MATHEMATICAL ANALYSIS OF HEPATITIS B TRANSMISSION MODEL

OUEDRAOGO Boukary; ZOROM Malicki; GOUBA Elisée

OUEDRAOGO Boukary Laboratoire d'Analyse Numérique d'Informatique et de BiomathÃématiques (LANIBIO), Département de Mathématiques, Université Joseph KI ZERBO, Burkina Faso
ZOROM Malicki Institut International d'ingénierie de l’Eau et de l'Environnement (2iE), Burkina Faso
GOUBA Elisée Laboratoire d'Analyse Numérique d'Informatique et de BiomathÃématiques (LANIBIO), Département de Mathématiques, Université Joseph KI ZERBO, Burkina Faso

Article ID: 2413

Keywords: SEIR model; mathematical modeling; basic reproduction number; stability; numerical simulation; sensitivity analysis

Abstract

In this article, we present the transmission dynamics of the acute and chronic hepatitis B epidemic problem. To control the spread of hepatitis in a community, we first develop a mathematical model for the transmission of the virus of hepatitis B. After framing the mathematical model, we show the existence and uniqueness of the solution, then mathematically analyze the model and determine the disease-free equilibrium state of the model. Besides, we determine the basic reproduction number $\mathcal{R}_0$ for this model which is interpreted epidemiologically. Next, we study the local stability of the disease-free-equilibrium state and show that if $\mathcal{R}_0<1$, then, the disease-free equilibrium is asymptotically stable, otherwise unstable. Finally, a sensitivity analysis is performed to determine the relative importance of the model parameters to disease transmission and prevalence. The paper ends with the numerical simulation to illustrate the theoretical results.

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