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Alzheimer Disease: Convergence Result from a Discrete Model Towards a Continuous One

In: Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics

Author

Listed:
  • M. Caléro

    (Université Claude Bernard Lyon 1, Université de Lyon, CNRS UMR 5208 Institut Camille Jordan
    Inria Grenoble Rhône-Alpes Center, Inria Team Dracula)

  • I. S. Ciuperca

    (Université Claude Bernard Lyon 1, Université de Lyon, CNRS UMR 5208 Institut Camille Jordan
    Inria Grenoble Rhône-Alpes Center, Inria Team Dracula)

  • L. Pujo-Menjouet

    (Université Claude Bernard Lyon 1, Université de Lyon, CNRS UMR 5208 Institut Camille Jordan
    Inria Grenoble Rhône-Alpes Center, Inria Team Dracula)

  • L. M. Tine

    (Université Claude Bernard Lyon 1, Université de Lyon, CNRS UMR 5208 Institut Camille Jordan
    Inria Grenoble Rhône-Alpes Center, Inria Team Dracula)

Abstract

Alzheimer disease (AD) is a neurodegenerative disease affecting more than 50 million people worldwide. AD is in part caused by the accumulation of Aβ peptides inside the brain to form oligomers or fibrils. Oligomers can interact with neurons via membrane receptors such as prion proteins (PrP c) and misfold them into oligomeric prions (PrP ol) able to transmit a death signal to neurons. The purpose of this talk is to show a convergence result from a discrete Alzheimer disease model (Helal et al., J Math Biol 78:57–81, 2018) to a continuous one (Ciuperca et al., Alzheimer’s disease and prion: an in vitro mathematical model, preprint).

Suggested Citation

  • M. Caléro & I. S. Ciuperca & L. Pujo-Menjouet & L. M. Tine, 2019. "Alzheimer Disease: Convergence Result from a Discrete Model Towards a Continuous One," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics, pages 397-431, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-23433-1_25
    DOI: 10.1007/978-3-030-23433-1_25
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