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Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes

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  • Khajanchi, Subhas
  • Bera, Sovan
  • Roy, Tapan Kumar

Abstract

A mathematical model for the CD8+ T-cell response to Human T cell leukemia/lymphoma virus type I (HTLV-I) infection is investigated in this paper. The proposed model, which involves four coupled nonlinear ordinary differential equations, describes the interaction of uninfected CD4+T cells, latently infected CD4+T cells, actively infected CD4+T cells and HTLV-I specific cytotoxic T-lymphocytes (CTLs). Our model exhibits three biologically feasible equilibria, namely infection-free steady state, HTLV-I free steady state and an endemic steady state. Our mathematical analysis establishes that the local and global dynamics are determined by the two threshold parameters R0 and R1, basic reproduction number for HTLV-I viral infection and for CTL response, respectively. For R0<1, the infection-free steady state E0 is globally asymptotically stable, and HTLV-I viruses are cleared. For R1≤11 in the interior of the feasible region. We perform the sensitivity analysis to find out the key parameters of the HTLV-I infection model with respect to R0 and R1. Implications of our findings to the dynamics of CTL response to HTLV-I infections in vivo and pathogenesis of HTLV-I associated myelopathy/tropical spastic paraparesis (HAM/TSP) are discussed.

Suggested Citation

  • Khajanchi, Subhas & Bera, Sovan & Roy, Tapan Kumar, 2021. "Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 354-378.
    • Handle: RePEc:eee:matcom:v:180:y:2021:i:c:p:354-378
    DOI: 10.1016/j.matcom.2020.09.009
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    References listed on IDEAS

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    1. Khajanchi, Subhas & Das, Dhiraj Kumar & Kar, Tapan Kumar, 2018. "Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 52-71.
    2. Sarkar, Kankan & Khajanchi, Subhas & Nieto, Juan J., 2020. "Modeling and forecasting the COVID-19 pandemic in India," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "The impact of the media awareness and optimal strategy on the prevalence of tuberculosis," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    4. Khajanchi, Subhas, 2018. "Modeling the dynamics of glioma-immune surveillance," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 108-118.
    5. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "Transmission dynamics of tuberculosis with multiple re-infections," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    6. Khajanchi, Subhas, 2015. "Bifurcation analysis of a delayed mathematical model for tumor growth," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 264-276.
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    2. Asamoah, Joshua Kiddy K. & Okyere, Eric & Yankson, Ernest & Opoku, Alex Akwasi & Adom-Konadu, Agnes & Acheampong, Edward & Arthur, Yarhands Dissou, 2022. "Non-fractional and fractional mathematical analysis and simulations for Q fever," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
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    5. Bera, Sovan & Khajanchi, Subhas & Roy, Tapan Kumar, 2022. "Dynamics of an HTLV-I infection model with delayed CTLs immune response," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    6. Zhang, Zhenzhen & Ma, Xia & Zhang, Yongxin & Sun, Guiquan & Zhang, Zi-Ke, 2023. "Identifying critical driving factors for human brucellosis in Inner Mongolia, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    7. Han, Lili & Song, Sha & Pan, Qiuhui & He, Mingfeng, 2023. "The impact of multiple population-wide testing and social distancing on the transmission of an infectious disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    8. Ahmed M. Elaiw & Abdulsalam S. Shflot & Aatef D. Hobiny & Shaban A. Aly, 2023. "Global Dynamics of an HTLV-I and SARS-CoV-2 Co-Infection Model with Diffusion," Mathematics, MDPI, vol. 11(3), pages 1-33, January.
    9. Ahmed M. Elaiw & Abdulsalam S. Shflot & Aatef D. Hobiny, 2022. "Global Stability of Delayed SARS-CoV-2 and HTLV-I Coinfection Models within a Host," Mathematics, MDPI, vol. 10(24), pages 1-35, December.

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