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Immune Response Model Fitting to CD4\(^+\) T Cell Data in Lymphocytic Choriomeningitis Virus LCMV infection

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Modeling, Dynamics, Optimization and Bioeconomics IV (ICABR 2017, DGS 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 365))

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Abstract

We make two fits of an ODE system with 5 equations that model immune response by CD4\(^+\) T cells with the presence of regulatory T cells (Tregs). We fit the simulations to data regarding gp61 and NP309 epitopes from mice infected with lymphocytic choriomeningitis virus LCMV. We optimized parameters relating to: the T cell maximum growth rate; the T cell capacity; the T cell homeostatic level; and the ending time of the immune activation phase after infection. We quantitatively and qualitatively compare the obtained results with previous fits in the literature using different ODE models and we show that we are able to calibrate the model and obtain good fits describing the data.

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Acknowledgements

The authors would like to thank the financial support by FCT–Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) as part of project UID/EEA/50014/2019 and within project “Modelling, Dynamics and Games” with reference PTDC/MAT–APL/31753/2017. Atefeh Afsar would like to thank the financial support of FCT–Fundação para a Ciência e a Tecnologia–through a Ph.D. grant of the MAP–PDMA program with reference PD/BD/142886/2018.

Author information

Authors and Affiliations

  1. LIAAD–INESC TEC, Department of Mathematics, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    Atefeh Afsar, Filipe Martins & Alberto A. Pinto

  2. LIAAD–INESC TEC, Faculdade de Ciências da Nutrição e Alimentação da Universidade do Porto, Rua do Campo Alegre, 823, 4150-180, Porto, Portugal

    Bruno M. P. M. Oliveira

Authors
  1. Atefeh Afsar
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  2. Filipe Martins
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  3. Bruno M. P. M. Oliveira
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  4. Alberto A. Pinto
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Corresponding author

Correspondence to Filipe Martins .

Editor information

Editors and Affiliations

  1. Department of Mathematics and LIAAD—INESC TEC, Faculty of Science, University of Porto, Porto, Portugal

    Alberto Pinto

  2. Department of Agricultural and Resource Economics, University of California, Berkeley, CA, USA

    David Zilberman

Appendix

Appendix

The parameters of our model and their default values as well as the fitted parameters are presented in the following two tables (Tables 1 and 2).

Table 1 Parameters values for our model of T cells and Tregs from [1, 2, 6, 13, 17, 21, 27]
Full size table
Table 2 Fitted parameters values for our model of T cells and Tregs, with ranges adopted from [1, 6, 13, 20, 21]
Full size table

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Afsar, A., Martins, F., Oliveira, B.M.P.M., Pinto, A.A. (2021). Immune Response Model Fitting to CD4\(^+\) T Cell Data in Lymphocytic Choriomeningitis Virus LCMV infection. In: Pinto, A., Zilberman, D. (eds) Modeling, Dynamics, Optimization and Bioeconomics IV. ICABR DGS 2017 2018. Springer Proceedings in Mathematics & Statistics, vol 365. Springer, Cham. https://doi.org/10.1007/978-3-030-78163-7_1

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