Global stability of two-patch within-host HBV infection dynamics with unidirectional viral spread

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DOI: https://doi.org/10.28924/2291-8639-24-2026-257
Published: Aug 17, 2026
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Raghad S. Alsulami, N. H. AlShamrani, A. M. Elaiw, A. D. Hobiny, Global stability of two-patch within-host HBV infection dynamics with unidirectional viral spread, Int. J. Anal. Appl., 24 (2026), 257.

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Raghad S. Alsulami, N. H. AlShamrani, A. M. Elaiw, A. D. Hobiny

Abstract

Hepatitis B virus (HBV) infects liver cells (hepatocytes). Persistent HBV infection may lead to the development of abnormal nodular formations within liver tissue. In this study, we propose and analyze a mathematical model describing the dynamics of a two-patch within-host HBV infection with unidirectional viral transmission from patch-1 to patch-2. The model captures interactions among six compartments: uninfected hepatocytes, infected hepatocytes, and free HBV particles in each of the two patches. A comprehensive mathematical analysis is carried out, including proofs of non-negativity and boundedness of solutions. The basic reproduction numbers in patch-1 \(\left(R_{1}\right)\) and patch-2 \(\left(R_{2}\right)\) are calculated using the next generation method. The global stability of all equilibrium points is rigorously examined using Lyapunov functions and LaSalle’s invariance principle. Numerical simulations are conducted, demonstrating strong agreement with the analytical findings. Finally, sensitivity analysis identifies the key parameters influencing viral persistence.

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