Global well-posedness and pattern formations of the immune system induced by chemotaxis

Changwook Yoon; Sewoong Kim; Hyung Ju Hwang; Changwook Yoon; Sewoong Kim; Hyung Ju Hwang

doi:10.3934/mbe.2020194

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 3426-3449. doi: 10.3934/mbe.2020194

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Global well-posedness and pattern formations of the immune system induced by chemotaxis

1.
College of Science & Technology, Korea University Sejong 30019, Republic of Korea
2.
Samsung Fire & Marine Insurance, Seoul 04523, Republic of Korea
3.
Department of Mathematics, POSTECH, Pohang 37673, Republic of Korea

Received: 01 April 2020 Accepted: 27 April 2020 Published: 05 May 2020

This paper studies a reaction-diffusion-advection system describing a directed movement of immune cells toward chemokines during the immune process. We investigate the global solvability of the model based on the bootstrap argument for minimal chemotaxis models. We also examine the stability of nonconstant steady states and the existence of periodic orbits from theoretical aspects of bifurcation analysis. Through numerical simulations, we observe the occurrence of steady or time-periodic pattern formations.
- immune system,
- chemotaxis,
- bifurcation,
- pattern formations
Citation: Changwook Yoon, Sewoong Kim, Hyung Ju Hwang. Global well-posedness and pattern formations of the immune system induced by chemotaxis[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3426-3449. doi: 10.3934/mbe.2020194

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Abstract

This paper studies a reaction-diffusion-advection system describing a directed movement of immune cells toward chemokines during the immune process. We investigate the global solvability of the model based on the bootstrap argument for minimal chemotaxis models. We also examine the stability of nonconstant steady states and the existence of periodic orbits from theoretical aspects of bifurcation analysis. Through numerical simulations, we observe the occurrence of steady or time-periodic pattern formations.

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