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A mathematical model of HTLV-I infection with two time delays
Xuejuan Lu1, Lulu Hui, Shengqiang Liu
1Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, 3041#, 2 Yi-Kuang street, Harbin, 150080, China. lujuan02@163.com.
Insights
This study models Human T-cell leukaemia virus type I (HTLV-I) infection dynamics with time delays. Immune delays can destabilize T-cell responses, while intracellular delays may offer stability, creating complex viral dynamics.
Area of Science:
- Mathematical biology
- Immunology
- Virology
Background:
- Human T-cell leukaemia virus type I (HTLV-I) causes chronic infections.
- CD8+ cytotoxic T lymphocytes (CTLs) are crucial for controlling viral infections.
- Time delays in immune responses can significantly alter disease dynamics.
Purpose of the Study:
- To develop a mathematical model for HTLV-I infection incorporating intracellular and immune time delays.
- To analyze the impact of these delays on the stability of viral and immune responses.
- To understand the conditions leading to viral clearance, chronic infection, or persistent CTL response.
Main Methods:
- Mathematical modeling of CD8+ cytotoxic T lymphocytes (CTLs) response to HTLV-I.
- Analysis of global dynamics based on reproductive numbers R0 and R1.
- Investigation of equilibrium stability and Hopf bifurcations.
- Numerical simulations to explore the effects of time delays.
Main Results:
- Viral clearance occurs if R0 < 1.
- Chronic infection without persistent CTL response if R1 < 1 < R0.
- Persistent CTL response and chronic infection if R1 > 1.
- Immune delay can destabilize the persistent CTL response equilibrium (HAM/TSP).
Conclusions:
- The model's dynamics are governed by viral (R0) and immune (R1) reproductive numbers.
- Time delays, particularly immune delays, play a critical role in HTLV-I infection stability.
- Intracellular delays may stabilize, while immune delays destabilize the system, leading to complex dynamics.
Abstract:
In this paper, we include two time delays in a mathematical model for the CD8+ cytotoxic T lymphocytes (CTLs) response to the Human T-cell leukaemia virus type I (HTLV-I) infection, where one is the intracellular infection delay and the other is the immune delay to account for a series of immunological events leading to the CTL response. We show that the global dynamics of the model system are determined by two threshold values R0, the corresponding reproductive number of a viral infection, and R1, the corresponding reproductive number of a CTL response, respectively. If R0 < 1, the infection-free equilibrium is globally asymptotically stable, and the HTLV-I viruses are cleared. If R1<1
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