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    A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion

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    Name:
    positivityInfectionR.pdf
    Size:
    1.197Mb
    Format:
    PDF
    Description:
    Accepted manuscript
    Embargo End Date:
    2022-09-08
    Download
    Type
    Article
    Authors
    Kou, Jisheng
    Chen, Huangxin
    Wang, Xiuhua
    Sun, Shuyu cc
    KAUST Department
    Computational Transport Phenomena Lab
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2021
    Embargo End Date
    2022-09-08
    Permanent link to this record
    http://hdl.handle.net/10754/671112
    
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    Abstract
    In this paper, we propose an efficient numerical method for a comprehensive infection model that is formulated by a system of nonlinear coupling advection-diffusion-reaction equations. Using some subtle mixed explicit-implicit treatments, we construct a linearized and decoupled discrete scheme. Moreover, the proposed scheme is capable of preserving the positivity of variables, which is an essential requirement of the model under consideration. The proposed scheme uses the cell-centered finite difference method for the spatial discretization, and thus, it is easy to implement. The diffusion terms are treated implicitly to improve the robustness of the scheme. A semi-implicit upwind approach is proposed to discretize the advection terms, and a distinctive feature of the resulting scheme is to preserve the positivity of variables without any restriction on the spatial mesh size and time step size. We rigorously prove the unique existence of discrete solutions and positivity-preserving property of the proposed scheme without requirements for the mesh size and time step size. It is worthwhile to note that these properties are proved using the discrete variational principles rather than the conventional approaches of matrix analysis. Numerical results are also provided to assess the performance of the proposed scheme.
    Citation
    Kou, J., Chen, H., Wang, X., & Sun, S. (2021). A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion. Communications on Pure & Applied Analysis, 0(0), 0. doi:10.3934/cpaa.2021094
    Publisher
    American Institute of Mathematical Sciences (AIMS)
    Journal
    Communications on Pure & Applied Analysis
    DOI
    10.3934/cpaa.2021094
    Additional Links
    https://www.aimsciences.org/article/doi/10.3934/cpaa.2021094
    ae974a485f413a2113503eed53cd6c53
    10.3934/cpaa.2021094
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

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