Stability of delayed HCV model with two target cells and Beddington-DeAngelis infection function and saturated CTL immune response

Shaimaa A. Azoz; Aeshah A. Raezah; Shaimaa A. Azoz; Aeshah A. Raezah

doi:10.3934/nhm.2026076

Networks and Heterogeneous Media

2026, Volume 21, Issue 6: 2007-2036. doi: 10.3934/nhm.2026076

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Research article

Stability of delayed HCV model with two target cells and Beddington-DeAngelis infection function and saturated CTL immune response

Shaimaa A. Azoz ^{1
,
,},
Aeshah A. Raezah ²

1.
Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt
2.
Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia

Received: 27 June 2026 Revised: 12 September 2026 Accepted: 29 September 2026 Published: 13 October 2026

In this paper, we present a mathematical model that describes the dynamics of a hepatitis C virus infection. The model takes two classes of target cells (hepatocytes and extrahepatic cells) into account as well as a saturated Cytotoxic T lymphocytes (CTLs) immune response in the liver. We found that the system solutions are positive and bounded, and the equilibrium points are computed. Through a careful examination of the model, we demonstrated that it exhibits global threshold dynamics that are fully captured by the threshold parameters. Numerical simulations were carried out to demonstrate the stability results.
- hepatitis C virus,
- global stability,
- Beddington-DeAngelis infection rate,
- time delay,
- CTL immune response
Citation: Shaimaa A. Azoz, Aeshah A. Raezah. Stability of delayed HCV model with two target cells and Beddington-DeAngelis infection function and saturated CTL immune response[J]. Networks and Heterogeneous Media, 2026, 21(6): 2007-2036. doi: 10.3934/nhm.2026076

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Abstract

In this paper, we present a mathematical model that describes the dynamics of a hepatitis C virus infection. The model takes two classes of target cells (hepatocytes and extrahepatic cells) into account as well as a saturated Cytotoxic T lymphocytes (CTLs) immune response in the liver. We found that the system solutions are positive and bounded, and the equilibrium points are computed. Through a careful examination of the model, we demonstrated that it exhibits global threshold dynamics that are fully captured by the threshold parameters. Numerical simulations were carried out to demonstrate the stability results.

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