Dynamics analysis of an HTLV‐1 infection model with mitotic division of actively infected cells and delayed CTL immune response

Li, Fuxiang; Ma, Wanbiao

doi:10.1002/mma.4797

Cited by 37 publications

(16 citation statements)

References 45 publications

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“…Since antigenic stimulation to generate HTLV-I specific CTLs involves a series of events that require a time delay [7]. Therefore, it is necessary to consider the effect of time delay in the model, and the form of CTL immune function f (y, z) = cy(t − τ ) has been used in [14]. Motivated by the works of Li and Shu [16], Lim and Maini [17], in this paper, we consider the following HTLV-I infection model with actively infected CD4 + T cells mitosis and delayed CTL immune response:…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of an HTLV-I infection model with the mitosis of CD4+ T cells and delayed CTL immune response

Song

2021

NAMC

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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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Section: Introductionmentioning

confidence: 99%

Mathematical analysis of an HTLV-I infection model with the mitosis of CD4+ T cells and delayed CTL immune response

Song

2021

NAMC

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“…[ 16 ] and [ 31 – 34 ]). HTLV-I dynamics models with the mitotic division of Tax-expressing HTLV-infected cells and CTL immune response have been developed in [ 15 , 35 – 37 ]. Li and Zhou [ 36 ] have assumed that Tax-expressing HTLV-infected cells proliferate at rate , with staying in the Tax-expressing HTLV-infected cells compartment, while being silent and, therefore, escaping from the immune system.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of a within-host HIV/HTLV-I co-infection

Ełaiw

AlShamrani

2021

Bol. Soc. Mat. Mex.

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Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that attack the T cells and impair their functions. Both HIV and HTLV-I can be transmitted between individuals through direct contact with certain body fluids from infected individuals. Therefore, a person can be co-infected with both viruses. HIV causes acquired immunodeficiency syndrome (AIDS), while HTLV-I is the causative agent for adult T-cell leukemia (ATL) and HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP). Several mathematical models have been developed in the literature to describe the within-host dynamics of HIV and HTLV-I mono-infections. However, modeling a within-host dynamics of HIV/HTLV-I co-infection has not been involved. The present paper is concerned with the formulation and investigation of a new HIV/HTLV-I co-infection model under the effect of Cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by virus-to-cell transmission. On the other side, HTLV-I has two modes of transmission, (i) horizontal transmission via direct cell-to-cell contact through the virological synapse, and (ii) vertical transmission through the mitotic division of Tax-expressing HTLV-infected cells. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We define a set of threshold parameters which govern the existence and stability of all equilibria of the model. We explore the global asymptotic stability of all equilibria by utilizing Lyapunov function and Lyapunov–LaSalle asymptotic stability theorem. We have presented numerical simulations to justify the applicability and effectiveness of the theoretical results. In addition, we evaluate the effect of HTLV-I infection on the HIV dynamics and vice versa.

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“…As studies of complexities in physics, tumor-associated responses can be better approached by establishing mathematical models with some appropriate simplified assumptions than via experimental procedures alone. [3][4][5][6] Over the last two decades, tumor immunology has attracted remarkable attention and various mathematical models have been developed to understand the interaction between cancer and immune cells. A review of early works concerning tumor-immune interactions can be found in Adam and Bellomo 7 and Eftimie et al 8 Given the complexity of this process, many models include four or more variables or equations.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of tumor surface growth with necrotic kernels

Zhang

Tian

Niu

et al. 2021

Math Methods in App Sciences

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A two‐dimensional tumor‐immune model with the time delay of the adaptive immune response is considered in this paper. The model is designed to account for the interaction between cytotoxic T lymphocytes (CTLs) and cancer cells on the surface of a solid tumor. The model considers the surface growth as a major growth pattern of solid tumors in order to describe the existence of necrotic kernels. The qualitative analysis shows that the immune‐free equilibrium is unstable, and the behavior of positive equilibrium is closely related to the ratio of the immune killing rate to tumor volume growth rate. The positive equilibrium is locally asymptotically stable when the ratio is smaller than a critical value. Otherwise, the occurrence of the delay‐driven Hopf bifurcation at the positive equilibrium is proved. Applying the center manifold reduction and normal form method, we obtain explicit formulas to determine the properties of the Hopf bifurcation. The global continuation of a local Hopf bifurcation is investigated based on the coincidence degree theory. The results reveal that the time of the adaptive immune system taken to response to tumors can lead to oscillation dynamics. We also carry out detailed numerical analysis for parameters and numerical simulations to illustrate our qualitative analysis. Numerically, we find that shorter immune response time can lead to longer patient survival time, and the period and amplitude of a stable periodic solution increase with the increasing immune response time. When CTLs recruitment rate and death rate vary, we show how the ratio of the immune killing rate to tumor volume growth rate and the first bifurcation value change numerically, which yields further insights to the tumor‐immune dynamics.

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Dynamics analysis of an HTLV‐1 infection model with mitotic division of actively infected cells and delayed CTL immune response

Cited by 37 publications

References 45 publications

Mathematical analysis of an HTLV-I infection model with the mitosis of CD4+ T cells and delayed CTL immune response

Mathematical analysis of an HTLV-I infection model with the mitosis of CD4+ T cells and delayed CTL immune response

Modeling and analysis of a within-host HIV/HTLV-I co-infection

Mathematical modeling of tumor surface growth with necrotic kernels

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