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Effect of Time Delay on Spatial Patterns in a Airal Infection Model with Diffusion

    Jia Liu Affiliation
    ; Qunying Zhang Affiliation
    ; Canrong Tian Affiliation

Abstract

This paper is concerned with the dynamics of a viral infection model with diffusion under the assumption that the immune response is retarded. A time delay is incorporated into the model described the delayed immune response after viral infection. Based upon a stability analysis, we demonstrate that the appearance, or the absence, of spatial patterns is determined by the delay under some conditions. Moreover, the spatial patterns occurs as a consequence of Hopf bifurcation. By applying the normal form and the center manifold theory, the direction as well as the stability of the Hopf bifurcation is explored. In addition, a series of numerical simulations are performed to illustrate our theoretical results.

Keyword : viral infection, diffusion, time delay, spatial patterns

How to Cite
Liu, J., Zhang, Q., & Tian, C. (2016). Effect of Time Delay on Spatial Patterns in a Airal Infection Model with Diffusion. Mathematical Modelling and Analysis, 21(2), 143-158. https://doi.org/10.3846/13926292.2016.1137503
Published in Issue
Mar 18, 2016
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