Modeling and mathematical analysis of an initial boundary value problem for hepatitis B virus infection

Abstract

In this work, we investigate the hepatitis B virus infection. We first derive a nonlinear PDE model for the studied biological phenomenon. The obtained initial boundary value problem is completely analyzed. To begin with the analysis of the model, we use Lou and Zhao Lemma concerning globally attractive steady states to prove boundedness of potential solutions. Then we prove global existence, uniqueness and positivity of the solution by a variational method combined with semigroups theory and some other useful tools from functional analysis. Moreover, the basic reproduction number R0 determining the extinction or the persistence of the HBV infection is thoroughly computed via a new method based on spectral properties of differential operators, the residue Theorem and some arguments from numerical analysis. Also, the global asymptotical properties of the HBV-free equilibrium of the model are derived via a skillful construction of a suitable Lyapunov function. Local stability of the endemic equilibrium of the model is studied as well. Finally, numerical simulations are performed to support the theoretical results obtained.