Mathematical analysis of an HTLV-I infection model with the mitosis of CD4+ T cells and delayed CTL immune response
Articles
Chenwei Song
Shanxi University
https://orcid.org/0000-0002-0567-8748
Rui Xu
Shanxi University
Published 2021-01-01
https://doi.org/10.15388/namc.2021.26.21050
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Keywords

HTLV-I infection
the mitosis of CD4 T cells
delayed CTL immune response
the reproduction ratio
Lyapunov functionals
Hopf bifurcation

How to Cite

Song C. and Xu R. (2021) “Mathematical analysis of an HTLV-I infection model with the mitosis of CD4+ T cells and delayed CTL immune response”, Nonlinear Analysis: Modelling and Control, 26(1), pp. 1-20. doi: 10.15388/namc.2021.26.21050.

Abstract

In this paper, we consider an improved Human T-lymphotropic virus type I (HTLV-I) infection model with the mitosis of CD4+ T cells and delayed cytotoxic T-lymphocyte (CTL) immune response by analyzing the distributions of roots of the corresponding characteristic equations, the local stability of the infection-free equilibrium, the immunity-inactivated equilibrium, and the immunity-activated equilibrium when the CTL immune delay is zero is established. And we discuss the existence of Hopf bifurcation at the immunity-activated equilibrium. We define the immune-inactivated reproduction ratio R0 and the immune-activated reproduction ratio R1. By using Lyapunov functionals and LaSalle’s invariance principle, it is shown that if R0 < 1, the infection-free equilibrium is globally asymptotically stable; if R1 < 1 < R0, the immunity-inactivated equilibrium is globally asymptotically stable; if R1 > 1, the immunity-activated equilibrium is globally asymptotically stable when the CTL immune delay is zero. Besides, uniform persistence is obtained when R1 > 1. Numerical simulations are carried out to illustrate the theoretical results.

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