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Axioms
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Applied Mathematical Modeling: Theoretical Foundations, Methods and Applications
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Applied Mathematical Modeling: Theoretical Foundations, Methods and Applications

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

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 6334

Special Issue Editors

Dr. Mikhail Kuptsov

E-Mail Website
Guest Editor
Department of Higher Mathematics, Ryazan State Radio Engineering University, 390005 Ryazan, Russia
Interests: differential equations; dynamical systems; stability theory; mathematical modeling (information processes, social network, radio engineering, macroeconomics, educational processes, etc.); stochastic methods; fuzzy measurements; e-learning
Dr. Sergey Leontyevich Yablochnikov

E-Mail Website
Guest Editor
Department of Ecology, Life Safety and Power Supply, Moscow Technical University of Communications and Informatics, 8a Aviamotornaya Street, Moscow 111024, Russia
Interests: dynamical systems; stability theory; mathematical modeling (information processes, social network, radio engineering, macroeconomics, educational processes, etc.); stochastic methods; fuzzy measurements; e-learning

Special Issue Information

Dear Colleagues,

Mathematical modeling is a universally deployed and highly effective tool for performing a wide range of scientific research, as well as for analyzing and predicting various phenomena and processes. In particular, the results of the implementation of mathematical modeling are the basis for the synthesis of computer simulations that simulate the real conditions and situations for the functioning of natural, technical, technological and socio-economic systems. The global and local problems of modern society, necessitate the development of models for their study and forecasting. Therefore, the purpose of this Special Issue of Axioms is to provide a unique opportunity for researchers around the world to present new results in the field of mathematical modeling.

We welcome authors to submit scientific articles that contain new results regarding the general methodology of mathematical modeling, and, especially, the results of applied research in the field of the synthesis of mathematical models based on the use of a set of real data on various objects, processes and phenomena (natural, technical and technological, economic, social, information, etc.). In applied mathematical models, it is necessary to pay attention to the issues of ensuring the adequacy of models to real data.

In general, we plan to consider a wide range of modern problems regarding mathematical modeling and hope authors will engage in this rich scientific discussion.

We look forward to receiving your contributions.

Dr. Mikhail Kuptsov
Dr. Sergey Leontyevich Yablochnikov
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

  • mathematical models
  • simulation models
  • deterministic and stochastic models
  • models with elements of game theory

Published Papers (5 papers)

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Research

19 pages, 410 KiB  
Article
Analytical Solution of Generalized Bratu-Type Fractional Differential Equations Using the Homotopy Perturbation Transform Method
by Ghaliah Alhamzi, Aafrin Gouri, Badr Saad T. Alkahtani and Ravi Shanker Dubey
Axioms 2024, 13(2), 133; https://doi.org/10.3390/axioms13020133 - 19 Feb 2024
Viewed by 848
Abstract
In this study, we present the generalized form of the higher-order nonlinear fractional Bratu-type equation. In this generalization, we deal with a generalized fractional derivative, which is quite useful from an application point of view. Furthermore, some special cases of the generalized fractional [...] Read more.
In this study, we present the generalized form of the higher-order nonlinear fractional Bratu-type equation. In this generalization, we deal with a generalized fractional derivative, which is quite useful from an application point of view. Furthermore, some special cases of the generalized fractional Bratu equation are recognized and examined. To solve these nonlinear differential equations of fractional order, we employ the homotopy perturbation transform method. This work presents a useful computational method for solving these equations and advances our understanding of them. We also plot some numerical outcomes to show the efficiency of the obtained results. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling: Theoretical Foundations, Methods and Applications)
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17 pages, 645 KiB  
Article
Stability Analysis in a Mathematical Model for Allergic Reactions
by Rawan Abdullah, Irina Badralexi and Andrei Halanay
Axioms 2024, 13(2), 102; https://doi.org/10.3390/axioms13020102 - 31 Jan 2024
Viewed by 875
Abstract
We present a mathematical model that captures the dynamics of the immune system during allergic reactions. Using delay differential equations, we depict the evolution of T cells, APCs, and IL6, considering cell migration between various body compartments. The biological [...] Read more.
We present a mathematical model that captures the dynamics of the immune system during allergic reactions. Using delay differential equations, we depict the evolution of T cells, APCs, and IL6, considering cell migration between various body compartments. The biological discussions and interpretations within the article revolve around drug desensitization, highlighting one potential application of the model. We conduct stability analysis on certain equilibrium points, demonstrating stability in some cases and only partial stability in others. Numerical simulations validate the theoretical findings. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling: Theoretical Foundations, Methods and Applications)
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18 pages, 1918 KiB  
Article
Study of Rotavirus Mathematical Model Using Stochastic and Piecewise Fractional Differential Operators
by Nadiyah Hussain Alharthi and Mdi Begum Jeelani
Axioms 2023, 12(10), 970; https://doi.org/10.3390/axioms12100970 - 16 Oct 2023
Cited by 1 | Viewed by 864
Abstract
This manuscript is related to undertaking a mathematical model (susceptible, vaccinated, infected, and recovered) of rotavirus. Some qualitative results are established for the mentioned challenging childhood disease epidemic model of rotavirus as it spreads across a population with a heterogeneous rate. The proposed [...] Read more.
This manuscript is related to undertaking a mathematical model (susceptible, vaccinated, infected, and recovered) of rotavirus. Some qualitative results are established for the mentioned challenging childhood disease epidemic model of rotavirus as it spreads across a population with a heterogeneous rate. The proposed model is investigated using a novel approach of fractal calculus. We compute the boundedness positivity of the solution of the proposed model. Additionally, the basic reproduction ratio and its sensitivity analysis are also performed. The global stability of the endemic equilibrium point is also confirmed graphically using some available values of initial conditions and parameters. Sufficient conditions are deduced for the existence theory, the Ulam–Hyers (UH) stability. Specifically, the numerical approximate solution of the rotavirus model is investigated using efficient numerical methods. Graphical presentations are presented corresponding to a different fractional order to understand the transmission dynamics of the mentioned disease. Furthermore, researchers have examined the impact of lowering the risk of infection on populations that are susceptible and have received vaccinations, producing some intriguing results. We also present a numerical illustration taking the stochastic derivative of the proposed model graphically. Researchers may find this research helpful as it offers insightful information about using numerical techniques to model infectious diseases. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling: Theoretical Foundations, Methods and Applications)
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17 pages, 354 KiB  
Article
Research on Price Discrimination Behavior Governance of E-Commerce Platforms—A Bayesian Game Model Based on the Right to Data Portability
by Jing Yu and Wensheng Jia
Axioms 2023, 12(10), 919; https://doi.org/10.3390/axioms12100919 - 27 Sep 2023
Viewed by 869
Abstract
The behavior of e-commerce platforms using big data algorithms to implement “big data killing” is not only rejected by regular customers, but also creates many difficulties for supervision by relevant government departments. In order to study how to curb the price discrimination behavior [...] Read more.
The behavior of e-commerce platforms using big data algorithms to implement “big data killing” is not only rejected by regular customers, but also creates many difficulties for supervision by relevant government departments. In order to study how to curb the price discrimination behavior of e-commerce platforms in the case of taking regular customers as the leaders, this paper introduces the right to data portability and considers two types of regular customers with high price sensitivity and low price sensitivity. Then, we build a Bayesian game model between e-commerce platforms and regular customers on the basis of the established general game model. Our experiments show that when the reuse value coefficient of personal data is high, the e-commerce platform will choose a uniform pricing strategy, which indicates that the right to data portability can curb the price discrimination behavior of the e-commerce platform to a certain extent. Moreover, when the proportion of high-sensitivity consumers among regular customers increases, e-commerce platforms will be prompted to choose the uniform pricing strategy, which indicates that consumers can curb price discrimination behaviour on e-commerce platforms by increasing their sensitivity for price change. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling: Theoretical Foundations, Methods and Applications)
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15 pages, 3952 KiB  
Article
Thrombin Generation Thresholds for Coagulation Initiation under Flow
by Anass Bouchnita, Kanishk Yadav, Jean-Pierre Llored, Alvaro Gurovich and Vitaly Volpert
Axioms 2023, 12(9), 873; https://doi.org/10.3390/axioms12090873 - 12 Sep 2023
Viewed by 1601
Abstract
In veins, clotting initiation displays a threshold response to flow intensity and injury size. Mathematical models can provide insights into the conditions leading to clot growth initiation under flow for specific subjects. However, it is hard to determine the thrombin generation curves that [...] Read more.
In veins, clotting initiation displays a threshold response to flow intensity and injury size. Mathematical models can provide insights into the conditions leading to clot growth initiation under flow for specific subjects. However, it is hard to determine the thrombin generation curves that favor coagulation initiation in a fast manner, especially when considering a wide range of conditions related to flow and injury size. In this work, we propose to address this challenge by using a neural network model trained with the numerical simulations of a validated 2D model for clot formation. Our surrogate model approximates the results of the 2D simulations, reaching an accuracy of 94% on the test dataset. We used the trained artificial neural network to determine the threshold for thrombin generation parameters that alter the coagulation initiation response under varying flow speed and injury size conditions. Our model predictions show that increased levels of the endogenous thrombin potential (ETP) and peak thrombin concentration increase the likelihood of coagulation initiation, while an elevated time to peak decreases coagulation. The lag time has a small effect on coagulation initiation, especially when the injury size is small. Our surrogate model can be considered as a proof-of-concept of a tool that can be deployed to estimate the risk of bleeding in specific patients based on their Thrombin Generation Assay results. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling: Theoretical Foundations, Methods and Applications)
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