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Pattern formation and transition to chaos in a chemotaxis model of acute inflammation

Valeria Giunta Orcid Logo, Maria Carmela Lombardo, Marco Sammartino

SIAM Journal on Applied Dynamical Systems, Volume: 20, Issue: 4, Pages: 1844 - 1881

Swansea University Author: Valeria Giunta Orcid Logo

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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...

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Published in: SIAM Journal on Applied Dynamical Systems
ISSN: 1536-0040
Published: Society for Industrial and Applied Mathematics 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa64695
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first_indexed 2023-10-10T11:09:05Z
last_indexed 2023-10-10T11:09:05Z
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spelling 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'Università 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
container_title SIAM Journal on Applied Dynamical Systems
container_volume 20
container_issue 4
container_start_page 1844
publishDate 2021
institution Swansea University
issn 1536-0040
doi_str_mv 10.1137/20M1358104
publisher Society for Industrial and Applied Mathematics
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str 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
document_store_str 0
active_str 0
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
_version_ 1784102074256982016
score 11.013148

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