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A nonlinear transport–diffusion model for the interactions between immune system cells and HPV-infected cells

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Abstract

In this paper, we present a nonlinear advection–diffusion model for the interactions of immune system cells with HPV-infected cells, where we considered the immune response from the innate system and the adaptive system. Our goal is to develop a simple, but biologically meaningful, model that allows us to investigate how the immune system interacts with HPV-infected cells via the action of natural killer cells and/or differentiated T cells. On the base of the solution, a numerical explicit scheme with respect to time is presented to approximate our proposed model. Numerical simulations show the temporal evolution of all model cells involved and point out circumstances under which it is possible to eliminate the infection in the model.

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Notes

  1. For better convergence results, we could use discretizations based on generalized Crank–Nicolson methods, but for our present goal it is nonessential.

  2. Proportion of the variance attributable to the factor of interest over the total variance and has a range between 0 and 1.

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Authors and Affiliations

  1. CIMAT, Guanajuato Gto, 36000, Mexico

    Francisco J. Solis

  2. ITESM, Monterrey Institute of Technology and Higher Education, Zapopan, 45138, Jalisco, Mexico

    Luz M. Gonzalez

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  1. Francisco J. Solis
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  2. Luz M. Gonzalez
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Correspondence to Francisco J. Solis.

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Solis, F.J., Gonzalez, L.M. A nonlinear transport–diffusion model for the interactions between immune system cells and HPV-infected cells. Nonlinear Dyn 111, 15557–15571 (2023). https://doi.org/10.1007/s11071-023-08616-2

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