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The analysis and application of an HBV model. (English) Zbl 1243.34054
Summary: A mathematical model is formulated to describe the spread of hepatitis B. The stability of equilibria and persistence of disease are analyzed. The results shows that the dynamics of the model is completely determined by the basic reproductive number ρ 0 . If ρ 0 <1, the disease-free equilibrium is globally stable. When ρ 0 >1, the disease-free equilibrium is unstable and the disease is uniformly persistent. Furthermore, under certain conditions, it is proved that the endemic equilibrium is globally attractive. Numerical simulations are conducted to demonstrate our theoretical results. The model is applied to HBV transmission in China. The parameter values of the model are estimated based on available HBV epidemic data in China. The simulation results matches the HBV epidemic data in China approximately.
MSC:
34C20Transformation and reduction of ODE and systems, normal forms
92D30Epidemiology
34C60Qualitative investigation and simulation of models (ODE)
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