified age groups) alongside ITNs. The impact of the vaccine varies depending on the intensity of transmission (which here we represent by the population prevalence prior to the introduction of ITNs). Here we vary the age group targeted for vaccination, and whether a PEV is included. In comparison to a setting in which ITNs are fully effective (panel A), the impact of the vaccination campaign is higher in a setting in which the impact of ITNs is diminished due to high levels of pyrethroid resistance in the mosquito population (panel B). In the results presented in the main text, we assume that mosquitoes become more heavily infected after feeding on humans with symptomatic malaria infections, compared to asymptomatic ones. This means that transmission from symptomatic humans is harder to block. Here we compare that model with a simpler one, in which we relax this assumption, fitting only a single distribution to the oocyst count data. In the left panel, we show the relationship between TRA and TBA obtained for this case (the black line), compared to the four relations obtained in Figure 3 (coloured lines). The middle panel shows the corresponding cumulative distribution of oocyst counts obtained. In the right panel, we repeat the modelling exercise shown in Figure 4, in which we explored the impact of a mass vaccination campaign with a TBV, varying the vaccine coverage and the duration of vaccine activity. We find that the more complicated model (solid lines), with four relations between TRA and TBA for the different presentations of malaria described in the transmission model, predicts a higher number of cases averted than the simpler model (dot-dashed lines). We discuss the reasons for this in the main text.
Supplementary Figure 6: Diagram illustrating the structure of the malaria transmission model. The estimated public health impact of a malaria vaccine was generated using an age-structured model of malaria transmission due to Griffin et al. (22,27), which tracks the malaria status of human population, as well as that of the mosquito population. The human population is described using six states: S (susceptible), T (treated symptomatic infection), D (untreated symptomatic infection), P (protected, due to drug prophylaxis) A (asymptomatic infection), U (asymptomatic sub-patent infection). The rate at which humans acquire new infections is determined by , the force of infection, and a proportion ( ) of new infections are symptomatic. Parameter indicates the proportion of symptomatic infections that are treated. The rates , , , and , define the mean duration of each infection stage, and governs the duration of prophylaxis due to drug treatment. As indicated by the red outlines, humans carrying an infection can infected feeding mosquitoes, which are described as SM (susceptible), EM (exposed, not yet infectious), and IM (infectious). A transmission-blocking vaccine acts to reduce the probability that a mosquito becomes infected after taking a bloodmeal from an infected human (again signified by the red outline). This figure was adapted by the authors from the one in Ref. (22).

Describing the two malaria vaccines
We commence this section by summarising the RTS,S modelling work due to White et al. (41). Here we will utilise their model of the RTS,S vaccine, and also use it to motivate a model of the duration of activity for a hypothetical TBV. In White et al. (41), the RTS,S vaccine's efficacy against infection, ( ), has the form: where ( ) is the antibody titre days after vaccination, !"# is the maximum efficacy of the vaccine, and parameters and determine the shape and scale of the dose-response curve. The impact of vaccination with this vaccine is incorporated in the transmission model by reducing the per-bite probability of become infected by an infectious mosquito by a factor of (1 − ( )). After vaccination, antibody titres are assumed to reach their peak value, then wane over time according to a bi-phasic exponential model: In the trial, some participants received a booster dose 18 months later. Antibody dynamics observed after the booster dose were modelled similarly: Throughout this work, we use the parameter values obtained for the older cohort (enrolled at age 5-17 months) of the randomised controlled phase 3 trial (see Table S2). For hypothetical antibody dynamics observed following vaccination with a TBV, ( ), we use a very similar model For simplicity, we assumed identical response to vaccination following a booster dose, as for the primary dose, using 345 = 0.7 throughout. For ()"* , we selected a value within the range of values observed in Ref.
(10) ( ()"* = 22). We retain the value of 0 and 6 obtained for the RTS,S vaccine. In the modelling scenarios where we explore the impact of a shorter-or longer-lasting vaccine activity, we simply halved or doubled these values.
For the TRA of the TBV vaccine considered in this work, we utilised a model fitted by Bompard et al. (10), who estimated the TRA as a function of titre via direct membrane feeding assay using antibodies produced in mice. The model has the following form: where is the antibody titre, and the parameter values are: = 12.63, $ ; = 2.50, and < ; = 0.06.

Description of the transmission model
In order to estimate the public health impact of introducing the malaria vaccines into a malariaendemic population, we utilised an existing model of malaria transmission due to Griffin et al. (22,27). A schematic of the model is displayed in Figure S6, which shows both the human and mosquito components. This age-structured model, which allows for the development of naturally acquired immunity in populations living in malaria-endemic settings, has been calibrated to data from a range of settings across Africa. Denoting age by , the human-component of the model can be written mathematically using partial differential equations in the following form: The human population is described using six states: S (susceptible), T (treated symptomatic infection), D (untreated symptomatic infection), P (protected, due to drug prophylaxis) A (asymptomatic infection), and U (asymptomatic sub-patent infection). A full list of parameter definitions is provided in Supplementary Table 3.The rates , , etc. define the mean duration of each infection stage ( Figure S6). The force of infection upon the human population at time is denoted by , with indicating the delay between being bitten by an infected mosquito and developing a blood-stage infection. The probability that, after becoming infected, an individual becomes symptomatic is given by . Parameter is the probability of receiving drug treatment for a newly acquired symptomatic infection, which for the settings considered here was set to 0.4. We used estimates of treatment coverage in African children under 5 years old as a proxy for treatment coverage of the population. Estimates for treatment coverage in Burkina Faso at the time that the mosquitoes were collected (2014) were estimated from national surveys, collected in Bennett et al. (51). Rather than solving these partial differential equations, the human population is discretised into age groups and the resulting system of ordinary differential equations is solved numerically.
The rate at which people receive mosquito bites is age-dependent, due to body size. In the model this is described by where , where is the relative biting rate at birth compared to adults, determines the time-scale of the increase in biting rate with age. In the model, the biting rate is also heterogeneous across the population. It is assumed that each person has a relative biting rate , which persists over their lifetime, having a log-normal distribution between people with a mean of 1 i.e. .
This mean that the force of infection at age and time , , is given by where is the EIR as measured for adults at time , is the EIR for an individual of age at time t, and is the probability of human infection if bitten by an infectious mosquito.
To describe the generation and impact of naturally acquired immunity, several auxiliary functions are used. In the model, immunity acts to (i) reduce the probability that receiving an infectious bite results in a blood-stage infection ( ); (ii) reduce the likelihood of becoming symptomatic after acquiring a new blood-stage infection (maternal and acquired clinical immunity, and respectively); (iii) reduce the likelihood of a blood-stage infection being detected by microscopy ( where in each case the constant represents the time during which immunity cannot be boosted after receiving a previous boost and the rate governs the duration of immunity. The probability of an infectious bite leading to a blood-stage infection is given by (S11) Where and are scale and shape parameters. Maternal clinical immunity is present from birth, and is related to the acquired-immunity of a 20-year-old in the population by a constant .
This immunity decays at rate . The probability that a newly acquired blood-stage infection becomes symptomatic is given by , which has the form: Where and are scale and shape parameters. As immunity can act to suppress parasite density, it can lead to blood-stage infections becoming sub-patent. In the model the probability that an asymptomatic infection (state A) will be detectable by microscopy is Where and are scale and shape parameters, and is a function of age given by with parameters , , and . The lower probability of detection also reduces onward infectivity in the model, as it is assumed to be due to lower parasite density. While the infectivity associated with state D ( ), T ( ), and U ( ) are constant (i.e. independent of levels of naturally acquired immunity), in state A infectious is given by  (27)).
The mosquito component of the model is much simpler than the human one. Mosquitoes can move between three different states: Susceptible ( ), exposed ( ), and infectious ( ): (S14) where is the probability that a mosquito survives the period from acquiring infection until sporozoites appear in the salivary glands ( , extrinsic incubation period), is the adult death rate, is the force of infection acting on mosquitoes and is the time-varying emergence rate. This emergence rate which determines the vector-to-host ratio is adjusted to determine endemicity at the different transmission sites. For Klesso and Longo, the average value of over the course of a year was 27.2 day -1 and 10.9 day -1 respectively (the size of the mosquito population in the model is expressed relative to that of the human population). The emergence rate is determined by the overall size of the mosquito population. For the full details of the larval-stage of the mosquito model, see Ref. (45). The human adult EIR is given by where is the rate at which a mosquito takes a human blood meal and is the normalizing constant for the biting rate over ages, with a population age distribution of , . (S15) The force of infection acting on mosquitoes is the sum of the contribution to mosquito infection from the different human infectious states, where , , and are the onward infectivity to mosquitoes of these different states and is the time-lag between parasitaemia with asexual parasite stages and gametocytemia (infectivity to mosquitoes) to account for the lag in gametocyte development characteristic of P. falciparum.

The impact of ITNs on the mosquito population
The impact of ITNs upon the mosquito population is to induce mortality and reduce the probability of their successfully acquiring a blood meal. Note that they can only prevent, at maximum, the proportion of mosquito bites that take place whilst people are in bed. Following a recent study of the feeding behaviour of Anopheles mosquitoes across Africa (35), we set this proportion to 0.79. Of the mosquitoes that would have acquired a blood-meal in the absence of the ITN, only a proportion, = , do in its presence. The remainder are either repelled (proportion = ), or killed (proportion = ), with = + = + = = 1. The efficacy of the net decays from its optimal value (indicating below by the subscript 0) over time as follows: where = is the half-life (in years) of the insecticide. The inclusion of parameter =? indicates the ITN still provides some protection (i.e. a physical barrier) against mosquitoes in the absence of any insecticide. The numerical values for these parameters are determined by the level of pyrethroid resistance in the mosquito population. The degree of resistance to the insecticide is determined by a bioassay and previous modelling work (48) (Equations 3 and 4). We note that parameter is usually equal to the mean of the negative binomial distribution but here it is not as we are using a zero-truncated distribution. The reported values for the means, given in the Results section, have been adjusted to reflect this truncation. Distributions were fitted to the oocyst counts observed in Klesso and Longo (presented in Figures 1, S1, S2), utilising the malaria status of the populations in the two study sites during the four time periods in which data was collected ( Figures  1A, S1A). The posterior distribution was obtained using the Metropolis-Hastings algorithm.   (50). The antibody decay rates presented here, were the ones observed for the older cohort in the multicentre phase 3 trial (children enrolled between 5-17 months old). For the peak antibody titres, we followed the modelling study by Hogan et al. (34), in which the median value from the 11 study sites was used.