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NSFD scheme and dynamic consistency of a delayed diffusive humoral immunity viral infection model

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Abstract

In this paper, we establish a delayed diffusive humoral immunity viral infection model with nonlinear incidence rate and capsids subject to the homogeneous Neumann boundary conditions. By constructing appropriate Lyapunov function, we show that the global threshold dynamics for the original continuous model. Meanwhile, nonstandard finite difference (NSFD) scheme for the original continuous model is also proposed by utilizing Micken’s method. Then, using the theory of M-matrix, it is shown that the discrete model is well-posedness. Additionally, the global stability for the steady states is investigated by constructing discrete Lyapunov function. These results imply that the NSFD scheme may preserve the dynamical properties of solutions for the original continuous model efficiently. Furthermore, some numerical simulations to illustrate the theoretical analysis are carried out.

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Acknowledgements

The authors thank the anonymous reviewers for their valuable comments and suggestions on improving the presentation of this paper. The work is supported by the National Natural Science Foundation of China (No. 11761038) and Science and Technology Project of Department of Education of Jiangxi Province (No. GJJ180583).

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Authors and Affiliations

  1. School of Mathematics and Physics, Jinggangshan University, Ji’an, 343009, China

    Xiaosong Tang, Tao Yu, Zhiyun Deng & Dengyu Liu

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  1. Xiaosong Tang

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  2. Tao Yu

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  3. Zhiyun Deng

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Tang, X., Yu, T., Deng, Z.et al. NSFD scheme and dynamic consistency of a delayed diffusive humoral immunity viral infection model.J. Appl. Math. Comput.64, 429–455 (2020). https://doi.org/10.1007/s12190-020-01362-3

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