Journal article 325 views
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation
SIAM Journal on Applied Dynamical Systems, Volume: 20, Issue: 4, Pages: 1844 - 1881
Swansea University Author:
Valeria Giunta
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DOI (Published version): 10.1137/20M1358104
Abstract
We investigate a reaction-diffusion-chemotaxis system that describes the immune response during an inflammatory attack. The model is a modification of the system proposed in Penner, Ermentrout, and Swigon [SIAM J. Appl. Dyn. Syst., 11 (2012), pp. 629--660]. We introduce a logistic term in the immune...
Published in: | SIAM Journal on Applied Dynamical Systems |
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ISSN: | 1536-0040 |
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Society for Industrial and Applied Mathematics
2021
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URI: | https://cronfa.swan.ac.uk/Record/cronfa64695 |
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v2 64695 2023-10-10 Pattern formation and transition to chaos in a chemotaxis model of acute inflammation 50456cce4b2c7be66f8302d418963b0c 0000-0003-1156-7136 Valeria Giunta Valeria Giunta true false 2023-10-10 SMA We investigate a reaction-diffusion-chemotaxis system that describes the immune response during an inflammatory attack. The model is a modification of the system proposed in Penner, Ermentrout, and Swigon [SIAM J. Appl. Dyn. Syst., 11 (2012), pp. 629--660]. We introduce a logistic term in the immune cell dynamics to reproduce the macrophages' activation, allowing us to describe the disease evolution from the early stages to the acute phase. We focus on the appearance of pattern solutions and their stability. We discover steady-state (Turing) and wave instabilities and classify the bifurcations deriving the corresponding amplitude equations. We study stationary radially symmetric solutions and show that they reproduce various inflammatory aggregates observed in the clinical practice. Moreover, the model supports oscillating-in-time spatial patterns, thus giving a theoretical explanation of the periodic appearance of inflammatory eruptions typical of recurrent erythema multiforme. A detailed numerical bifurcation analysis indicates that the inclusion of the logistic growth term is crucial for the occurrence of a sequence of bifurcations leading to spatio-temporal chaos. In the parameter space, there are large regions where the model system displays critical behavior. Journal Article SIAM Journal on Applied Dynamical Systems 20 4 1844 1881 Society for Industrial and Applied Mathematics 1536-0040 Inflammation model, chemotaxis, pattern formation, bifurcation analysis, transition to chaos, criticality 1 7 2021 2021-07-01 10.1137/20M1358104 https://doi.org/10.1137/20M1358104 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University Ministero dell'Istruzione, dell'UniversitĂ e della Ricerca. 2023-12-01T17:38:45.2770325 2023-10-10T12:06:31.4354750 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Valeria Giunta 0000-0003-1156-7136 1 Maria Carmela Lombardo 2 Marco Sammartino 3 |
title |
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation |
spellingShingle |
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation Valeria Giunta |
title_short |
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation |
title_full |
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation |
title_fullStr |
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation |
title_full_unstemmed |
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation |
title_sort |
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation |
author_id_str_mv |
50456cce4b2c7be66f8302d418963b0c |
author_id_fullname_str_mv |
50456cce4b2c7be66f8302d418963b0c_***_Valeria Giunta |
author |
Valeria Giunta |
author2 |
Valeria Giunta Maria Carmela Lombardo Marco Sammartino |
format |
Journal article |
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SIAM Journal on Applied Dynamical Systems |
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20 |
container_issue |
4 |
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1844 |
publishDate |
2021 |
institution |
Swansea University |
issn |
1536-0040 |
doi_str_mv |
10.1137/20M1358104 |
publisher |
Society for Industrial and Applied Mathematics |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
url |
https://doi.org/10.1137/20M1358104 |
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description |
We investigate a reaction-diffusion-chemotaxis system that describes the immune response during an inflammatory attack. The model is a modification of the system proposed in Penner, Ermentrout, and Swigon [SIAM J. Appl. Dyn. Syst., 11 (2012), pp. 629--660]. We introduce a logistic term in the immune cell dynamics to reproduce the macrophages' activation, allowing us to describe the disease evolution from the early stages to the acute phase. We focus on the appearance of pattern solutions and their stability. We discover steady-state (Turing) and wave instabilities and classify the bifurcations deriving the corresponding amplitude equations. We study stationary radially symmetric solutions and show that they reproduce various inflammatory aggregates observed in the clinical practice. Moreover, the model supports oscillating-in-time spatial patterns, thus giving a theoretical explanation of the periodic appearance of inflammatory eruptions typical of recurrent erythema multiforme. A detailed numerical bifurcation analysis indicates that the inclusion of the logistic growth term is crucial for the occurrence of a sequence of bifurcations leading to spatio-temporal chaos. In the parameter space, there are large regions where the model system displays critical behavior. |
published_date |
2021-07-01T17:38:46Z |
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1784102074256982016 |
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11.021648 |