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A random model for immune response to virus in fluctuating environments


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Author: Asai, Yusuke
Caraballo Garrido, Tomás
Han, Xiaoying
Kloeden, Peter E.
Coordinator/Director: Sadovnichiy, Victor A.
Zgurovsky, Mikhail Z.
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2016
Published in: Advances in Dynamical Systems and Control
ISBN/ISSN: 9783319406725
Document type: Chapter of Book
Abstract: In this work we study a model for virus dynamics with a random immune response and a random production rate of susceptible cells from cell proliferation. In traditional models for virus dynamics, the rate at which the viruses are cleared by the immune system is constant, and the rate at which susceptible cells are provided is constant or a function depending on the population of all cells. However, the human body in general is never stationary, and thus these rates can barely be constant. Here we assume that the human body is a random environment and models the rates by random processes, which result in a system of random differential equations. We then analyze the long term behavior of the random system, in particular the existence and geometric structure of the random attractor, by using the theory of random dynamical systems. Numerical simulations are provided to illustrate the theoretical result.
Cite: Asai, Y., Caraballo Garrido, T., y Han, X. (2016). A random model for immune response to virus in fluctuating environments. En M.Z. Zgurovsky, V.A. Sadovnichiy (Ed.), Advances in Dynamical Systems and Control (pp. 211-225). Springer
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DOI: 10.1007/978-3-319-40673-2_10

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