Submit to Special Issue Submit Abstract to Special Issue Review for Symmetry Propose a Special Issue

Journal Menu

Journal Browser

► Journal Browser

Mathematical Modeling in Biology and Life Sciences

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Keywords
Benefits of Publishing in a Special Issue
Published Papers

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 11585

Share This Special Issue

Special Issue Editors

Dr. Yueping Dong

E-Mail Website
Guest Editor

School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China
Interests: mathematical modelling; numerical analysis; engineering, applied and computational; mathematics; nonlinear dynamics

Prof. Dr. Wanbiao Ma

E-Mail Website
Guest Editor

Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Interests: differential equation models in epidemiology; virology and mirobiology and population biology; stability and bifurcation of ordinary/delayed differential equations
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Yasuhiro Takeuchi

E-Mail Website
Guest Editor

Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan
Interests: infection; mathematical models; avian influenza; HIV; functional equations; infectious disease epidemiology; immunology of infectious diseases; emerging infectious diseases; infectious disease control and prevention; analysis; ecology; stability; epidemiological modeling; neural networks; vaccination

Special Issue Information

Dear Colleagues,

The progress in biology and life sciences over the last several decades has been revolutionary. However, many aspects of the biological mechanisms remain unclear due to complex interactions at the molecular, cellular, individual and population levels. As modern biology and life science research become more quantitative, mathematical modeling becomes increasingly important. These methods have been widely used to study complex biological processes and phenomena, test biological hypotheses, answer questions that cannot be tackled in clinical research alone, and provide both qualitative and quantitative findings.

Symmetry permeates all aspects of life sciences, from biological molecules to ecosystems and biomes, which has a strict mathematical interpretation: invariance under transformation. It plays an important role in the construction and analysis of mathematical models of biological forms and processes. More evidence is beginning to show that taking an interdisciplinary approach has the potential to lead to breakthroughs in the study of biology and life sciences.

This Special Issue welcomes all contributions on the recent advances in the study of biology and life sciences by means of mathematical modeling and methods.

Dr. Yueping Dong
Prof. Dr. Wanbiao Ma
Prof. Dr. Yasuhiro Takeuchi
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. 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

population dynamics
infectious disease modelling
complex network
virus dynamics and mutation
cancer immune modelling
potential symmetries
differential equations
dynamical systems

Benefits of Publishing in a Special Issue

Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (11 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

Jump to: Review

20 pages, 1156 KiB

Open AccessArticle

Mathematical Modeling in Bioinformatics: Application of an Alignment-Free Method Combined with Principal Component Analysis

by Dorota Bielińska-Wąż, Piotr Wąż, Agata Błaczkowska, Jan Mandrysz, Anna Lass, Paweł Gładysz and Jacek Karamon

Symmetry 2024, 16(8), 967; https://doi.org/10.3390/sym16080967 - 30 Jul 2024

Viewed by 695

Abstract

In this paper, an alignment-free bioinformatics technique, termed the 20D-Dynamic Representation of Protein Sequences, is utilized to investigate the similarity/dissimilarity between Baculovirus and Echinococcus multilocularis genome sequences. In this method, amino acid sequences are depicted as 20D-dynamic graphs, comprising sets of “material points” in a 20-dimensional space. The spatial distribution of these material points is indicative of the sequence characteristics and is quantitatively described by sequence descriptors akin to those employed in dynamics, such as coordinates of the center of mass of the 20D-dynamic graph and the tensor of the moment of inertia of the graph (defined as a symmetric matrix). Each descriptor unveils distinct features of similarity and is employed to establish similarity relations among the examined sequences, manifested either as a symmetric distance matrix (“similarity matrix”), a classification map, or a phylogenetic tree. The classification maps are introduced as a new way of visualizing the similarity relations obtained using the 20D-Dynamic Representation of Protein Sequences. Some classification maps are obtained using the Principal Component Analysis (PCA) for the center of mass coordinates and normalized moments of inertia of 20D-dynamic graphs as input data. Although the method operates in a multidimensional space, we also apply some visualization techniques, including the projection of 20D-dynamic graphs onto a 2D plane. Studies on model sequences indicate that the method is of high quality, both graphically and numerically. Despite the high similarity observed among the sequences of E. multilocularis, subtle discrepancies can be discerned on the 2D graphs. Employing this approach has led to the discovery of numerous new similarity relations compared to our prior study conducted at the DNA level, using the 4D-Dynamic Representation of DNA/RNA Sequences, another alignment-free bioinformatics method also introduced by us. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Figure 1

18 pages, 3743 KiB

Open AccessArticle

Anthropometric Formulas Repurposed to Predict Body Fat Content from Ultrasound Measurements of Subcutaneous Fat Thickness

by Paul Muntean, Monica Miclos-Balica, George Andrei Macavei, Oana Munteanu, Adrian Neagu and Monica Neagu

Symmetry 2024, 16(8), 962; https://doi.org/10.3390/sym16080962 - 29 Jul 2024

Viewed by 417

Abstract

Body composition assessment helps conducting a healthy life or tracking the effectiveness of a weight management therapy. Ultrasound (US)-based body composition research has gained momentum because of the emergence of portable and inexpensive instruments bundled with user-friendly software. Previously, US-based assessment of body fat percentage (% BF) was found precise, but inaccurate in certain populations. Therefore, this study sought to compute % BF from subcutaneous fat thicknesses (SFs) given by US converting an anthropometric formula that involves skinfold thicknesses (SKFs) measured at the same sites. The symmetry of the body with respect to the central sagittal plane is an underlying assumption in both anthropometry and US-based body composition assessment, so measurements were taken on the right side of the body. Relying on experimental data on skinfold compressibility, we adapted 33 SKF formulas for US use and tested their validity against air displacement plethysmography on a study group of 97 women (BMI = 25.4 ± 6.4 kg/m², mean ± SD) and 107 men (BMI = 26.7 ± 5.7 kg/m²). For both sexes, the best proprietary formula had Lin’s concordance correlation coefficient (CCC) between 0.7 and 0.73, standard error of estimate (SEE) < 3% BF and total error (TE) > 6% BF—mainly because of the underestimation of % BF in overweight and obese subjects. For women (men) the best adapted formula had CCC = 0.85 (0.80), SEE = 3.2% (2.4%) BF, and TE = 4.6% (5.4%) BF. Remarkably, certain adapted formulas were more accurate for overweight and obese people than the proprietary equations. In conclusion, anthropometric equations provide useful starting points in the quest for novel formulas to estimate body fat content from ultrasound measurements. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Figure 1

16 pages, 2249 KiB

Open AccessArticle

Integrating Genomic, Climatic, and Immunological Factors to Analyze Seasonal Patterns of Influenza Variants

by Anass Bouchnita and Behzad Djafari-Rouhani

Symmetry 2024, 16(8), 943; https://doi.org/10.3390/sym16080943 - 23 Jul 2024

Viewed by 578

Abstract

Influenza, often referred to as the flu, is an extremely contagious respiratory illness caused by influenza viruses, impacting populations globally with significant health consequences annually. A hallmark of influenza is its seasonal patterns, influenced by a mix of geographic, evolutionary, immunological, and environmental factors. Understanding these seasonal trends is crucial for informing public health decisions, including the planning of vaccination campaigns and their formulation. In our study, we introduce a genotype-structured infectious disease model for influenza transmission, immunity, and evolution. In this model, the population of infected individuals is structured according to the virus they harbor. It considers a symmetrical fitness landscape where the influenza A and B variants are considered. The model incorporates the effects of population immunity, climate, and epidemic heterogeneity, which makes it suitable for investigating influenza seasonal dynamics. We parameterize the model to the genomic surveillance data of flu in the US and use numerical simulations to elucidate the scenarios that result in the alternating or consecutive prevalence of flu variants. We show that the speed of virus evolution determines the alternation and co-circulation patterns of seasonal influenza. Our simulations indicate that slow immune waning reduces how often variants change, while cross-immunity regulates the co-circulation of variants. The framework can be used to predict the composition of future influenza outbreaks and guide the development of cocktail vaccines and antivirals that mitigate influenza in both the short and long term. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Figure 1

16 pages, 2465 KiB

Open AccessArticle

Dynamics and Optimal Harvesting for Fishery Models with Reserved Areas

by Wenjun Gao, Xiu Jia and Ruiqing Shi

Symmetry 2024, 16(7), 800; https://doi.org/10.3390/sym16070800 - 26 Jun 2024

Viewed by 1030

Abstract

This paper analyzes the dynamic behavior of a fishery model described by differential algebraic equations. Two patches, namely free fishing area and protected area, are included in the model. The migration of fish is symmetrical, i.e., the fish can migrate between the two patches. It is observed that a singularity-induced bifurcation occurs when the economic benefit of harvesting changes. When the economic benefit is positive, a state feedback controller is added to stabilize the system. Some examples and numerical simulations are presented to verify the theoretical results. In addition, harvesting of prey populations is used as a control measure to obtain the maximum economic benefits and ecological sustainability. The optimal solution is derived by using Pontryagin’s maximum principle. Through extensive numerical simulations, it is shown that the optimal solution is capable of achieving ecosystem sustainability. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Figure 1

18 pages, 1347 KiB

Open AccessArticle

Modeling the Nonmonotonic Immune Response in a Tumor–Immune System Interaction

by Yu Liu, Yuhang Ma, Cuihong Yang, Zhihang Peng, Yasuhiro Takeuchi, Malay Banerjee and Yueping Dong

Symmetry 2024, 16(6), 676; https://doi.org/10.3390/sym16060676 - 31 May 2024

Viewed by 378

Abstract

Tumor–immune system interactions are very complicated, being highly nonlinear and not well understood. A large number of tumors can potentially weaken the immune system through various mechanisms such as secreting cytokines that suppress the immune response. In this paper, we propose a tumor–immune system interaction model with a nonmonotonic immune response function and adoptive cellular immunotherapy (ACI). The model has a tumor-free equilibrium and at most three tumor-presence equilibria (low, moderate and high ones). The stability of all equilibria is studied by analyzing their characteristic equations. The consideration of nonmonotonic immune response results in a series of bifurcations such as the saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. In addition, numerical simulation results show the coexistence of periodic orbits and homoclinic orbits. Interestingly, along with various bifurcations, we also found two bistable scenarios: the coexistence of a stable tumor-free as well as a high-tumor-presence equilibrium and the coexistence of a stable-low as well as a high-tumor-presence equilibrium, which can show symmetric and antisymmetric properties in a range of model parameters and initial cell concentrations. The new findings indicate that under ACI, patients can possibly reach either a stable tumor-free state or a low-tumor-presence state in the presence of nonmonotonic immune response once the immune system is activated. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Figure 1

22 pages, 1792 KiB

Open AccessArticle

Delay Effects on Plant Stability and Symmetry-Breaking Pattern Formation in a Klausmeier-Gray-Scott Model of Semiarid Vegetation

by Ikram Medjahdi, Fatima Zohra Lachachi, María Ángeles Castro and Francisco Rodríguez

Symmetry 2024, 16(5), 609; https://doi.org/10.3390/sym16050609 - 14 May 2024

Viewed by 696

Abstract

The Klausmeier–Gray–Scott model of vegetation dynamics consists of a system of two partial differential equations relating plant growth and soil water. It is capable of reproducing the characteristic spatial patterns of vegetation found in plant ecosystems under water limitations. Recently, a discrete delay was incorporated into this model to account for the lag between water infiltration into the soil and the following water uptake by plants. In this work, we consider a more ecologically realistic distributed delay to relate plant growth and soil water availability and analyse the effects of different delay types on the dynamics of both mean-field and spatial Klausmeier–Gray–Scott models. We consider distributed delays based on Gamma kernels and use the so-called linear chain trick to analyse the stability of the uniformly vegetated equilibrium. It is shown that the presence of delays can lead to the loss of stability in the constant equilibrium and to a reduction of the parameter region where steady-state vegetation patterns can arise through symmetry-breaking by diffusion-driven instability. However, these effects depend on the type of delay, and they are absent for distributed delays with weak kernels when vegetation mortality is low. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Figure 1

16 pages, 5602 KiB

Open AccessArticle

Molecular-Memory-Induced Counter-Intuitive Noise Attenuator in Protein Polymerization

by Xiaojun Bai, Sizhe Wang, Xin Zhang and Haohua Wang

Symmetry 2024, 16(3), 315; https://doi.org/10.3390/sym16030315 - 6 Mar 2024

Viewed by 909

Abstract

Gene expression comprises many asymmetric and complex processes. Transcriptional details revealed by the whole genome indicate that genes resort to transcriptional bursting and accumulate molecular memory. However, it is still unclear how the interplay of transcriptional bursting and memory regulates robustness and expression noise. Here, we consider a model of multiple coupled processes of protein polymerization to focus on decoding the effect of molecular memory. Using non-Markovian transformation technology, we first define the memory index to measure the correlation window of expression to decipher the mechanism of regulation. The results indicate that memory from synthesis can amplify expression noise, while memory originating from polymerization can reduce the lower bound of the noise of gene products; that is, the memory from different sources plays distinct regulatory roles to induce non-symmetry. Moreover, it is counterintuitive that the dual regulation from memory and bursting expression can directly suppress system noise, violating the principle that transcriptional bursting enhances noise. Our results not only provide a theoretical framework for investigating the function of memory but also imply that expression noise is not part of a half-power relationship with, nor mediated by, memory. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Figure 1

13 pages, 916 KiB

Open AccessArticle

Steady State Kinetics for Enzymes with Multiple Binding Sites Upstream of the Catalytic Site

by Manuel I. Osorio, Mircea Petrache, Dino G. Salinas, Felipe Valenzuela-Ibaceta, Fernando González-Nilo, William Tiznado, José M. Pérez-Donoso, Denisse Bravo and Osvaldo Yáñez

Symmetry 2023, 15(12), 2176; https://doi.org/10.3390/sym15122176 - 8 Dec 2023

Viewed by 1847

Abstract

The Michaelis–Menten mechanism, which describes the binding of a substrate to an enzyme, is a simplification of the process on a molecular scale. A more detailed model should include the binding of the substrate to precatalytic binding sites (PCBSs) prior to the transition to the catalytic site. Our work shows that the incorporation of PCBSs, in steady-state conditions, generates a Michaelis–Menten-type expression, in which the kinetic parameters KM and Vmax adopt more complex expressions than in the model without PCBSs. The equations governing reaction kinetics can be seen as generalized symmetries, relative to time translation actions over the state space of the underlying chemical system. The study of their structure and defining parameters can be interpreted as looking for invariants associated with these time evolution actions. The expression of

K_{M}

decreases as the number of PCBSs increases, while

V_{m a x}

reaches a minimum when the first PCBSs are incorporated into the model. To evaluate the trend of the dynamic behavior of the system, numerical simulations were performed based on schemes with different numbers of PCBSs and six conditions of kinetic constants. From these simulations, with equal kinetic constants for the formation of the Substrate/PCBS complex, it is observed that

K_{M}

and

V_{m a x}

are lower than those obtained with the Michaelis–Menten model. For the model with PCBSs, the

V_{m a x}

reaches a minimum at one PCBS and that value is maintained for all of the systems evaluated. Since

K_{M}

decreases with the number of PCBSs, the catalytic efficiency increases for enzymes fitting this model. All of these observations are consistent with the general equation obtained. This study allows us to explain, on the basis of the PCBS to

K_{M}

and

V_{m a x}

ratios, the effect on enzyme parameters due to mutations far from the catalytic site, at sites involved in the first enzyme/substrate interaction. In addition, it incorporates a new mechanism of enzyme activity regulation that could be fundamental to search for new activity-modulating sites or for the design of mutants with modified enzyme parameters. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Graphical abstract

17 pages, 369 KiB

Open AccessArticle

Dynamics of Competitive Two-Strain Stochastic SIR Epidemics on Heterogeneous Networks

by Xiaojie Jing and Guirong Liu

Symmetry 2023, 15(10), 1813; https://doi.org/10.3390/sym15101813 - 23 Sep 2023

Viewed by 869

Abstract

Mathematical modeling in epidemiology, biology, and life sciences requires the use of stochastic models. In this paper, we derive a competitive two-strain stochastic SIR epidemic model by considering the change in state of the epidemic process due to an event. Based on the density-dependent process theory, we construct a six-dimensional deterministic model that can be used to describe the diffusion limit of the stochastic epidemic on a heterogeneous network. Furthermore, we show the explicit expressions for the variances of infectious individuals with strain 1 and strain 2 when the level of infection is increasing exponentially. In particular, we find that the expressions of the variances are symmetric. Finally, simulations for epidemics spreading on networks are performed to confirm our analytical results. We find a close agreement between the simulations and theoretical predictions. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Figure 1

11 pages, 1715 KiB

Open AccessArticle

Stability Analysis of a Mathematical Model for Adolescent Idiopathic Scoliosis from the Perspective of Physical and Health Integration

by Yuhua Zhang and Haiyin Li

Symmetry 2023, 15(8), 1609; https://doi.org/10.3390/sym15081609 - 20 Aug 2023

Viewed by 980

Abstract

In this paper, we take physical and health integration as the entry point. Firstly, based on the transformation mechanism of adolescent idiopathic scoliosis we construct a time delay differential model. Moreover, using the theory of characteristic equation we discuss the stability of a [...] Read more.

τ = 0

and

τ \neq 0

. Furthermore, through numerical simulation, it has been verified the delay,

τ

, exceeds a critical value, the positive equilibrium loses its stability and Hopf bifurcation occurs. Lastly, we determine that sports have a positive effect on adolescent idiopathic scoliosis, directly reducing the number of people with adolescent idiopathic scoliosis. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

► Show Figures

Figure 1

Review

Jump to: Research

23 pages, 402 KiB

Open AccessReview

Reaction–Diffusion Equations in Mathematical Models Arising in Epidemiology

by Vasyl’ Davydovych, Vasyl’ Dutka and Roman Cherniha

Symmetry 2023, 15(11), 2025; https://doi.org/10.3390/sym15112025 - 7 Nov 2023

Cited by 1 | Viewed by 1581

Abstract

The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most of our attention is given to the studies in which not only results of numerical simulations are presented but analytical results as well. In particular, traveling fronts (waves), exact solutions, and the estimation of key epidemic parameters of the epidemic models with governing PDEs (typically reaction–diffusion equations) are discussed. The review may serve as a valuable resource for researchers and practitioners in the field of mathematical modeling in epidemiology. Full article

(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)

Show export options Show export options

Select all

Export citation of selected articles as:

Displaying articles 1-11

Journal Menu

Journal Browser

Mathematical Modeling in Biology and Life Sciences

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (11 papers)

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI