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Symmetry
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Symmetry/Asymmetry of Differential Equations in Biomathematics
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Symmetry/Asymmetry of Differential Equations in Biomathematics

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 4174

Special Issue Editors

Dr. Liang Zhang

E-Mail Website
Guest Editor
College of Science, Northwest A&F University, Yangling 712100, China
Interests: differential equations; biomathematics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Junli Liu

E-Mail Website
Guest Editor
School of Science, Xi'an Polytechnic University, Xi'an 710048, China
Interests: biomathematics; differential equations and applications
Prof. Dr. Tailei Zhang

E-Mail Website
Guest Editor
School of Science, Chang'an University, Xi'an 710064, China
Interests: theoretical research and application of ordinary differential equations; mathematical modeling and research of biomathematics; population dynamics and infectious disease dynamics

Special Issue Information

Dear Colleagues,

It is well known that differential equations are powerful tools for the study of biomathematics, and symmetry/asymmetry is a common phenomenon in the real world. The study of the symmetry/asymmetry of differential equations in biomathematics is of great significance in revealing the interaction or motion changes among organisms.

This Special Issue focuses on recent advancements and applications of differential equations in biomathematics, emphasizing the role of symmetry and asymmetry in biological systems. Topics include the development and analysis of mathematical models in biology, novel computational methods for solving differential equations, and the investigation of complex biological systems through the lens of symmetry and asymmetry. We invite original research articles, reviews, and methodological contributions that provide new insights into the interplay between symmetry, asymmetry, and differential equations in the context of biomathematics. Contributions should address the challenges and opportunities in understanding the underlying mechanisms governing various biological phenomena, as well as the development of innovative mathematical techniques and computational tools to analyze and predict the behavior of biological systems.

This Special Issue aims to foster interdisciplinary collaboration between mathematicians, biologists, and computational scientists, promoting the exchange of ideas and the advancement of biomathematics as a field. We encourage submissions that explore the application of differential equations to a wide range of biological disciplines, such as ecology, epidemiology, genetics, neuroscience, and physiology, and that demonstrate the potential of biomathematical approaches to contribute to the resolution of pressing issues in life sciences.

Dr. Liang Zhang
Prof. Dr. Junli Liu
Prof. Dr. Tailei Zhang
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

  • differential equations
  • dynamical systems
  • symmetry/asymmetry
  • population model
  • epidemic model
  • dynamical behavior
  • simulation

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Published Papers (4 papers)

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Research

12 pages, 2061 KiB  
Article
Optimal Harvesting Strategies for Timber and Non-Timber Forest Products with Nonlinear Harvesting Terms
by Yaning Zhang, Lina Hao and Shan Zhang
Symmetry 2024, 16(7), 806; https://doi.org/10.3390/sym16070806 - 27 Jun 2024
Viewed by 603
Abstract
Forest resources are renewable, and the rational exploitation and utilization of forest resources are not only conducive to sustainable development on a population scale, they can also lead to higher economic benefits. Based on the actual timber harvest problem, this paper establishes the [...] Read more.
Forest resources are renewable, and the rational exploitation and utilization of forest resources are not only conducive to sustainable development on a population scale, they can also lead to higher economic benefits. Based on the actual timber harvest problem, this paper establishes the joint harvest model of timber and non-timber with nonlinear harvest items. In the numerical simulation, by comparing the existing proportional harvest model, it is concluded that the optimal harvest strategy of nonlinear harvest items in this paper can obtain larger ecological benefits and be more conducive to the sustainable development of a population. Firstly, using the qualitative theory of ordinary differential equations, the dynamic behavior of the model is studied, and the existence and stability of the equilibrium point of the model are proven. Secondly, the optimal control solution is obtained by using the optimal control theory. Finally, the optimal harvesting strategy of timber and non-timber products is given based on the numerical simulation results, and a comparison of the effects of different parameters on the optimal harvest strategy, which provides a certain theoretical basis for the sustainable development of the ecological economy of forestry, is carried out. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry of Differential Equations in Biomathematics)
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15 pages, 3198 KiB  
Article
Bogdanov–Takens Bifurcation of Kermack–McKendrick Model with Nonlinear Contact Rates Caused by Multiple Exposures
by Jun Li and Mingju Ma
Symmetry 2024, 16(6), 688; https://doi.org/10.3390/sym16060688 - 4 Jun 2024
Viewed by 482
Abstract
In this paper, we consider the influence of a nonlinear contact rate caused by multiple contacts in classical SIR model. In this paper, we unversal unfolding a nilpotent cusp singularity in such systems through normal form theory, we reveal that the system undergoes [...] Read more.
In this paper, we consider the influence of a nonlinear contact rate caused by multiple contacts in classical SIR model. In this paper, we unversal unfolding a nilpotent cusp singularity in such systems through normal form theory, we reveal that the system undergoes a Bogdanov-Takens bifurcation with codimension 2. During the bifurcation process, numerous lower codimension bifurcations may emerge simultaneously, such as saddle-node and Hopf bifurcations with codimension 1. Finally, employing the Matcont and Phase Plane software, we construct bifurcation diagrams and topological phase portraits. Additionally, we emphasize the role of symmetry in our analysis. By considering the inherent symmetries in the system, we provide a more comprehensive understanding of the dynamical behavior. Our findings suggest that if this occurrence rate is applied to the SIR model, it would yield different dynamical phenomena compared to those obtained by reducing a 3-dimensional dynamical model to a planar system by neglecting the disease mortality rate, which results in a stable nilpotent cusp singularity with codimension 2. We found that in SIR models with the same occurrence rate, both stable and unstable Bogdanov-Takens bifurcations occur, meaning both stable and unstable limit cycles appear in this system. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry of Differential Equations in Biomathematics)
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17 pages, 962 KiB  
Article
Stability and Hopf Bifurcation of a Delayed Predator–Prey Model with a Stage Structure for Generalist Predators and a Holling Type-II Functional Response
by Zi-Wei Liang and Xin-You Meng
Symmetry 2024, 16(5), 597; https://doi.org/10.3390/sym16050597 - 11 May 2024
Viewed by 836
Abstract
In this paper, we carry out some research on a predator–prey system with maturation delay, a stage structure for generalist predators and a Holling type-II functional response, which has already been proposed. First, for the delayed model, we obtain the conditions for the [...] Read more.
In this paper, we carry out some research on a predator–prey system with maturation delay, a stage structure for generalist predators and a Holling type-II functional response, which has already been proposed. First, for the delayed model, we obtain the conditions for the occurrence of stability switches of the positive equilibrium and possible Hopf bifurcation values owing to the growth of the value of the delay by applying the geometric criterion. It should be pointed out that when we suppose that the characteristic equation has a pair of imaginary roots λ=±iω(ω>0), we just need to consider iω(ω>0) due to the symmetry, which alleviates the computation requirements. Next, we investigate the nature of Hopf bifurcation. Finally, we conduct numerical simulations to verify the correctness of our findings. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry of Differential Equations in Biomathematics)
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16 pages, 864 KiB  
Article
Dynamics of a Stochastic SVEIR Epidemic Model with Nonlinear Incidence Rate
by Xinghao Wang, Liang Zhang and Xiao-Bing Zhang
Symmetry 2024, 16(4), 467; https://doi.org/10.3390/sym16040467 - 11 Apr 2024
Cited by 1 | Viewed by 1056
Abstract
This paper delves into the analysis of a stochastic epidemic model known as the susceptible–vaccinated–exposed–infectious–recovered (SVEIR) model, where transmission dynamics are governed by a nonlinear function. In the theoretical analysis section, by suitable stochastic Lyapunov functions, we establish that when the threshold value, [...] Read more.
This paper delves into the analysis of a stochastic epidemic model known as the susceptible–vaccinated–exposed–infectious–recovered (SVEIR) model, where transmission dynamics are governed by a nonlinear function. In the theoretical analysis section, by suitable stochastic Lyapunov functions, we establish that when the threshold value, denoted as R0s, falls below 1, the epidemic is destined for extinction. Conversely, if the reproduction number R0 of the deterministic model surpasses 1, the model manifests an ergodic endemic stationary distribution. In the numerical simulations and data interpretation section, leveraging a graphical analysis with COVID-19 data, we illustrate that random fluctuations possess the capacity to quell disease outbreaks, underscoring the role of vaccines in curtailing the spread of diseases. This study not only contributes to the understanding of epidemic dynamics but also highlights the pivotal role of stochasticity and vaccination strategies in epidemic control and management. The inherent balance and patterns observed in epidemic spread and control strategies, reflect a symmetrical interplay between stochasticity, vaccination, and disease dynamics. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry of Differential Equations in Biomathematics)
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