Bayesian inference of set-point viral load transmission models

When modelling HIV epidemics, it is important to incorporate set-point viral load and its heritability. As set-point viral load distributions can differ significantly amongst epidemics, it is imperative to account for the observed local variation. This can be done by using a heritability model and fitting it to a local set-point viral load distribution. However, as the fitting procedure needs to take into account the actual transmission dynamics (i.e., social network, sexual behaviour), a complex model is required. Furthermore, in order to use the estimates in subsequent modelling analyses to inform prevention policies, it is important to assess parameter robustness. In order to fit set-point viral load models without the need to capture explicitly the transmission dynamics, we present a new protocol. Firstly, we approximate the transmission network from a phylogeny that was inferred from sequences collected in the local epidemic. Secondly, as this transmission network only comprises a single instance of the transmission network space, and our aim is to assess parameter robustness, we infer the transmission network distribution. Thirdly, we fit the parameters of the selected set-point viral load model on multiple samples from the transmission network distribution using approximate Bayesian inference. Our new protocol enables researchers to fit set-point viral load models in their local context, and diagnose the model parameter's uncertainty. Such parameter estimates are essential to enable subsequent modelling analyses, and thus crucial to improve prevention policies.