Threshold Geometry, Bifurcation, and Data-Driven Analysis of a Vaccination-Treatment Model for Hepatitis B
Abstract
Despite the availability of excellent vaccines and antiviral medicines, hepatitis B virus (HBV) remains a major public health problem. In this work, we develop a mathematical vaccination-treatment model for HBV transmission to investigate threshold conditions for illness persistence as well as the level of intervention. The analysis gives the characterisation of both disease-free and endemic equilibria and determines the basic reproduction number, ℛ0, by the next-generation matrix approach. The model indicates that ℛ0=1 is a critical threshold dividing disease-free from endemic states and characterises a forward transcritical bifurcation regarding the transmission parameter. Numerical equilibrium continuation and stability assessments confirm the analytical results. A two-parameter study of transmission and vaccination rates identifies threshold geometries and assesses impacts of important parameters using sensitivity analysis. The model is calibrated with India-specific data, such as HBsAg prevalence, HBV incidence and mortality rates and fits epidemiological targets closely through limited nonlinear calibration. Additionally, multi-start optimisation and practical identifiability profiling are used to investigate parameter uncertainty. Robustness analyses reveal that the calibrated ℛ0*=1.1744 is associated with a super-threshold regime; however, parameter flexibility permits both sub-threshold and super-threshold regimes. This combined analytical and data-driven framework connects epidemic thresholds, bifurcation structures, intervention efficacy, and parameter uncertainty. It provides a quantitative framework for analysing HBV persistence and evaluating control options, especially in the absence of epidemiological evidence.
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BibTeX
@misc{ahmad2026threshold,
title = {{Threshold Geometry, Bifurcation, and Data-Driven Analysis of a Vaccination-Treatment Model for Hepatitis B}},
author = {Mustaq Ahmad and A. S. Bhadauria},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39204},
eprint = {2609.39204},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39204},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Threshold Geometry, Bifurcation, and Data-Driven Analysis of a Vaccination-Treatment Model for Hepatitis B
AU - Mustaq Ahmad
AU - A. S. Bhadauria
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2609.39204
UR - https://arxiv.org/abs/2609.39204
AB - Despite the availability of excellent vaccines and antiviral medicines, hepatitis B virus (HBV) remains a major public health problem. In this work, we develop a mathematical vaccination-treatment model for HBV transmission to investigate threshold conditions for illness persistence as well as the level of intervention. The analysis gives the characterisation of both disease-free and endemic equilibria and determines the basic reproduction number, ℛ_0, by the next-generation matrix approach. The model indicates that ℛ_0=1 is a critical threshold dividing disease-free from endemic states and characterises a forward transcritical bifurcation regarding the transmission parameter. Numerical equilibrium continuation and stability assessments confirm the analytical results. A two-parameter study of transmission and vaccination rates identifies threshold geometries and assesses impacts of important parameters using sensitivity analysis. The model is calibrated with India-specific data, such as HBsAg prevalence, HBV incidence and mortality rates and fits epidemiological targets closely through limited nonlinear calibration. Additionally, multi-start optimisation and practical identifiability profiling are used to investigate parameter uncertainty. Robustness analyses reveal that the calibrated ℛ_0^*=1.1744 is associated with a super-threshold regime; however, parameter flexibility permits both sub-threshold and super-threshold regimes. This combined analytical and data-driven framework connects epidemic thresholds, bifurcation structures, intervention efficacy, and parameter uncertainty. It provides a quantitative framework for analysing HBV persistence and evaluating control options, especially in the absence of epidemiological evidence.
ER -