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  for this model which is interpreted epidemiologically. Next, we study the local stability of the disease-free-equilibrium state and show that if  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.

SEIR model, mathematical modeling, basic reproduction number, stability, numerical simulation, sensitivity analysis.

Received: February 7, 2023; Accepted: March 27, 2023; Published: June 17, 2023

How to cite this article: OUEDRAOGO Boukary, ZOROM Malicki and GOUBA Elisée, Mathematical analysis of hepatitis B transmission model, Advances in Differential Equations and Control Processes 30(3) (2023), 213-236. http://dx.doi.org/10.17654/0974324323013

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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