Study the modified mathematical model of hepatitis B virus infection with immune response

Volume 38, Issue 3, pp 371--378 https://dx.doi.org/10.22436/jmcs.038.03.06

Publication Date: January 07, 2025 Submission Date: July 27, 2024 Revision Date: October 08, 2024 Accteptance Date: December 02, 2024

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Authors

E. M. Ahmed - Department of Mathematics, Faculty of Sciences and Arts, King Abdulaziz University, Rabigh, Saudi Arabia. N. H. Aljahdaly - Department of Mathematics, Faculty of Sciences and Arts, King Abdulaziz University, Rabigh, Saudi Arabia.

Abstract

Hepatitis B is a viral infection caused by the hepatitis B virus (HBV), which primarily targets liver cells. Numerous studies in the literature have employed mathematical modeling to investigate the dynamics of HBV infection. This article develops a mathematical model that captures that captures the effects of the immune system response on uninfected cells as well as free viruses. The analysis of the model focuses on key mathematical properties, including positivity, boundedness, equilibrium points, the basic reproduction number (\(R_0\)), and local stability. Numerical simulations and sensitivity analyses are performed to further understand the model's behavior under various parameter settings. The results demonstrate that while the parameter representing the immune response’s effect on viral clearance does not alter (\(R_0\)), it has a significant impact on improving numerical outcomes. Sensitivity analysis reveals that an HBV outbreak can become widespread if certain parameters change. Specifically, a reduction in the rate of viral production by infected cells, the natural death rate of uninfected cells, and the natural death rate of free viruses increases the risk of the infection becoming a pandemic. Conversely, an increase in the growth rate of uninfected cells, the natural death rate of free viruses, and the probability of the virus successfully infecting uninfected cells and producing new infected cells, also contributes to the spread of the infection. These findings highlight the factors that influence the dynamics of HBV transmission.

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Keywords

• Mathematical model
• theoretical analysis
• numerical solutions
• Hepatitis B

MSC

•  92C50
•  34D20
•  92D30
•  37N25
•  65L07

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