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Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 7009-7021. doi: 10.3934/mbe.2019352
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A fit of CD4+ T cell immune response to an infection by lymphocytic choriomeningitis virus

  • 1.
    Departamento de Matemática, Faculdade de Ciências da Universidade do Porto and LIAAD-INESC. Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
  • 2.
    Faculdade de Ciências da Nutrição e Alimentação da Universidade do Porto, and LIAAD-INESC. Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
  • We fit an immune response model to data reporting the CD4+ T cell numbers from the 28 days following the infection of mice with lymphocytic choriomeningitis virus LCMV. We used an ODE model that was previously used to describe qualitatively the behaviour of CD4+ T cells, regulatory T cells (Tregs) and interleukine-2 (IL-2) density. The model considered two clonotypes of T cells in order to fit simultaneously the two time series for the gp61 and NP309 epitopes. We observed the proliferation of T cells and, to a lower extent, Tregs during the immune activation phase following infection and subsequently, during the contraction phase, a smooth transition from faster to slower death rates. The six parameters that were optimized were: the beginning and ending times of the immune response, the growth rate of T cells, their capacity, and the two related with the homeostatic numbers of T cells that respond to each epitope. We showed that the ODE model was able to be calibrated thus providing a quantitative description of the data.

    Citation: Atefeh Afsar, Filipe Martins, Bruno M. P. M. Oliveira, Alberto A. Pinto. A fit of CD4+ T cell immune response to an infection by lymphocytic choriomeningitis virus[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7009-7021. doi: 10.3934/mbe.2019352

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  • We fit an immune response model to data reporting the CD4+ T cell numbers from the 28 days following the infection of mice with lymphocytic choriomeningitis virus LCMV. We used an ODE model that was previously used to describe qualitatively the behaviour of CD4+ T cells, regulatory T cells (Tregs) and interleukine-2 (IL-2) density. The model considered two clonotypes of T cells in order to fit simultaneously the two time series for the gp61 and NP309 epitopes. We observed the proliferation of T cells and, to a lower extent, Tregs during the immune activation phase following infection and subsequently, during the contraction phase, a smooth transition from faster to slower death rates. The six parameters that were optimized were: the beginning and ending times of the immune response, the growth rate of T cells, their capacity, and the two related with the homeostatic numbers of T cells that respond to each epitope. We showed that the ODE model was able to be calibrated thus providing a quantitative description of the data.




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