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

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

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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).

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Authors and Affiliations

  1. CNRS UMR 5208 Institut Camille Jordan, Université Claude Bernard Lyon 1, Université de Lyon, Villeurbanne Cedex, France

    M. Caléro, I. S. Ciuperca, L. Pujo-Menjouet & L. M. Tine

  2. Inria Team Dracula, Inria Grenoble Rhône-Alpes Center, Villeurbanne, France

    M. Caléro, I. S. Ciuperca, L. Pujo-Menjouet & L. M. Tine

Authors
  1. M. Caléro
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  2. I. S. Ciuperca
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  3. L. Pujo-Menjouet
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  4. L. M. Tine
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Corresponding author

Correspondence to L. M. Tine .

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Editors and Affiliations

  1. Federal University of Rio de Janeiro, President, BIOMAT Consortium – International Institute for Interdisciplinary Sciences, Rio de Janeiro, Rio de Janeiro, Brazil

    Rubem P. Mondaini

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Caléro, M., Ciuperca, I.S., Pujo-Menjouet, L., Tine, L.M. (2019). Alzheimer Disease: Convergence Result from a Discrete Model Towards a Continuous One. In: Mondaini, R. (eds) Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-23433-1_25

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