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Title: Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response

Abstract

In this paper, the dynamical behaviors for a five-dimensional virus infection model with diffusion and two delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses and a general incidence function are investigated. The reproduction numbers for virus infection, antibody immune response, CTL immune response, CTL immune competition and antibody immune competition, respectively, are calculated. By using the Lyapunov functionals and linearization methods, the threshold conditions on the global stability of the equilibria for infection-free, immune-free, antibody response, CTL response and antibody and CTL responses, respectively, are established if the space is assumed as homogeneous. When the space is inhomogeneous, the effects of diffusion, intracellular delay and production delay are obtained by the numerical simulations.

Authors:
 [1]; ; ;  [2]
  1. Shanxi University of Finance and Economics, School of Applied Mathematics (China)
  2. Xinjiang University, College of Mathematics and System Sciences (China)
Publication Date:
OSTI Identifier:
22769260
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ANTIBODIES; COMPUTERIZED SIMULATION; DIFFUSION; FUNCTIONALS; LYAPUNOV METHOD; LYMPHOCYTES

Citation Formats

Miao, Hui, Teng, Zhidong, Abdurahman, Xamxinur, and Li, Zhiming. Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response. United States: N. p., 2018. Web. doi:10.1007/S40314-017-0543-9.
Miao, Hui, Teng, Zhidong, Abdurahman, Xamxinur, & Li, Zhiming. Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response. United States. doi:10.1007/S40314-017-0543-9.
Miao, Hui, Teng, Zhidong, Abdurahman, Xamxinur, and Li, Zhiming. Sun . "Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response". United States. doi:10.1007/S40314-017-0543-9.
@article{osti_22769260,
title = {Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response},
author = {Miao, Hui and Teng, Zhidong and Abdurahman, Xamxinur and Li, Zhiming},
abstractNote = {In this paper, the dynamical behaviors for a five-dimensional virus infection model with diffusion and two delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses and a general incidence function are investigated. The reproduction numbers for virus infection, antibody immune response, CTL immune response, CTL immune competition and antibody immune competition, respectively, are calculated. By using the Lyapunov functionals and linearization methods, the threshold conditions on the global stability of the equilibria for infection-free, immune-free, antibody response, CTL response and antibody and CTL responses, respectively, are established if the space is assumed as homogeneous. When the space is inhomogeneous, the effects of diffusion, intracellular delay and production delay are obtained by the numerical simulations.},
doi = {10.1007/S40314-017-0543-9},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 3,
volume = 37,
place = {United States},
year = {2018},
month = {7}
}