Dynamic analysis of a mathematical model for hepatitis b virus infection with immune response and drug therapies

Name: Pensiri Yosyingyong

keyword: Delay model

LCSH: Habitat (Ecology) -- Mathematical models

; Hepatitis B virus

LCSH: Hepatitis B — Mathematical models

; Diffusive

LCSH: Hepatitis B — Treatment — Mathematical models

; Optimal control

LCSH: Immune response — Mathematical models

; Immune response

; T-lymphocyte (CTLs)

Abstract: In this thesis, we have formulated three mathematical models to study Hepatitis B virus (HBV) infection. Our initial model explains hepatitis B virus (HBV) infection within hepatocytes, incorporating intracellular HBV DNA-containing capsids, antibodies, and cytotoxic T-lymphocytes (CTLs). Further, two drug therapies (blocking new infection and inhibiting viral production) are included in the model. This model accounts for two time delays: one for the productively infected hepatocytes and another for the antigenic stimulation that generates CTLs. We compute the basic reproduction number by the next-generation method and verify the positivity and boundedness of the solutions. Further, the stability analysis is performed. The numerical simulation results demonstrate that the method of preventing new infections give more efficient in reducing the number of infected hepatocytes in comparison to the method of inhibiting viral production. Moreover, both time delays exert an influence on the infection number and duration of infection, meaning that a long delay results in a more severe HBV infection. The second model is an optimal control model of HBV infection, we consider both drug types as control variables to seek a optimal control treatment strategy to reduce infection. We establish the existence, uniqueness, non-negativity, and boundedness of model solutions. Further, we derive the basic reproduction number for stability analysis of the infection-free equilibrium and conduct sensitivity analysis to identify the most influential parameters for disease control. Then, optimal control and Pontryagin's Maximum Principle (PMP) are utilised to maximize concentrations of uninfected hepatocytes, antibodies, and cytotoxic T-lymphocytes at minimum cost. Our numerical results indicate that intracellular delays play a crucial role in decelerating the rate of infection. Furthermore, both optimal control strategies significantly reduce the concentrations of infected hepatocytes, intracellular HBV DNA-containing capsids, free viruses, antibodies, and cytotoxic T-lymphocytes. These control therapies prove to be effective measures for mitigating HBV infection. To enhance the realism of the model for hepatitis B virus (HBV) infection in the third model, we have broadened the scope of our research with spatial diffusion. We have considered the assumption that hepatocytes remain stationary, while viruses and cytotoxic T lymphocytes (CTLs) can move within the liver. In our analysis, we compute the basic reproduction number and the CTL immune response reproduction number, which are critical thresholds for equilibrium stability. We analyze both local and global stability for each equilibrium point. Our numerical results demonstrate that spatial diffusion does not significantly impact the global dynamics of HBV infection, however, it affects the speed of time for the free virus to reach its equilibrium state.

NARESUAN UNIVERSITY. NARESUAN UNIVERSITY LIBRARY

Address: PHITSANULOK

Email: library@nu.ac.th

Name: Ratchada Viriyapong

Created: 2569

Modified: 2026-04-02

Issued: 2026-04-02

วิทยานิพนธ์/Thesis

application/pdf

eng

DegreeName: Doctor of Philosophy

Level: Doctoral Degree

Descipline: Mathematics

Grantor: Naresuan University

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