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Numerical analysis of an age-structured model for HIV viral dynamics with latently infected T cells based on collocation methods

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  • Li, Mengna
  • Yang, Zhanwen

Abstract

In this paper, we consider the numerical threshold for an age-structured HIV model with latently infected T cells. Based on the continuous collocation methods, a semi-discrete scheme is constructed by discretizing the age variable and a numerical basic reproduction number Rh is provided. With the study of higher-order convergence to the real basic reproduction number R0, the relations between Rh and local stability of disease-free are presented. From the viewpoint of full discretization, an equivalent block-Leslie matrix expression is obtained by embedding into a piecewise-discontinuous polynomial space rather than the piecewise-continuous polynomial space. An implicit full-discrete scheme is considered based on a linearly implicit Euler (IMEX) method, of which the computational cost is almost the same as an explicit scheme. It is more important that the dynamical behavior of the age-semi-discretization system is also preserved for any time step whenever Rh is the threshold for the numerical dynamical system of the age-semi-discretization. Finally, numerical applications are shown to HIV models to illustrate our analysis.

Suggested Citation

  • Li, Mengna & Yang, Zhanwen, 2025. "Numerical analysis of an age-structured model for HIV viral dynamics with latently infected T cells based on collocation methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 289-305.
    • Handle: RePEc:eee:matcom:v:230:y:2025:i:c:p:289-305
    DOI: 10.1016/j.matcom.2024.09.028
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