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Mathematics
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Nonlinear Dynamics Research in Biomedicine
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Nonlinear Dynamics Research in Biomedicine

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 2093

Special Issue Editors

Prof. Dr. Anastasia Sveshnikova

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Guest Editor
1. Faculty of Physics, Lomonosov Moscow State University, 1/2 Leninskie Gory, 119991 Moscow, Russia
2. Center for Theoretical Problems of Physico-Chemical Pharmacology, Russian Academy of Sciences, 30 Srednyaya Kalitnikovskaya Str., 109029 Moscow, Russia
3. National Medical Research Center of Pediatric Hematology, Oncology and Immunology Named after Dmitry Rogachev, 1 Samory Mashela St, 117198 Moscow, Russia
Interests: systems biology; computational modelling; blood coagulation; intracellular signalling; enzyme kinetics
Prof. Dr. Fazoil Ataullakhanov

E-Mail Website
Guest Editor
1. Dmitry Rogachev National Medical Research Center of Pediatric Hematology, Oncology and Immunology, Ministry of Healthcare of Russian Federation, Samory Mashela Str., 1, GSP-7, 117198 Moscow, Russia
2. Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, Srednyaya Kalitnikovskaya Str., 30, 109029 Moscow, Russia
3. Department of Biophysics, Physics Faculty, Lomonosov Moscow State University, Leninskie Gory, 1, Build. 2, GSP-1, 119991 Moscow, Russia
4. Moscow Institute of Physics and Technology, National Research University, Institutskiy Per., 9, 141701 Dolgoprudny, Russia
5. Perelman School of Medicine, University of Pennsylvania, 3400 Civic Center Blvd., Philadelphia, PA 19104, USA
Interests: biophysics; theoretical biology; energy metabolism; red blood cells; blood coagulation; reaction-diffusion systems; microtubule dynamics

Special Issue Information

Dear Colleagues,

The mathematical modelling of complex biological and physiological systems is a powerful tool for gaining a fundamental understanding of the processes of life. However, the construction of a comprehensive model requires both profound knowledge of the system and large amounts of experimental data. Here, the methods and approaches of nonlinear dynamics are of immense utility, allowing both the reduction of systems of equations and the investigation of possible modes of their functioning.

The aim of this Special Issue is to highlight papers that demonstrate the usefulness of nonlinear dynamics methods to the investigation of physiological systems’ structure, the determination of key modules and control stages in biological systems, and the application of the acquired knowledge to the problems of biomedicine.

Potential topics include but are not limited to the following:

  • Stability and bifurcation analysis of biological systems;
  • Nonlinear biological systems: oscillations, auto waves and self-organizing systems;
  • Reduction, decomposition and structure determination of biological systems;
  • Human population dynamics and epidemiology;
  • Asymptotic analysis of dynamical biological processes.

Prof. Dr. Anastasia Sveshnikova
Prof. Dr. Fazoil Ataullakhanov
Guest Editors

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • mathematical modeling
  • nonlinear biological systems
  • asymptotic analysis
  • bifurcation analysis
  • self-organizing systems
  • сooperativity

Published Papers (2 papers)

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Research

15 pages, 1288 KiB  
Article
Modeling of Viral Infection with Inflammation
by Anastasia Mozokhina, Latifa Ait Mahiout and Vitaly Volpert
Mathematics 2023, 11(19), 4095; https://doi.org/10.3390/math11194095 - 27 Sep 2023
Viewed by 579
Abstract
Viral infection spreads in cell culture or tissue as a reaction–diffusion wave. It is characterized by three main parameters: virus replication number, Rv, which determines whether infection progresses, wave speed, c, which correlates with the virus virulence, and viral load, [...] Read more.
Viral infection spreads in cell culture or tissue as a reaction–diffusion wave. It is characterized by three main parameters: virus replication number, Rv, which determines whether infection progresses, wave speed, c, which correlates with the virus virulence, and viral load, J(v), which determines the infection transmission rate. In this work, we study how the inflammation triggered by viral infection influences its progression. We obtain analytical expressions for Rv,c, and J(v) and show how they depend on the intensity of inflammation characterized by one or two parameters. Analytical and numerical results show that inflammation decreases the viral replication number, virus virulence, and infectivity, though there are different cases depending on the parameters of the model. Full article
(This article belongs to the Special Issue Nonlinear Dynamics Research in Biomedicine)
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20 pages, 1135 KiB  
Article
Role of Glucose Risk Factors on Human Breast Cancer: A Nonlinear Dynamical Model Evaluation
by Abeer Hamdan Alblowy, Normah Maan and Sana Abdulkream Alharbi
Mathematics 2022, 10(19), 3640; https://doi.org/10.3390/math10193640 - 05 Oct 2022
Cited by 1 | Viewed by 1139
Abstract
Understanding of the glucose risk factors-mediated mechanism in human breast cancer remains challenging. In this perception, for the first time, we proposed a complex nonlinear dynamical model that may provide a basic insight into the mechanism of breast cancer for the patient with [...] Read more.
Understanding of the glucose risk factors-mediated mechanism in human breast cancer remains challenging. In this perception, for the first time, we proposed a complex nonlinear dynamical model that may provide a basic insight into the mechanism of breast cancer for the patient with existing glucose risk factors. The impact of glucose risk factors on the cancer cells’ population is evaluated using the formulated analytical model. The dynamical features of the cancer cells are described by a system of ordinary differential equations. Furthermore, the Routh–Hurwitz stability criterion is used to analyze the dynamical equilibrium of the cells’ population. The occurrence of zero bifurcation as well as two and three of the Jacobian matrix are obtained based on the sums of principal minors of order one. The glucose risk factors are exploited as the bifurcation parameters (acted as necessary and sufficient conditions) to detect the Hopf bifurcation. The presence of excess glucose in the body is found to affect negatively the breast cancer cells’ dynamics, stimulating chaos in the normal and tumor cells and thus drastically deteriorating the efficiency of the human immune system. The theoretical results are validated using the numerical simulations. It is concluded that the present findings may be beneficial for the future breast cancer therapeutic drug delivery and cure. Full article
(This article belongs to the Special Issue Nonlinear Dynamics Research in Biomedicine)
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