Evaluation of two lead malaria transmission blocking vaccine candidate antibodies in natural parasite-vector combinations

Transmission blocking vaccines (TBV) which aim to control malaria by inhibiting human-to-mosquito transmission show considerable promise though their utility against naturally circulating parasites remains unknown. The efficacy of two lead candidates targeting Pfs25 and Pfs230 antigens to prevent onwards transmission of naturally occurring parasites to a local mosquito strain is assessed using direct membrane feeding assays and murine antibodies in Burkina Faso. The transmission blocking activity of both candidates depends on the level of parasite exposure (as assessed by the mean number of oocysts in control mosquitoes) and antibody titers. A mathematical framework is devised to allow the efficacy of different candidates to be directly compared and determine the minimal antibody titers required to halt transmission in different settings. The increased efficacy with diminishing parasite exposure indicates that the efficacy of vaccines targeting either Pfs25 or Pfs230 may increase as malaria transmission declines. This has important implications for late-stage candidate selection and assessing how they can support the drive for malaria elimination.


Prevalence-intensity model
The prevalence-intensity model links mean oocyst counts to the prevalence of oocysts in the mosquito population for each batch of mosquitoes. This provides a measure of the degree of parasite aggregation and explains the relationship between TBA and TRA 1,2 .
Let indicates the intervention group under investigation (be it 0=control mosquitoes, 1=anti-Pfs 25 or 2=anti-Pfs 230-C test antibodies) and be the batch of mosquitoes fed on the same parasite-source and maintained together. The mean number of oocysts in a mosquito population (the intensity) in batch given intervention is denoted and is described by a negative binomial distribution with parameters ∝ (constant success probability) and (a function describing the over-dispersion parameter, [1] The number of blood-fed mosquitoes dissected is denoted and is the proportion of these with identifiable oocysts (the prevalence). The relationship between prevalence and intensity for data with a negative binomial distribution is given by the following equation, Allowing to vary (as a constant or dependent on mean parasite intensity) changes the shape of the relationship between oocyst prevalence and intensity. Here the full model uses a simple linear function, It is assumed that the number of mosquitoes infected, denoted is described by a binomial distribution then parameters and can be estimated for each treatment group using the following equation, Data from all intervention groups are fit at the same time allowing models with and without antibody specific and parameters to be directly compared. Models setting = 0 were also run to determine whether the degree of overdispersion changed with parasite intensity.
The transmission blocking activity of intervention is defined by the percentage reduction in the prevalence of oocysts and is denoted . For each treatment ( ) and blood-source ( ), = 0 (1 − ). [5] Transmission blockade is then decomposed into two functions capturing the impact of antibody titre (titre effect, ) and parasite exposure (exposure effect, ): The relationship between titre and vaccine efficacy is typically described using the Hill equation, where is the antibody specific titre used of intervention , is the mean titre on the experiment (a constant used to center the data and help the fitting process), and 1−3 are parameters to be fitted. Equation [7] is compared to four simpler functions, a constant model where efficacy is independent of titre ( = 1 ) and a linear model ( = 2 + 1 ), a simple exponential function ( = 1 − exp(− 1 )), and a sigmoid function ( = 1/(1 + exp(− 1 + 2 )). To determine whether functions varied between antibodies models using common or discrete parameter between antibodies were compared.
Following visual inspection of data TBA appears to decline at an approximate exponential rate with increasing parasite exposure (as defined as the mean oocyst intensity in the control group of mosquitoes from the same blood-source, 0 ). A variety of different functional forms were tested for the relationship and the full equation is given below, Parameters 1−3 are estimated from the fitting process. Setting these parameters to zero or one reduces Equation 8 to simpler (nested) functions which were fit and compared to ensure the most parsimonious model. The different titre effect and exposure effect models were compared against one another (a full list of the models tested is given in Supplementary information B). Equations [1] to [8] were fit to the full dataset simultaneously to enable the uncertainty in prevalence estimates (both control and intervention) and intensity estimates (in the control group only) to be accounted for in the best fit model and propagated in the uncertainty around the best fit line.
The model is fit to the individual oocyst data assuming a negative binomial distribution (using which generates TBA from TRA and intensity, where is the exposure effect described in equation [8] and parameters ′ 1 , ′ 2 and 1 , 2 are obtained by fitting respectively TRA and TBA titre effect functions (see equation [7]). In the best fit models, these parameters are distinct for anti-Pfs 25 and anti-Pfs 230-C antibodies, which indicate that the shape of the relationship between TRA and TBA is specific to each antibody.

Supplementary information B. Model selection (DIC tables)
1.  the prevalence-intensity model (C). The code notation indicates the different parameters in the OPENBUGS code used to fit the model (as presented in Supplementary information D).