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.