Epidemic thresholds across sexual behavior groups in the UK Biobank

Background Sexual partnership heterogeneity strongly conditions the epidemic potential of sexually transmitted infections (STIs), while bisexual partnerships can connect otherwise distinct sexual networks and enable spillover across populations. An actionable summary of this structure is the configuration-model critical bond transmissibility <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="IM1"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> , which links right-tail heterogeneity in partner counts to a static percolation threshold (interpreted here as a structural susceptibility index under a lifetime-partner proxy). Methods We analyzed the lifetime number of sexual partners of 405,740 UK Biobank participants (aged 40–69), stratified into men with male partners (MSM), men with female-only partners (MSW), women with male-only partners (WSM), and women with female partners (WSW). Candidate heavy-tail models were fitted to the fixed top-50% tail in each stratum using discrete maximum likelihood on identical integer support. Robustness to digit preference was assessed under prespecified RAW/EXCLUDE/EM-like modes. Epidemic thresholds were estimated from empirical moments, and a two-group next-generation matrix was used to derive minimal bisexual-bridging conditions for cross-group transmission. Results In non-MSM strata, the tails were heavy but finite, with discretized lognormal or stretched-exponential models outperforming a pure power law and strictly positive thresholds (WSM <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="IM2"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>0.055</mml:mn> </mml:math> ; MSW <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="IM3"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>0.005</mml:mn> </mml:math> ; WSW <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="IM4"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>0.006</mml:mn> </mml:math> ). In MSM, extreme right-tail heterogeneity yielded a near-zero threshold ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="IM5"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>3</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:math> ), indicating high structural susceptibility to sustained spread. Threshold ordering was robust across sensitivity modes. The bridging analysis showed that modest cross-group mixing (illustratively <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="IM6"> <mml:mo>∼</mml:mo> </mml:math> 5%–7%) can sustain transmission under plausible within-group controls. Conclusion Sexual network tail structure differs sharply by sexual behavior stratum and translates into large, interpretable gaps in epidemic thresholds. These results support targeted, tail-sensitive STI prevention and explicit control of bridging pathways.