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Stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection. (English) Zbl 1266.92059

Summary: The stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. We show the existence of nonnegative equilibria under some appropriate conditions. The existence of a Hopf bifurcation with delay \(\tau\) at the endemic equilibria is established by analyzing the distribution of the characteristic values. The explicit formulae which determine the direction of the bifurcations, stability, and other properties of the bifurcating periodic solutions are given by using the normal form theory and the center manifold theorem. Numerical simulation verifies the theoretical results.

MSC:

92C60 Medical epidemiology
34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional-differential equations
92-08 Computational methods for problems pertaining to biology
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