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.
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Acknowledgments
This work has been partially supported by the Chinese NSF Grant No. 1157112, the Spanish Ministerio de Economía y Competitividad project MTM2015-63723-P and the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía) under grant 2010/FQM314, and Proyecto de Excelencia P12-FQM-1492.
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Asai, Y., Caraballo, T., Han, X., Kloeden, P.E. (2016). A Random Model for Immune Response to Virus in Fluctuating Environments. In: Sadovnichiy, V., Zgurovsky, M. (eds) Advances in Dynamical Systems and Control. Studies in Systems, Decision and Control, vol 69. Springer, Cham. https://doi.org/10.1007/978-3-319-40673-2_10
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DOI: https://doi.org/10.1007/978-3-319-40673-2_10
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