Hopf bifurcation in a model for adult T‐cell leukemia

Abstract

This paper is concerned with Hopf bifurcation and its stability for the model related to the disease of human T‐cell lymphotropic virus type I (HTLV‐I). In fact, we are considering Hopf bifurcation of the system because it plays an important role in indicating when the disease can return to a steady state condition. The model consists of CD4+ T‐cell subsets of healthy, latently infected, and actively infected cells, as well as for leukemia cells. Latently infected T‐cells may harbor the virus for several years until they become activated and able to infect susceptible T‐cells. In this model, we apply techniques such as the center manifold and normal‐form theorem to simplify bifurcating and the dimension of the dynamical system. The results are applied to clinical data as an example.