<p>Hepatitis B virus (HBV) is a major global health concern, driving high morbidity and mortality through its progression to hepatocellular carcinoma (HCC), a leading cause of liver cancer deaths. Despite advances in vaccination and treatment, persistent infections remain a challenge, particularly in resource-limited regions. Existing models have examined HBV dynamics, but more comprehensive approaches are needed to integrate vaccination and metabolic risk factors, which strongly influence disease progression. This study presents a novel mathematical model to examine the influence of vaccination and metabolic risk factors on the dynamics of Hepatitis B virus (HBV) and its progression to hepatocellular carcinoma (HCC), also known as liver cancer. The model’s validity is established through rigorous qualitative analysis, including existence and uniqueness proofs via the Lipschitz criterion. Stability analysis confirms that the HBV-free equilibrium is locally asymptotically stable. The basic reproductive ratio is derived, and numerical simulations are conducted using the Laplace Adomian Decomposition Method (LADM).Simulation results highlight that achievi ng full vaccination coverage (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\nu = 1\)</EquationSource> </InlineEquation>) effectively minimizes HBV susceptibility. However, when vaccination rates <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\left( {\nu < 0.5} \right)\)</EquationSource> </InlineEquation>, reducing transmission requires additional half of the regular period needed to reach zero susceptibility. The progression rate (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>) from persistent HBV to HCC is analyzed, revealing that higher values of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> lead to increased HBV persistence, a surge in HCC cases, and lower recovery rates. Treatment demand peaks approximately 1.7 years post-infection but gradually declines as more individuals undergo treatment. Moreover, liver cancer incidence is directly proportional to persistent HBV infections, with sharp increases observed at higher <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> values. Metabolic risk factors (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(k\)</EquationSource> </InlineEquation>) play a crucial role in reducing HBV persistence and liver cancer incidence, cutting persistent HBV cases by over 50% within five years and lowering HCC cases by nearly one-third within three years. Improved metabolic regulation also leads to a decline in treatment demand. These findings underscore the vital role of vaccination and metabolic control in mitigating HBV progression and alleviating the burden of liver cancer (HCC).</p>

Mathematical modelling of hepatitis B virus dynamics evaluating the role of vaccination and metabolic factors in disease progression

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发表日期：

2025年10月22日

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Mutiu Lawal Olaosebikan,
Mutairu Kayode Kolawole,
Adedapo Ismaila Alaje,
Asimiyu Olalekan Oladapo,
Ibrahim Adeshola Adediran

摘要

Hepatitis B virus (HBV) is a major global health concern, driving high morbidity and mortality through its progression to hepatocellular carcinoma (HCC), a leading cause of liver cancer deaths. Despite advances in vaccination and treatment, persistent infections remain a challenge, particularly in resource-limited regions. Existing models have examined HBV dynamics, but more comprehensive approaches are needed to integrate vaccination and metabolic risk factors, which strongly influence disease progression. This study presents a novel mathematical model to examine the influence of vaccination and metabolic risk factors on the dynamics of Hepatitis B virus (HBV) and its progression to hepatocellular carcinoma (HCC), also known as liver cancer. The model’s validity is established through rigorous qualitative analysis, including existence and uniqueness proofs via the Lipschitz criterion. Stability analysis confirms that the HBV-free equilibrium is locally asymptotically stable. The basic reproductive ratio is derived, and numerical simulations are conducted using the Laplace Adomian Decomposition Method (LADM).Simulation results highlight that achievi ng full vaccination coverage ( \(\nu = 1\) ) effectively minimizes HBV susceptibility. However, when vaccination rates \(\left( {\nu < 0.5} \right)\) , reducing transmission requires additional half of the regular period needed to reach zero susceptibility. The progression rate ( \(\alpha\) ) from persistent HBV to HCC is analyzed, revealing that higher values of \(\alpha\) lead to increased HBV persistence, a surge in HCC cases, and lower recovery rates. Treatment demand peaks approximately 1.7 years post-infection but gradually declines as more individuals undergo treatment. Moreover, liver cancer incidence is directly proportional to persistent HBV infections, with sharp increases observed at higher \(\alpha\) values. Metabolic risk factors ( \(k\) ) play a crucial role in reducing HBV persistence and liver cancer incidence, cutting persistent HBV cases by over 50% within five years and lowering HCC cases by nearly one-third within three years. Improved metabolic regulation also leads to a decline in treatment demand. These findings underscore the vital role of vaccination and metabolic control in mitigating HBV progression and alleviating the burden of liver cancer (HCC).