Inference for Within- and Between-Partnership Transmission Rates for HIV Infection

TL;DR

The paper develops a tractable stochastic pair-based SI framework to quantify HIV transmission within and between serodiscordant couples using a retrospective cohort. It provides exact analytical solutions for the pair-state dynamics and a likelihood-based inference procedure to estimate the external rate $\\lambda$ and the internal rate $\\tau$, including a gender-specific extension. The results show identifiable contributions from both routes with quantified uncertainty, yielding ML estimates around $\\lambda \\approx 0.003$ and $\\tau \\approx 0.05$ in the non-gender case and revealing gender-specific dynamics in the full model. The approach is generalizable to other settings and can inform intervention strategies by clarifying whether to prioritize blocking community acquisition or reducing within-couple spread.

Abstract

HIV transmission within serodiscordant couples remains a significant public health challenge, particularly in sub-Saharan Africa. Estimating the rate of such infection, alongside the rates of introduction of infection from outside the partnership, is a special case of the more general epidemiological challenge of inferring intensities of within- and between-group intensities of transmission. This study presents a stochastic susceptible-infected (SI) pair model for estimating key epidemiological parameters governing HIV transmission within and between couples, which we further extend to account for gender-specific differences in infection dynamics. Using a likelihood-based inference approach, we estimate transmission parameters and associated uncertainty from observed data. These values can be used to inform infection prevention strategies for HIV, and the methodology proposed can be generalised to other epidemiological settings.

Figures (3)

• Figure 1: 2D likelihood surface of the external ($\lambda$) and internal ($\tau$) forces of infection. The plot displays the maximum likelihood estimate (MLE), the closed-form approximation (CFA), and analytical estimates, along with 67% and 95% confidence interval (CI) ellipses. The CFA provides a quick estimate derived from a deterministic simplification of the underlying stochastic model.
• Figure 2: Each diagonal panel shows the profile likelihood curve for one parameter, computed by varying that parameter while fixing the others at their maximum likelihood estimates (MLE). The red dashed line indicates the MLE, and the grey shaded region corresponds to the $95\%$ confidence interval. The lower triangle panels display heatmaps of the joint likelihood (on the original likelihood scale) for each pair of parameters, again holding the remaining parameters at their MLEs. These last also show a blue line for the asymptotic solution.
• Figure 3: Validation of parameter estimation performance. The estimated external transmission rate ($\lambda$) and internal transmission rate ($\tau$) are plotted against their true values. Each point represents a simulated dataset, and the solid diagonal line corresponds to the identity line ($y = x$), indicating perfect estimation. The close alignment of points to the diagonal demonstrates the accuracy and reliability of the inference framework across a range of parameter values.