A virtual epidemics approach to HIV dynamics in the United States (1981–2030)

Necibe Tuncer; Yuganthi R. Liyanage; Vincent D. Holmlund; Maia Martcheva; Necibe Tuncer; Yuganthi R. Liyanage; Vincent D. Holmlund; Maia Martcheva

doi:10.3934/mbe.2026085

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 8: 2323-2366. doi: 10.3934/mbe.2026085

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A virtual epidemics approach to HIV dynamics in the United States (1981–2030)

1.
Department of Mathematics and Statistics, Florida Atlantic University, Boca Raton, FL 33431, USA
2.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
3.
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA

Received: 05 March 2026 Revised: 04 May 2026 Accepted: 23 June 2026 Published: 24 July 2026

The human immunodeficiency virus (HIV) epidemic in the United States has changed substantially since it was first identified in 1981; yet, progress toward ending the HIV epidemic targets remains uncertain. In this study, we examined the progress of the United States using HIV epidemic data from 1981 to 2025 and project trends through 2030 using mathematical transmission models. Two models were considered: A transmission model without pre-exposure prophylaxis (PrEP) and an extended model incorporating PrEP-related behavioral dynamics. Structural and practical identifiability analyses were used to assess whether model parameters could be reliably estimated from available surveillance data. Although both models were structurally identifiable under fixed assumptions, only the model without PrEP was practically identifiable with current surveillance data. We introduced the concept of virtual epidemics (VEs) and generated a collection of epidemic trajectories by repeatedly fitting the identifiable model to bootstrapped surveillance data. These VEs reproduced historical HIV incidence trends and yielded a range of plausible future outcomes. Our simulations suggested that, under current patterns of diagnosis, treatment, and prevention, the goal of reducing $ 90\% $ of the HIV epidemic in new infections by 2030 was unlikely to be met without additional intervention efforts.
- virtual epidemics,
- evolutionary game theory,
- structural identifiability,
- practical identifiability,
- HIV
Citation: Necibe Tuncer, Yuganthi R. Liyanage, Vincent D. Holmlund, Maia Martcheva. A virtual epidemics approach to HIV dynamics in the United States (1981–2030)[J]. Mathematical Biosciences and Engineering, 2026, 23(8): 2323-2366. doi: 10.3934/mbe.2026085

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Abstract

The human immunodeficiency virus (HIV) epidemic in the United States has changed substantially since it was first identified in 1981; yet, progress toward ending the HIV epidemic targets remains uncertain. In this study, we examined the progress of the United States using HIV epidemic data from 1981 to 2025 and project trends through 2030 using mathematical transmission models. Two models were considered: A transmission model without pre-exposure prophylaxis (PrEP) and an extended model incorporating PrEP-related behavioral dynamics. Structural and practical identifiability analyses were used to assess whether model parameters could be reliably estimated from available surveillance data. Although both models were structurally identifiable under fixed assumptions, only the model without PrEP was practically identifiable with current surveillance data. We introduced the concept of virtual epidemics (VEs) and generated a collection of epidemic trajectories by repeatedly fitting the identifiable model to bootstrapped surveillance data. These VEs reproduced historical HIV incidence trends and yielded a range of plausible future outcomes. Our simulations suggested that, under current patterns of diagnosis, treatment, and prevention, the goal of reducing $ 90\% $ of the HIV epidemic in new infections by 2030 was unlikely to be met without additional intervention efforts.

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