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Symmetry
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Lie Symmetries at Work in Biology and Medicine
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Lie Symmetries at Work in Biology and Medicine

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Life Sciences".

Deadline for manuscript submissions: closed (30 April 2021) | Viewed by 10744

Special Issue Editor

Assoc. Prof. Dr. Maria Clara Nucci

E-Mail Website
Guest Editor
Department of Mathematics, University of Perugia, 06123 Perugia, Italy
Interests: Lie symmetries in classical and quantum mechanics; Lie symmetries in biomathematics; magnetohydrodynamics; bits and pieces of the history of mathematics

Special Issue Information

Dear Colleagues,

Let us ponder those systems of differential equations that are proposed as mathematical models in Life Sciences. Numerical analysis is the most commonly used approach, although arbitrary parameters are in the way, and one has to guess which numbers to replace them with. Indeed, a crunching number approach. One may also look at the asymptotic behavior of solutions. However, to infinity and beyond may dismiss what happens in finite time. Therefore, the next best thing to do is search for Lie symmetries of those systems. They may be trivial, and they may be hidden, but, it is symmetries that allow for both a qualitative and even better quantitative analysis of a model, before going to infinity. This Special Issue invites contributions to show that Lie symmetries are indeed at work in biology and medicine.

Leading papers:
V. Torrisi and M.C. Nucci, "Application of Lie group analysis to a mathematical model which describes HIV transmission" in "The Geometrical Study of Differential Equations" (J.A. Leslie and T.P. Hobart, Eds.), A.M.S., Providence (2001) pp. 11-20.
M.C. Nucci, "Using Lie symmetries in epidemiology", Electron. J. Diff. Eqns. Conference 12, pp. 87-101 (2004).
M. Edwards and M.C. Nucci, "Application of Lie group analysis to a core group model for sexually transmitted diseases", J. Nonlinear Math. Phys. 13, pp. 211-230 (2006).
M.C. Nucci and K.M. Tamizhmani, "Lagrangians for biological models", J. Nonlinear Math. Phys. 19, 1250021 (2012).
M.C. Nucci and G. Sanchini, "Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model", Symmetry 7, pp. 1613-1632 (2015).

Assoc. Prof. Dr. Maria Clara Nucci
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Lie symmetries
  • Noether symmetries
  • Differential equations in Biology and Medicine

Published Papers (3 papers)

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Research

20 pages, 582 KiB  
Article
Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling
by Gemma Massonis and Alejandro F. Villaverde
Symmetry 2020, 12(3), 469; https://doi.org/10.3390/sym12030469 - 16 Mar 2020
Cited by 8 | Viewed by 4518
Abstract
A dynamic model is structurally identifiable (respectively, observable) if it is theoretically possible to infer its unknown parameters (respectively, states) by observing its output over time. The two properties, structural identifiability and observability, are completely determined by the model equations. Their analysis is [...] Read more.
A dynamic model is structurally identifiable (respectively, observable) if it is theoretically possible to infer its unknown parameters (respectively, states) by observing its output over time. The two properties, structural identifiability and observability, are completely determined by the model equations. Their analysis is of interest for modellers because it informs about the possibility of gaining insight into a model’s unmeasured variables. Here we cast the problem of analysing structural identifiability and observability as that of finding Lie symmetries. We build on previous results that showed that structural unidentifiability amounts to the existence of Lie symmetries. We consider nonlinear models described by ordinary differential equations and restrict ourselves to rational functions. We revisit a method for finding symmetries by transforming rational expressions into linear systems. We extend the method by enabling it to provide symmetry-breaking transformations, which allows for a semi-automatic model reformulation that renders a non-observable model observable. We provide a MATLAB implementation of the methodology as part of the STRIKE-GOLDD toolbox for observability and identifiability analysis. We illustrate the use of the methodology in the context of biological modelling by applying it to a set of problems taken from the literature. Full article
(This article belongs to the Special Issue Lie Symmetries at Work in Biology and Medicine)
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15 pages, 344 KiB  
Article
A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples
by Roman Cherniha, Joanna Stachowska-Pietka and Jacek Waniewski
Symmetry 2020, 12(3), 396; https://doi.org/10.3390/sym12030396 - 04 Mar 2020
Cited by 3 | Viewed by 2303
Abstract
Fluid and solute transport in poroelastic media is studied. Mathematical modeling of such transport is a complicated problem because of the volume change of the specimen due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the [...] Read more.
Fluid and solute transport in poroelastic media is studied. Mathematical modeling of such transport is a complicated problem because of the volume change of the specimen due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the variables adds also substantial complication in both theoretical and experimental investigations. The one-dimensional version of the theory is less complex and may serve as an approximation in some problems, and therefore, a one-dimensional (in space) model of fluid and solute transport through a poroelastic medium with variable volume is developed and analyzed. In order to obtain analytical results, the Lie symmetry method is applied. It is shown that the governing equations of the model admit a non-trivial Lie symmetry, which is used for construction of exact solutions. Some examples of the solutions are discussed in detail. Full article
(This article belongs to the Special Issue Lie Symmetries at Work in Biology and Medicine)
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13 pages, 355 KiB  
Article
Nonclassical Symmetry Solutions for Non-Autonomous Reaction-Diffusion Equations
by Bronwyn H. Bradshaw-Hajek
Symmetry 2019, 11(2), 208; https://doi.org/10.3390/sym11020208 - 12 Feb 2019
Cited by 9 | Viewed by 3116
Abstract
The behaviour of many systems in chemistry, combustion and biology can be described using nonlinear reaction diffusion equations. Here, we use nonclassical symmetry techniques to analyse a class of nonlinear reaction diffusion equations, where both the diffusion coefficient and the coefficient of the [...] Read more.
The behaviour of many systems in chemistry, combustion and biology can be described using nonlinear reaction diffusion equations. Here, we use nonclassical symmetry techniques to analyse a class of nonlinear reaction diffusion equations, where both the diffusion coefficient and the coefficient of the reaction term are spatially dependent. We construct new exact group invariant solutions for several forms of the spatial dependence, and the relevance of some of the solutions to population dynamics modelling is discussed. Full article
(This article belongs to the Special Issue Lie Symmetries at Work in Biology and Medicine)
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