Background Mathematical models are essential for understanding viral dynamics, with the basic viral model widely used to describe infection kinetics. Quasi-steady-state approximation (QSSA) is often applied to improve computational efficiency and simplify the system. However, the existing viral QSSA model incorrectly assumes that infected cells evolve on the same fast timescale as the virus, leading to biologically invalid simplifications. Results In this study, we resolved this issue by developing a revised QSSA viral model that correctly accounts for timescale separation and prevents the erroneous loss of infected cell initial values during model reduction. We introduce a mathematical method to estimate the initial condition of infected cells and define a validity condition (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12915_2025_2354_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">${C}_{v}=\delta /c$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>C</mi> <mi>v</mi> </msub> <mo>=</mo> <mi>δ</mi> <mo stretchy="false">/</mo> <mi>c</mi> </mrow> </math></EquationSource> </InlineEquation>), under which QSSA is accurate only when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12915_2025_2354_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">${C}_{v}\ll 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>C</mi> <mi>v</mi> </msub> <mo>≪</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, ensuring proper timescale separation. Comparative analysis shows that the revised QSSA model retains biological fidelity while improving predictive accuracy and computational efficiency. Sensitivity analysis confirmed that it preserves key dynamic responses to parameter changes, further validating its robustness. Parameter estimation demonstrated that the revised QSSA model more accurately recovers true parameter values under strong timescale separation. Conclusions This work resolves a key flaw in existing QSSA models, enabling more accurate and consistent modeling of viral dynamics. By correcting the infected cell loss issue, our findings provide a robust framework for virological applications, particularly useful when experimental data are limited.

Enhancing viral dynamics modeling: reliable initial estimation and validity conditions for quasi-steady state approximation (QSSA)

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2025年10月23日

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Jong Hyuk Byun,
Il Hyo Jung,
Shingo Iwami,
Yong Dam Jeong,
Kwang Su Kim

摘要

Background

Mathematical models are essential for understanding viral dynamics, with the basic viral model widely used to describe infection kinetics. Quasi-steady-state approximation (QSSA) is often applied to improve computational efficiency and simplify the system. However, the existing viral QSSA model incorrectly assumes that infected cells evolve on the same fast timescale as the virus, leading to biologically invalid simplifications.

Results

In this study, we resolved this issue by developing a revised QSSA viral model that correctly accounts for timescale separation and prevents the erroneous loss of infected cell initial values during model reduction. We introduce a mathematical method to estimate the initial condition of infected cells and define a validity condition ( ${C}_{v}=\delta /c$ $C_{v} = δ / c$ ), under which QSSA is accurate only when ${C}_{v}\ll 1$ $C_{v} ≪ 1$ , ensuring proper timescale separation. Comparative analysis shows that the revised QSSA model retains biological fidelity while improving predictive accuracy and computational efficiency. Sensitivity analysis confirmed that it preserves key dynamic responses to parameter changes, further validating its robustness. Parameter estimation demonstrated that the revised QSSA model more accurately recovers true parameter values under strong timescale separation.

Conclusions

This work resolves a key flaw in existing QSSA models, enabling more accurate and consistent modeling of viral dynamics. By correcting the infected cell loss issue, our findings provide a robust framework for virological applications, particularly useful when experimental data are limited.