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Chemotactic effects in reaction-diffusion equations for inflammation
Cordula Reisch1, Dirk Langemann2
1TU Braunschweig, Institute of Computational Mathematics, AG PDE, Universitätsplatz 2, 38106, Braunschweig, Germany. c.reisch@tu-bs.de.
Abstract:
Predator-prey systems are used to model time-dependent virus and lymphocyte population during a liver infection and to discuss the influence of chemotactic behavior on the chronification tendency of such infections. Therefore, a model family of reaction-diffusion equations is presented, and the long-term behavior of the solutions is estimated by a critical value containing the reaction strength, the diffusion rate, and the extension of the liver domain. Fourier techniques are applied to evaluate the influence of chemotactic behavior of the immune response to the long-term behavior of locally linearized models. It turns out that the chemotaxis is a subordinated influence with respect to the chronification of liver infections.
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