Article citationsMore>>

Ruan, S.G. and Wei, J.J. (2003) On the Zeros of Transcendental Functions with Applications to Stability of Delay Differential Equations with Two Delays. Dynamics of Continuous Discrete and Impulsive Systems Series A, 10, 863-874.

has been cited by the following article:

• TITLE: Dynamics of an HTLV-I Model Incorporating Viral Replication Delay and CTL Immunity

  AUTHORS: Yinji Huang

  KEYWORDS: HTLV-I Model, Viral Replication Delay, Stability, Hopf Bifurcation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.8, August 26, 2025

  ABSTRACT: Human T-cell leukemia/lymphoma virus type I (HTLV-I) is a pathogenic retrovirus, and cytotoxic T lymphocytes (CTLs) or specific CD8+ cytotoxic T lymphocytes are considered crucial factors in the human immune system against viral infections. Therefore, studying the impact of CTL immune response on HTLV-I infection is essential. This paper investigates a class of HTLV-I infection models that consider latent infected CD4+ T cells and viral replication delay (the time from initial infection of healthy CD4+ T cells to becoming latent CD4+ T infected cells). By analyzing the model, the basic reproduction number for immunological inactivation R 0 and the basic reproduction number for immunological activation R 1 are defined. Using R 0 and R 1 as thresholds, the local stability of the infection-free equilibrium E 0 , the immunological inactivation equilibrium point E 1 , and the immunological activation equilibrium point E * is established by analyzing the distribution of roots of the corresponding characteristic equations when τ=0 . Additionally, the local stability for τ≠0 and the existence of Hopf bifurcations with delay as a bifurcation parameter are discussed.