Why accurate risk stratification matters in HIV population modeling

Dobromir Dimitrov; Laura Matrajt; Xinze Ren; Sarah E. Stansfield; Mia Moore; Dobromir Dimitrov; Laura Matrajt; Xinze Ren; Sarah E. Stansfield; Mia Moore

doi:10.3934/mbe.2026084

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 8: 2307-2322. doi: 10.3934/mbe.2026084

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Why accurate risk stratification matters in HIV population modeling

1.
Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, Seattle, WA 98109, USA
2.
Department of Applied Mathematics, University of Washington, Seattle, WA 98109, USA

Received: 10 March 2026 Revised: 17 June 2026 Accepted: 07 July 2026 Published: 22 July 2026

Accurate representation of behavioral risk heterogeneity significantly influences the projections of Human Immunodeficiency Virus transmission models without receiving the deserved attention when models are structured. As a result, models widely vary in how they stratify risk and how individuals progress through risk groups. We systematically evaluated how these two structural features—the number of risk groups and assumptions about risk progression (comparing three mechanisms of fixed, age-based, or mixed risk)—shape epidemic projections. Using deterministic HIV models stratified by HIV stage and behavioral risk, we simulated populations over 250 years under standardized initial conditions. Our results show that risk-progression mechanisms strongly influence long-term epidemic behavior. Fixed-risk models gradually shift the population toward lower-risk groups, thus reducing HIV incidence over time. In contrast, age-based progression sustains a larger high-risk population and produces a substantially higher long-term incidence, while mixed progression yields intermediate outcomes. The granularity of risk stratification further modifies the projections: models with more risk groups generate significantly different incidence trajectories and equilibrium population sizes under age-based and mixed progression, whereas fixed-risk models produce similar long-term results with a different number of risk groups. These findings highlight that both risk-progression assumptions and the level of stratification can meaningfully alter HIV forecasts. Therefore, the careful treatment of population risk heterogeneity is essential to generate reliable projections and to guide intervention strategies.
- mathematical modeling,
- heterogeneity,
- HIV prevention
Citation: Dobromir Dimitrov, Laura Matrajt, Xinze Ren, Sarah E. Stansfield, Mia Moore. Why accurate risk stratification matters in HIV population modeling[J]. Mathematical Biosciences and Engineering, 2026, 23(8): 2307-2322. doi: 10.3934/mbe.2026084

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Abstract

Accurate representation of behavioral risk heterogeneity significantly influences the projections of Human Immunodeficiency Virus transmission models without receiving the deserved attention when models are structured. As a result, models widely vary in how they stratify risk and how individuals progress through risk groups. We systematically evaluated how these two structural features—the number of risk groups and assumptions about risk progression (comparing three mechanisms of fixed, age-based, or mixed risk)—shape epidemic projections. Using deterministic HIV models stratified by HIV stage and behavioral risk, we simulated populations over 250 years under standardized initial conditions. Our results show that risk-progression mechanisms strongly influence long-term epidemic behavior. Fixed-risk models gradually shift the population toward lower-risk groups, thus reducing HIV incidence over time. In contrast, age-based progression sustains a larger high-risk population and produces a substantially higher long-term incidence, while mixed progression yields intermediate outcomes. The granularity of risk stratification further modifies the projections: models with more risk groups generate significantly different incidence trajectories and equilibrium population sizes under age-based and mixed progression, whereas fixed-risk models produce similar long-term results with a different number of risk groups. These findings highlight that both risk-progression assumptions and the level of stratification can meaningfully alter HIV forecasts. Therefore, the careful treatment of population risk heterogeneity is essential to generate reliable projections and to guide intervention strategies.

References

[1]	M. Kot, Elements of Mathematical Ecology, Cambridge University Press, 2001.
[2]	Y. Kuang, Basic properties of mathematical population models, J. Biomath., 17 (2002), 129–142.
[3]	F. Brauer, C. Castillo-Chavez, Z. Feng, Mathematical Models in Epidemiology, New York: Springer, 2019.
[4]	D. T. Dimitrov, H. V. Kojouharov, Analysis and numerical simulation of phytoplankton-nutrient systems with nutrient loss, Math. Comput. Simul., 70 (2005), 33–43. https://doi.org/10.1016/j.matcom.2005.03.001 doi: 10.1016/j.matcom.2005.03.001
[5]	J. W. Eaton, N. Bacaer, A. Bershteyn, V. Cambiano, A. Cori, R. E. Dorrington, et al., Assessment of epidemic projections using recent HIV survey data in South Africa: a validation analysis of ten mathematical models of HIV epidemiology in the antiretroviral therapy era, Lancet Glob. Health, 3 (2015), e598–e608.
[6]	D. Dimitrov, M. C. Boily, B. R. Mâsse, E. R. Brown, Impact of pill sharing on drug resistance due to a wide-scale oral prep intervention in generalized epidemics, J AIDS Clinic Res., (2012), S5–004. https://doi.org/10.4172/2155-6113.S5-004 doi: 10.4172/2155-6113.S5-004
[7]	R. Silhol, R. L. Anderson, O. Stevens, J. Stannah, R. D. Booton, S. Baral, et al., Measuring HIV acquisitions among partners of key populations: estimates from HIV transmission dynamic models, JAIDS, J. Acquired Immune Defic. Syndr., 95 (2024), e59–e69. https://doi.org/10.1097/QAI.0000000000003334 doi: 10.1097/QAI.0000000000003334
[8]	O. Stevens, R. Anderson, J. Stover, Y. Teng, J. Stannah, R. Silhol, et al., Comparison of empirically derived and model-based estimates of key population HIV incidence and the distribution of new infections by population group in sub-Saharan Africa, JAIDS, J. Acquired Immune Defic. Syndr., 95 (2024), e46–e58. https://doi.org/10.1097/QAI.0000000000003321 doi: 10.1097/QAI.0000000000003321
[9]	S. E. Stansfield, J. Heitner, K. M. Mitchell, , C. M. Doyle, R. M. Milwid, M. Moore, et al., Population-level impact of expanding PrEP coverage by offering long-acting injectable PrEP to MSM in three high-resource settings: a model comparison analysis, J. Int. AIDS Soc., 26 (2023), e26109. https://doi.org/10.1002/jia2.26109 doi: 10.1002/jia2.26109
[10]	S. de Montigny, B. J. S. Adamson, B. R. Masse, L. P. Garrison, J. G. Kublin, P. B. Gilbert, et al., Projected effectiveness and added value of HIV vaccination campaigns in South Africa: A modeling study, Sci. Rep., 8 (2018), 6066. https://doi.org/10.1038/s41598-018-24268-4 doi: 10.1038/s41598-018-24268-4
[11]	C. van Schalkwyk, M. Mahy, L. F. Johnson, J. W. Imai-Eaton, Updated data and methods for the 2023 UNAIDS HIV estimates, JAIDS, J. Acquired Immune Defic. Syndr., 95 (2024), e1–e4. https://doi.org/10.1097/QAI.0000000000003344 doi: 10.1097/QAI.0000000000003344
[12]	B. Adamson, L. Garrison, R. V. Barnabas, J. J. Carlson, J. Kublin, D. Dimitrov, Competing biomedical HIV prevention strategies: potential cost-effectiveness of HIV vaccines and PrEP in Seattle, WA, J. Int. AIDS Soc., 22 (2019), e25373. https://doi.org/10.1002/jia2.25373 doi: 10.1002/jia2.25373
[13]	K. M. Mitchell, B. Hoots, D. Dimitrov, D. German, C. Flynn, J. E. Farley, et al., Improvements in the HIV care continuum needed to meaningfully reduce HIV incidence among men who have sex with men in Baltimore, US: a modelling study for HPTN 078, J. Int. AIDS Soc., 22 (2019), e25246. https://doi.org/10.1002/jia2.25246 doi: 10.1002/jia2.25246
[14]	P. Vickerman, F. Terris-Prestholt, S. Delany, L. Kumaranayake, H. Rees, C. Watts, Are targeted HIV prevention activities cost-effective in high prevalence settings? Results from a sexually transmitted infection treatment project for sex workers in Johannesburg, South Africa, Sex. Transm. Dis., 33 (2006), S122–S32. https://doi.org/10.1097/01.olq.0000221351.55097.36 doi: 10.1097/01.olq.0000221351.55097.36
[15]	M. Kot, D. T. Dimitrov, The dynamics of a simple, risk-structured HIV model, Math. Biosci. Eng., 17 (2020), 4184–4209. https://doi.org/10.3934/mbe.2020232. doi: 10.3934/mbe.2020232
[16]	B. Wallace, D. Dimitrov, L. Hébert-Dufresne, A. M. Berdahl, Hotspot model shows how location-based superspreading accelerates and reshapes epidemics, PNAS Nexus, 4 (2025), pgaf299. https://doi.org/10.1093/pnasnexus/pgaf299. doi: 10.1093/pnasnexus/pgaf299
[17]	Y. Zhao, D. T. Wood, H. V. Kojouharov, Y. Kuang, D. T. Dimitrov, Impact of population recruitment on the HIV epidemics and the effectiveness of HIV prevention interventions, Bull. Math. Biol., 78 (2016) 2057–2090. https://doi.org/10.1007/s11538-016-0211-z. doi: 10.1007/s11538-016-0211-z
[18]	D. T. Dimitrov, Y. Kuang, B. R. Masse, Assessing the public health impact of HIV interventions: The critical role of demographics, JAIDS, J. Acquired Immune Defic. Syndr., 66 (2014), e60–e62. https://doi.org/10.1097/QAI.0000000000000133 doi: 10.1097/QAI.0000000000000133
[19]	Y. Q. Zhao, D. T. Dimitrov, H. Liu, Y. Kuang, Mathematical insights in evaluating state dependent effectiveness of HIV prevention interventions, Bull. Math. Biol., 75 (2013), 649–675. https://doi.org/10.1007/s11538-013-9824-7 doi: 10.1007/s11538-013-9824-7
[20]	R. V. Anderle, R. B. de Oliveira, F. A. Rubio, J. Macinko, I. Dourado, D. Rasella, Modelling HIV/AIDS epidemiological complexity: a scoping review of agent-based models and their application, PLoS One, 19 (2024), e0297247. https://doi.org/10.1371/journal.pone.0297247 doi: 10.1371/journal.pone.0297247
[21]	R. Giddings, P. Indravudh, G. F. Medley, F. Bozzani, M. Gafos, S. Malhotra, et al., Infectious disease modelling of HIV prevention interventions: a systematic review and narrative synthesis of compartmental models, Pharmacoeconomics, 41 (2023), 693–707. https://doi.org/10.1007/s40273-023-01260-z doi: 10.1007/s40273-023-01260-z
[22]	B. L. Rapatski, F. Suppe, J. A. Yorke, HIV epidemics driven by late disease stage transmission, JAIDS, J. Acquired Immune Defic. Syndr., 38 (2005), 241–253. https://doi.org/10.1097/01.qai.0000146596.21084.02 doi: 10.1097/01.qai.0000146596.21084.02
[23]	A. Bershteyn, J. Gerardin, D. Bridenbecker, C. W. Lorton, J. Bloedow, R. S. Baker, et al., IImplementation and applications of EMOD, an individual-based multi-disease modeling platform, Pathog Dis., 76 (2018), fty059. https://doi.org/10.1093/femspd/fty059 doi: 10.1093/femspd/fty059
[24]	C. C. Kerr, R. M. Stuart, R. T. Gray, A. J. Shattock, N. Fraser-Hurt, C. Benedikt, et al., Optima: a model for HIV epidemic analysis, program prioritization, and resource optimization, JAIDS, J. Acquired Immune Defic. Syndr., 69 (2015), 365–376. https://doi.org/10.1097/QAI.0000000000000605 doi: 10.1097/QAI.0000000000000605
[25]	C. Selinger, A. Bershteyn, D. T. Dimitrov, B. J. S. Adamson, P. Revill, T. B. Hallett, et al., Targeting and vaccine durability are key for population-level impact and cost-effectiveness of a pox-protein HIV vaccine regimen in South Africa, Vaccine, 37 (2019), 2258–2267. https://doi.org/10.1016/j.vaccine.2019.02.073 doi: 10.1016/j.vaccine.2019.02.073
[26]	S. E. Stansfield, M. Moore, L. Jamieson, G. Meyer-Rath, L. F. Johnson, D. Kaftan, et al., Estimated impact of long-acting injectable PrEP in South Africa: a model comparison analysis, J. Int. AIDS Soc., 28 (2025), e26453. https://doi.org/10.1002/jia2.26453 doi: 10.1002/jia2.26453
[27]	T. D. Hollingsworth, R. M. Anderson, C. Fraser, HIV-1 transmission, by stage of infection, J. Infect. Dis., 198 (2008), 687–693. https://doi.org/10.1086/590501 doi: 10.1086/590501
[28]	M. C. Boily, R. F. Baggaley, L. Wang, B. Masse, R. G. White, R. J. Hayes, et al., Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies, Lancet Infect. Dis., 9 (2009), 118–129. https://doi.org/10.1016/S1473-3099(09)70021-0 doi: 10.1016/S1473-3099(09)70021-0
[29]	G. Akudibillah, A. Pandey, J. Medlock, Maximizing the benefits of ART and PrEP in resource-limited settings, Epidemiol. Infect., 145 (2017), 942–956. https://doi.org/10.1017/S0950268816002958 doi: 10.1017/S0950268816002958
[30]	R. A. Alsallaq, J. Buttolph, C. M. Cleland, T. Hallett, I. Inwani, K. Agot, et al., The potential impact and cost of focusing HIV prevention on young women and men: A modeling analysis in western Kenya, PLOS One, 12 (2017), e0175447. https://doi.org/10.1371/journal.pone.0175447 doi: 10.1371/journal.pone.0175447
[31]	K. M. Mitchell, D. Dimitrov, R. Silhol, L. Geidelberg, M. Moore, A. Liu, et al., The potential effect of COVID-19-related disruptions on HIV incidence and HIV-related mortality among men who have sex with men in the USA: a modelling study, Lancet HIV, 8 (2021), e206–e215. https://doi.org/10.1016/S2352-3018(21)00022-9 doi: 10.1016/S2352-3018(21)00022-9
[32]	M. Moore, M. C. Boily, D. J. Donnell, D. Dimitrov, Reducing the Global HIV Burden: The Importance of Uneven Exposure to the Results of HIV Prevention Trials, Infectious Diseases and Our Planet. Cham: Springer International Publishing, (2020), 217–239. https://doi.org/10.1007/978-3-030-50826-5_8
[33]	K. A. Risher, A. Cori, G. Reniers, M. Marston, C. Calvert, A. Crampin, et al., Age patterns of HIV incidence in eastern and southern Africa: a modelling analysis of observational population-based cohort studies, Lancet HIV, 8 (2021), e429–e439. https://doi.org/10.1016/S2352-3018(21)00069-2 doi: 10.1016/S2352-3018(21)00069-2
[34]	K. Zuma, L. Simbayi, N. Zungu, S. Moyo, E. Marinda, S. Jooste, et al., The HIV epidemic in South Africa: key findings from 2017 national population-based survey, Int. J. Environ. Res. Public Health, 19 (2022), 8125. https://doi.org/10.3390/ijerph19138125 doi: 10.3390/ijerph19138125
[35]	P. Heuveline, Impact of the HIV epidemic on population and household structure: the dynamics and evidence to date, Aids, 18 (2004), S45–S53. https://doi.org/10.1097/00002030-200406002-00006 doi: 10.1097/00002030-200406002-00006
[36]	J. M. Hyman, J. Li, E. A. Stanley, The differential infectivity and staged progression models for the transmission of HIV, Math. Biosci., 155 (1999), 77–109. https://doi.org/10.1016/S0025-5564(98)10057-3 doi: 10.1016/S0025-5564(98)10057-3
[37]	L. J. Abu-Raddad, I. A. Longini, No HIV stage is dominant in driving the HIV epidemic in sub-Saharan Africa, Aids, 22 (2008), 1055–1061. https://doi.org/10.1097/QAD.0b013e3282f8af84 doi: 10.1097/QAD.0b013e3282f8af84
[38]	CDC. AtlasPlus-Charts, 2026. Available from: https://gis.cdc.gov/grasp/nchhstpatlas/charts.html.

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