Stochastic Field Theory of HIV Latency: Instanton Dynamics and the Path to Viral Rebound
Abstract
The transition from clinical latency to active HIV infection is a stochastic process. Traditional deterministic models based on ordinary differential equations (ODEs) fail to capture the extinction boundary and the subsequent rebound of the virus because they neglect demographic noise in the small-population limit. We map the resulting Master Equation onto a coherent-state path integral using the Doi-Peliti second-quantization formalism and verify that the stochastic Hamiltonian reproduces the correct mean-field ODEs on the classical manifold ϕ̅i = 1. In the semiclassical (large system-size) limit we derive eight coupled Hamilton-Jacobi equations, identify the virus-free and endemic fixed points, and obtain the basic reproduction number R0 for the four-species network. For the analytically tractable case of single-virion bursting (n=1) we show that the stochastic Hamiltonian \emph{factorizes} into two bilinear terms, exposing a non-trivial zero-energy surface that constitutes the instanton trajectory. A quasi-steady-state reduction then yields a first-order linear ODE whose closed-form solution gives the instanton action Sinst in terms of biological parameters. Calibrating to clinical data---infected-cell half-life δI−1≈ 2 d, viral burst size N≈ 103, clearance rate δV≈ 23 d−1, reactivation rate η≈ 10−3 d−1, and latent reservoir size L0≈ 106 cells---we obtain a mean first-passage time (MFPT) to viral rebound of ≈ 6 months for a typical patient, with a range of days to years depending on reservoir size. These predictions are qualitatively consistent with observed post-interruption rebound timescales.
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BibTeX
@misc{bernalalvarado2026stochastic,
title = {{Stochastic Field Theory of HIV Latency: Instanton Dynamics and the Path to Viral Rebound}},
author = {Jose de Jesus Bernal-Alvarado and David Delepine and Georges Delepine},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25136},
eprint = {2609.25136},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25136},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stochastic Field Theory of HIV Latency: Instanton Dynamics and the Path to Viral Rebound
AU - Jose de Jesus Bernal-Alvarado
AU - David Delepine
AU - Georges Delepine
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25136
UR - https://arxiv.org/abs/2609.25136
AB - The transition from clinical latency to active HIV infection is a stochastic process. Traditional deterministic models based on ordinary differential equations (ODEs) fail to capture the extinction boundary and the subsequent rebound of the virus because they neglect demographic noise in the small-population limit. We map the resulting Master Equation onto a coherent-state path integral using the Doi-Peliti second-quantization formalism and verify that the stochastic Hamiltonian reproduces the correct mean-field ODEs on the classical manifold ϕ̅_i = 1. In the semiclassical (large system-size) limit we derive eight coupled Hamilton-Jacobi equations, identify the virus-free and endemic fixed points, and obtain the basic reproduction number R_0 for the four-species network. For the analytically tractable case of single-virion bursting (n=1) we show that the stochastic Hamiltonian \emph{factorizes} into two bilinear terms, exposing a non-trivial zero-energy surface that constitutes the instanton trajectory. A quasi-steady-state reduction then yields a first-order linear ODE whose closed-form solution gives the instanton action S_inst in terms of biological parameters. Calibrating to clinical data---infected-cell half-life δ_I^−1≈ 2 d, viral burst size N≈ 10^3, clearance rate δ_V≈ 23 d^−1, reactivation rate η≈ 10^−3 d^−1, and latent reservoir size L_0≈ 10^6 cells---we obtain a mean first-passage time (MFPT) to viral rebound of ≈ 6 months for a typical patient, with a range of days to years depending on reservoir size. These predictions are qualitatively consistent with observed post-interruption rebound timescales.
ER -