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Axioms
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Dynamical Systems: Theory and Applications in Mathematical Biology
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Dynamical Systems: Theory and Applications in Mathematical Biology

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 29 October 2024 | Viewed by 3538

Special Issue Editors

Dr. Mahmoud Ibrahim

E-Mail Website
Guest Editor
1. Bolyai Institute, University of Szeged, Szeged, Hungary
2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Interests: autonomous dynamical systems; non-autonomous dynamical systems, qualitative theory of ODEs and DDEs (limit cycles and periodic solutions); stability analysis in nonlinear systems, chaotic theory; bifurcation theory; mathematical biology; infectious diseases; time-periodic models; cell biology modeling; modeling the spread
Dr. Attila Dénes

E-Mail Website
Guest Editor
Bolyai Institute, University of Szeged, Szeged, Hungary
Interests: ordinary and delay differential equations; dynamical systems; nonautonomous dynamics; stability theory; mathematical biology; population dynamics; mathematical epidemiology

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to presenting the latest research and developments in mathematical biology, with a specific focus on the applications of dynamical systems theory to biological systems. Dynamical systems theory is a branch of mathematics that provides a framework for analysing and understanding the behaviour of complex systems that change over time. Various types of equations, such as differential, functional, delay, and partial differential equations are often used to model these systems, and the theory allows for the analysis of long-term behaviour, including analysis of stability, periodicity, chaos, and bifurcations. Amongst its key applications is in the study of population dynamics, where dynamical models can be used to describe the growth, decline, and extinction of populations over time, considering factors such as birth rates, death rates, and interactions between species. This approach can help researchers to understand the effects of environmental changes, such as habitat destruction or climate change, on populations in plants and animals.

Researchers are welcome to submit their original research papers and review articles related to the application of dynamical systems theory in mathematical biology. The topics that are covered may include, but are not restricted to:

  • Autonomous and non-autonomous dynamical systems.
  • Linear and nonlinear dynamical systems.
  • Qualitative theory of solutions of dynamic systems.
  • Stability of ordinary, functional, partial, delay differential and difference equations.
  • Stability and threshold dynamics
  • Periodic and almost periodic solutions.
  • Bifurcations and chaos.
  • Persistence of solutions.
  • Mathematical models for infectious diseases.
  • Computational modelling and simulation.
  • Mathematical models of cell biology processes

Dr. Mahmoud Ibrahim
Dr. Attila Dénes
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. Axioms 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

  • dynamical systems theory
  • mathematical biology
  • population dynamics
  • mathematical epidemiology
  • nonlinear dynamical systems
  • non-autonomous systems
  • ODEs, PDEs, DDEs
  • stability analysis
  • global dynamics
  • threshold dynamics
  • periodic solutions
  • persistence theory
  • bifurcations and chaos
  • computational modelling
  • infectious diseases
  • vector-borne diseases
  • zoonotic diseases
  • cell biology modelling
  • climate change

Published Papers (3 papers)

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Research

15 pages, 1266 KiB  
Article
Dynamic Analysis of a Delayed Differential Equation for Ips subelongatus Motschulsky-Larix spp.
by Zhenwei Li and Yuting Ding
Axioms 2024, 13(4), 232; https://doi.org/10.3390/axioms13040232 - 1 Apr 2024
Viewed by 592
Abstract
The protection of forests and the mitigation of pest damage to trees play a crucial role in mitigating the greenhouse effect. In this paper, we first establish a delayed differential equation model for Ips subelongatus Motschulsky-Larix spp., where the delay parameter represents the [...] Read more.
The protection of forests and the mitigation of pest damage to trees play a crucial role in mitigating the greenhouse effect. In this paper, we first establish a delayed differential equation model for Ips subelongatus Motschulsky-Larix spp., where the delay parameter represents the time required for trees to undergo curing. Second, we analyze the stability of the equilibrium of the model and derive the normal form of Hopf bifurcation using a multiple-time-scales method. Then, we analyze the stability and direction of Hopf bifurcating periodic solutions. Finally, we conduct simulations to analyze the changing trends in pest and tree populations. Additionally, we investigate the impact of altering the rate of artificial planting on the system and provide corresponding biological explanations. Full article
(This article belongs to the Special Issue Dynamical Systems: Theory and Applications in Mathematical Biology)
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14 pages, 885 KiB  
Article
Sensitivity Analysis of a 2D Stochastic Agent-Based and PDE Diffusion Model for Cancer-on-Chip Experiments
by Marcello Pompa, Davide Torre, Gabriella Bretti and Andrea De Gaetano
Axioms 2023, 12(10), 930; https://doi.org/10.3390/axioms12100930 - 28 Sep 2023
Viewed by 736
Abstract
The present work extends a previous paper where an agent-based and two-dimensional partial differential diffusion model was introduced for describing immune cell dynamics (leukocytes) in cancer-on-chip experiments. In the present work, new features are introduced for the dynamics of leukocytes and for their [...] Read more.
The present work extends a previous paper where an agent-based and two-dimensional partial differential diffusion model was introduced for describing immune cell dynamics (leukocytes) in cancer-on-chip experiments. In the present work, new features are introduced for the dynamics of leukocytes and for their interactions with tumor cells, improving the adherence of the model to what is observed in laboratory experiments. Each system’s solution realization is a family of biased random walk trajectories, affected by the chemotactic gradients and in turn affecting them. A sensitivity analysis with respect to the model parameters is performed in order to assess the effect of their variation on both tumor cells and on leukocyte dynamics. Full article
(This article belongs to the Special Issue Dynamical Systems: Theory and Applications in Mathematical Biology)
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25 pages, 1235 KiB  
Article
Analysis of the Solution of a Model of SARS-CoV-2 Variants and Its Approximation Using Two-Step Lagrange Polynomial and Euler Techniques
by Muhammad Usman, Mujahid Abbas and Andrew Omame
Axioms 2023, 12(5), 480; https://doi.org/10.3390/axioms12050480 - 16 May 2023
Cited by 2 | Viewed by 1099
Abstract
In this paper, a vaccination model for SARS-CoV-2 variants is proposed and is studied using fractional differential operators involving a non-singular kernel. It is worth mentioning that variability in transmission rates occurs because of the particular population that is vaccinated, and hence, the [...] Read more.
In this paper, a vaccination model for SARS-CoV-2 variants is proposed and is studied using fractional differential operators involving a non-singular kernel. It is worth mentioning that variability in transmission rates occurs because of the particular population that is vaccinated, and hence, the asymptomatic infected classes are classified on the basis of their vaccination history. Using the Banach contraction principle and the Arzela–Ascoli theorem, existence and uniqueness results for the proposed model are presented. Two different numerical approaches, the fractional Euler and Lagrange polynomial methods, are employed to approximate the model’s solution. The model is then fitted to data associated with COVID-19 deaths in Pakistan between 1 January 2022 and 10 April 2022. It is concluded that our model is much aligned with the data when the order of the fractional derivative ζ=0.96. The two different approaches are then compared with different step sizes. It is observed that they behave alike for small step sizes and exhibit different behaviour for larger step sizes. Based on the numerical assessment of the model presented herein, the impact of vaccination and the fractional order are highlighted. It is also noted that vaccination could remarkably decrease the spikes of different emerging variants of SARS-CoV-2 within the population. Full article
(This article belongs to the Special Issue Dynamical Systems: Theory and Applications in Mathematical Biology)
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