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\begin{document}

\title{Dynamical analysis of a generalized hepatitis B epidemic model and its
dynamically consistent discrete model}



\author[1]{Manh  Tuan Hoang}%
\affil[1]{FPT University}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
The aim of this work is to study qualitative dynamical properties of a
generalized hepatitis B epidemic model and its dynamically consistent
discrete model. Positivity, boundedness, the basic reproduction number
and asymptotic stability properties of the model are analyzed
rigorously. By the Lyapunov stability theory and the Poincare-Bendixson
theorem in combination with the Bendixson-Dulac criterion, we show that
a disease-free equilibrium point is globally asymptotically stable if
the basic reproduction number \$\textbackslash{}mathcal\{R\}\_0
\textbackslash{}leq 1\$ and a disease-endemic equilibrium point is
globally asymptotically stable whenever
\$\textbackslash{}mathcal\{R\}\_0 \textgreater{} 1\$. Next, we apply the
Mickens' methodology to propose a dynamically consistent nonstandard
finite difference (NSFD) scheme for the continuous model. By rigorously
mathematical analyses, it is proved that the constructed NSFD scheme
preserves essential mathematical features of the continuous model for
all finite step sizes. Finally, numerical experiments are conducted to
illustrate the theoretical findings and to demonstrate advantages of the
NSFD scheme over standard ones. The obtained results in this work not
only improve but also generalize some existing recognized works.%
\end{abstract}%



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