Transmission network parameters estimated from HIV sequences for a nationwide epidemic

Abstract

Background: Many studies of sexual behavior have shown that individuals vary greatly in their number of sexual partners over time, but it has proved difficult to obtain parameter estimates relating to the dynamics of human immunodeficiency virus (HIV) transmission except in small-scale contact tracing studies. Recent developments in molecular phylodynamics have provided new routes to obtain these parameter estimates, and current clinical practice provides suitable data for entire infected populations.

Methods: A phylodynamic analysis was performed on partial pol gene sequences obtained for routine clinical care from 14,560 individuals, representing approximately 60% of the HIV-positive men who have sex with men (MSM) under care in the United Kingdom.

Results: Among individuals linked to others in the data set, 29% are linked to only 1 individual, 41% are linked to 2-10 individuals, and 29% are linked to ≥10 individuals. The right-skewed degree distribution can be approximated by a power law, but the data are best fitted by a Waring distribution for all time depths. For time depths of 5-7 years, the distribution parameter ρ lies within the range that indicates infinite variance.

Conclusions: The transmission network among UK MSM is characterized by preferential association such that a randomly distributed intervention would not be expected to stop the epidemic.

Figure 1.

Flowchart of data manipulation and processing. NJ, neighbor-joining; UK HIVRDB, United Kingdom Human Immunodeficiency Virus Drug Resistance Database.

Figure 2.

Cluster size distribution of the human immunodeficiency virus transmission network among men who have sex with men in the United Kingdom. Horizontal scale unit, 2; vertical scale, number of clusters; left axis, cluster size of 2–9 (black); right axis, cluster size of 10–106 (gray).

Figure 3.

Estimation of network structure. The reconstruction of the largest network cluster is shown at 3 time depths: 3 years, 5 years and 7 years. Networks were initially reconstructed from the dated trees generated by BEAST at all time depths of 1–16 years. The networks for time depths of 3–7 years were used in the distribution fitting (Table 1; Figure 2).

Figure 4.

Comparison of the fit of different distributions to the observed network structure. The fit of 4 different distributions, including 2 based on explicit preferential attachment models, to the observed data is shown as the difference between the Akaike information criterion for small sample sizes (AICC) value for each distribution at each time depth and the lowest AICC value at that time depth for time depths 3–7 years (see Table 1).

Figure 5.

Test of the difference in fit between the Waring and negative binomial distributions. Populations were simulated using the parameter values estimated from the data under a Waring distribution (A) and a negative binomial distribution (B), and both distributions were tested for goodness of fit using the Akaike information criterion for small sample sizes (AICC). The simulations show that the negative binomial never fits as well to a Waring distribution as the Waring distribution, although the difference is not great. However, the converse does not hold: the Waring distribution can provide a fit that is not perceptively poorer to a negative binomial distribution.