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

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.