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Axioms
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Advances in Applied Mathematical Modelling
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Advances in Applied Mathematical Modelling

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

Deadline for manuscript submissions: closed (20 January 2023) | Viewed by 17803

Special Issue Editor

Dr. Xi Deng

E-Mail Website
Guest Editor
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
Interests: computational fluid dynamics; numerical methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Applied mathematical modelling is based on constructing and solving ordinary or partial differential equation systems that describe a wide variety of phenomena in engineering and environmental processes, manufacturing, and industrial systems. Recent developments in applied mathematical modelling are accomplished via high-fidelity modelling with physics-driven and data-driven approaches, high-accuracy numerical methods with advanced algorithms, and high-performance computing with modern hardware. Thus, advances in applied mathematical modelling should reflect a combination of concepts, methods, and principles in multi-scale, multi-physics, or multi-disciplinary problems.

This Special Issue will be a platform for papers developing further insights into real-world problems through novel mathematical modelling, novel applications, or a combination of these. The proposed Special Issue intends to cover topics of applied mathematics and mathematical modelling on various aspects including, but not limited to:

  • Numerical and modelling analysis; 
  • Optimization and evolutionary algorithm models and methods; 
  • Numerical modelling of real-world problems;
  • Numerical solution of large systems of linear and nonlinear equations; 
  • Novel modelling with multi-disciplinary approaches;
  • New discoveries or novel applications via modelling;
  • High-performance computing with modern hardware.

Dr. Xi Deng
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. 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

  • mathematical modelling
  • applied mathematics
  • numerical mathematics
  • mathematical physics

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

Published Papers (8 papers)

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Research

17 pages, 941 KiB  
Article
On Using Piecewise Fractional Differential Operator to Study a Dynamical System
by Shahid Khan, Zareen A. Khan, Hussam Alrabaiah and Salman Zeb
Axioms 2023, 12(3), 292; https://doi.org/10.3390/axioms12030292 - 10 Mar 2023
Cited by 6 | Viewed by 1720
Abstract
This research work is devoted to undertaking a dynamical system representing SARS-CoV-19 disease under the concept of piecewise fractional-order derivative using the Caputo concept since long-memory and short-memory terms are not well explained by ordinary fractional differential equations. It has been found that [...] Read more.
This research work is devoted to undertaking a dynamical system representing SARS-CoV-19 disease under the concept of piecewise fractional-order derivative using the Caputo concept since long-memory and short-memory terms are not well explained by ordinary fractional differential equations. It has been found that for such disruption, piecewise operators of fractional derivatives have been found useful in many cases. Therefore, we study a compartmental model of susceptible and infected individuals under the concept of piecewise derivative. We establish the existence theory of the considered model by using some Banach and Schauder fixed-point theorems. Keeping the importance of stability, a pertinent result related to the said area is also developed. The said concept of stability is based on the concept given by Ulam and Hyers. Further, to derive the numerical results, we use the Euler method to develop a numerical scheme for the considered model. Using real available data, we have presented various graphical presentations of two compartments against different fractional orders and various values of isolation parameters. The crossover behaviors in the dynamics can be clearly observed, which is explained by the piecewise operators, not the usual fractional-order derivative. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)
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30 pages, 5072 KiB  
Article
Complex Dynamic Behaviors of a Modified Discrete Leslie–Gower Predator–Prey System with Fear Effect on Prey Species
by Sijia Lin, Fengde Chen, Zhong Li and Lijuan Chen
Axioms 2022, 11(10), 520; https://doi.org/10.3390/axioms11100520 - 1 Oct 2022
Cited by 15 | Viewed by 1778
Abstract
A discrete modified Leslie–Gower prey-predator model considering the effect of fear on prey species is proposed and studied in this paper. First, we discuss the existence of equilibria and the local stability of the model. Second, we use the iterative method and comparison [...] Read more.
A discrete modified Leslie–Gower prey-predator model considering the effect of fear on prey species is proposed and studied in this paper. First, we discuss the existence of equilibria and the local stability of the model. Second, we use the iterative method and comparison principle to obtain the set of conditions which ensures the global attractivity of positive equilibrium point. The results show that prey and predator can coexist stably when the intrinsic growth rates of both prey and predator are maintained within a certain range. Then, we study the global attractivity of the boundary equilibrium point. Our results suggest that when the intrinsic rate of prey is small enough or the fear factor is large enough, the prey will tend to go extinct, while the predator can survive stably due to the availability of other food sources. Subsequently, we discuss flip bifurcation, transcritical bifurcation at the equilibria of the system, by using the center manifold theorem and bifurcation theory. We find that system changes from chaotic state to four-period orbit, two-period orbit, stable state, and finally prey species will be driven to extinction, while predator species survive in a stable state for enough large birth rate of prey species with the increasing of fear effect. Finally, we verify the feasibility of the main results by numerical simulations, and discuss the influence of the fear effect. The results show that the fear effect within a certain range can enhance the stability of the system. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)
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21 pages, 452 KiB  
Article
A Numerical Method for a Heat Conduction Model in a Double-Pane Window
by Aníbal Coronel, Fernando Huancas, Esperanza Lozada and Alex Tello
Axioms 2022, 11(8), 422; https://doi.org/10.3390/axioms11080422 - 22 Aug 2022
Cited by 4 | Viewed by 1608
Abstract
In this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction problem. The [...] Read more.
In this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction problem. The designed scheme is mainly based on approximations satisfying the facts that all inner grid points has second-order temporal and spatial truncation errors, while at the boundary points and at inter-facial points has second-order temporal truncation error and first-order spatial truncation error, respectively. We prove that the finite difference scheme introduced is unconditionally stable, convergent, and has a rate of convergence two in space and time for the L∞-norm. Moreover, we give a numerical example to confirm our theoretical results. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)
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21 pages, 527 KiB  
Article
Global Attractivity of Symbiotic Model of Commensalism in Four Populations with Michaelis–Menten Type Harvesting in the First Commensal Populations
by Lili Xu, Yalong Xue, Qifa Lin and Chaoquan Lei
Axioms 2022, 11(7), 337; https://doi.org/10.3390/axioms11070337 - 12 Jul 2022
Cited by 7 | Viewed by 1864
Abstract
This article revisits the stability property of a symbiotic model of commensalism with Michaelis–Menten type harvesting in the first commensal populations. By constructing some suitable Lyapunov functions, we provide a thorough analysis of the dynamic behaviors of the subsystem composed of the second [...] Read more.
This article revisits the stability property of a symbiotic model of commensalism with Michaelis–Menten type harvesting in the first commensal populations. By constructing some suitable Lyapunov functions, we provide a thorough analysis of the dynamic behaviors of the subsystem composed of the second and third species. After that, by applying the stability results of this subsystem and combining with the differential inequality theory, sufficient conditions which ensure the global attractivity of the equilibria are obtained. The results obtained here essentially improve and generalize some known results. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)
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15 pages, 928 KiB  
Article
The SLI-SC Mathematical Model of African Swine Fever Transmission among Swine Farms: The Effect of Contaminated Human Vector
by Pearanat Chuchard, Din Prathumwan, Kamonchat Trachoo, Wasan Maiaugree and Inthira Chaiya
Axioms 2022, 11(7), 329; https://doi.org/10.3390/axioms11070329 - 6 Jul 2022
Cited by 3 | Viewed by 2429
Abstract
In this paper, a mathematical model for African swine fever is modified by considering the swine farm with the contaminated human vector that is able to infect and spread the disease among swine farms. In the developed model, we have divided the swine [...] Read more.
In this paper, a mathematical model for African swine fever is modified by considering the swine farm with the contaminated human vector that is able to infect and spread the disease among swine farms. In the developed model, we have divided the swine farm density into three related groups, namely the susceptible swine farm compartment, latent swine farm compartment, and infectious swine farm compartment. On the other hand, the human vector population density has been separated into two classes, namely the susceptible human vector compartment and the infectious human vector compartment. After that, we use this model and a quarantine strategy to analyze the spread of the infection. In addition, the basic reproduction number R0 is determined by using the next-generation matrix, which can analyze the stability of the model. Finally, the numerical simulations of the proposed model are illustrated to confirm the results from theorems. The results showed that the transmission coefficient values per unit of time per individual between the human vector and the swine farm resulted in the spread of African swine fever. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)
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14 pages, 386 KiB  
Article
Dynamic Behaviors of an Obligate Commensal Symbiosis Model with Crowley–Martin Functional Responses
by Lili Xu, Yalong Xue, Xiangdong Xie and Qifa Lin
Axioms 2022, 11(6), 298; https://doi.org/10.3390/axioms11060298 - 20 Jun 2022
Cited by 10 | Viewed by 1840
Abstract
A two species obligate commensal symbiosis model with Crowley–Martin functional response was proposed and studied in this paper. For an autonomous case, local and global dynamic behaviors of the system were investigated, respectively. The conditions that ensure the existence of the positive equilibrium [...] Read more.
A two species obligate commensal symbiosis model with Crowley–Martin functional response was proposed and studied in this paper. For an autonomous case, local and global dynamic behaviors of the system were investigated, respectively. The conditions that ensure the existence of the positive equilibrium is coincidentla to the conditions of global stability of a positive equilibrium. For nonautonomous cases, persistent and extinction properties of the system are investigated. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)
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27 pages, 4076 KiB  
Article
On Discrete Poisson–Mirra Distribution: Regression, INAR(1) Process and Applications
by Radhakumari Maya, Muhammed Rasheed Irshad, Christophe Chesneau, Soman Latha Nitin and Damodaran Santhamani Shibu
Axioms 2022, 11(5), 193; https://doi.org/10.3390/axioms11050193 - 21 Apr 2022
Cited by 14 | Viewed by 2538
Abstract
Several pieces of research have spotlighted the importance of count data modelling and its applications in real-world phenomena. In light of this, a novel two-parameter compound-Poisson distribution is developed in this paper. Its mathematical functionalities are investigated. The two unknown parameters are estimated [...] Read more.
Several pieces of research have spotlighted the importance of count data modelling and its applications in real-world phenomena. In light of this, a novel two-parameter compound-Poisson distribution is developed in this paper. Its mathematical functionalities are investigated. The two unknown parameters are estimated using both maximum likelihood and Bayesian approaches. We also offer a parametric regression model for the count datasets based on the proposed distribution. Furthermore, the first-order integer-valued autoregressive process, or INAR(1) process, is also used to demonstrate the utility of the suggested distribution in time series analysis. The unknown parameters of the proposed INAR(1) model are estimated using the conditional maximum likelihood, conditional least squares, and Yule–Walker techniques. Simulation studies for the suggested distribution and the INAR(1) model based on this innovative distribution are also undertaken as an assessment of the long-term performance of the estimators. Finally, we utilized three real datasets to depict the new model’s real-world applicability. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)
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17 pages, 774 KiB  
Article
Research on the n-Stage Delay Distribution Method Based on a Compensation Mechanism in a Random Environment
by Lei Zhou, Yue Qi and Fachao Li
Axioms 2022, 11(2), 67; https://doi.org/10.3390/axioms11020067 - 8 Feb 2022
Viewed by 2167
Abstract
With the development of logistics, the delayed distribution problem based on a compensation mechanism has appeared. The core of this problem is to decide whether to delay the distribution at the beginning of each stage and how to compensate the customers if delay [...] Read more.
With the development of logistics, the delayed distribution problem based on a compensation mechanism has appeared. The core of this problem is to decide whether to delay the distribution at the beginning of each stage and how to compensate the customers if delay occurs. In this paper, beginning with the 2 and 3-stage delay distribution problem, the characteristics and computational complexity of the model are analyzed, and a formal model description of the n-stage problem is given. The expected value and variance are used as the centralized quantization description strategy for random variables, and the expected value model and the generalized expectation value model for solving the delay distribution problem are given. The solution algorithm is given, and the dependence of the single transport cost of each transport vehicle and the penalty for each car delay in a period-of-time distribution are analyzed. Combined with specific examples, theoretical analysis and example calculations show that the formal description model is a good platform for further combinations of solution methods. This method extends the general delayed distribution problem to multi-stage delayed distribution, which has guiding significance for decision-makers. The proposed model has solid system structure features and interpretability, and could be used in a wide variety of applications. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)
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