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Fractal Fract
Special Issues
Recent Developments on Mathematical Models of Deadly Disease
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Recent Developments on Mathematical Models of Deadly Disease

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 5971

Special Issue Editors

Dr. Sunil Kumar

E-Mail Website
Guest Editor
Department of Mathematics, National Institute of Technology, Jamshedpur-831014, Jharkhand, India
Interests: mathematical modelling; fractional calculus; nonlinear dynamics and chaos; ecological modelling, disease models
Prof. Dr. Shaher Momani

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan
Interests: numerical analysis; differential equations; fractional calculus; fluid mechanics; nonlinear dynamics

Special Issue Information

Dear Colleagues,

Many mathematical models of biological science, and various laws, are expressed in terms of ordinary and partial differential equations. Non-linear systems play an important role in physics, engineering, and biological science. Biological sciences are the study of life and living organisms, their life cycles, adaptations, and environment. There are many different areas of study under the umbrella of biological sciences, including biochemistry, microbiology, and evolutionary biology. In recent years, the whole world has faced a major challenge in rapidly spreading and deadly infectious disease, such as COVID-19, Ebola, HIV, hepatitis, measles, dengue fever, polio, cholera, tuberculosis, chickenpox, smallpox, and many other that cannot be listed here. The fractional derivative has been recognized as a powerful modeling tool on differential equations arising in several biological and physical phenomena. Therefore, the main interest of this Special Issue is to describe and analyze new mathematical models of biological science and techniques for solving such biological problems with the help of fractional modeling.

This Special Issue will provide a platform in the recent and the original research results on both non-linear biological and physical systems. We invite authors to contribute original research articles for the Special Issue “Recent Development on Mathematical Models of Deadly Disease” the following potential topics that include, but are not limited to:

  • Mathematical modeling on biological problems;
  • Fractional dynamics on disease models;
  • Theoretical, computational, and experimental results on diseases models;
  • Fractional models in solid mechanics and fluid mechanics;
  • New analysis results on diseases models;
  • Mathematical methods for diseases models;
  • Theory on new trends of derivative with fractional
  • Analytical and numerical methods to solve fractional models in physics

Dr. Sunil Kumar
Prof. Dr. Shaher Momani
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. Fractal and Fractional 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 2700 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

  • fractional calculus
  • fractional-order disease models
  • fractional derivative
  • stability analysis
  • nonlinear systems
  • network modeling

Published Papers (5 papers)

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Research

19 pages, 775 KiB  
Article
A Spectral Collocation Method for Solving the Non-Linear Distributed-Order Fractional Bagley–Torvik Differential Equation
by Ahmed Z. Amin, Mohamed A. Abdelkawy, Emad Solouma and Ibrahim Al-Dayel
Fractal Fract. 2023, 7(11), 780; https://doi.org/10.3390/fractalfract7110780 - 26 Oct 2023
Cited by 3 | Viewed by 962
Abstract
One of the issues in numerical solution analysis is the non-linear distributed-order fractional Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. We solve the problem by proposing a numerical solution based on the shifted Legendre Gauss–Lobatto (SL-GL) collocation technique. The solution of [...] Read more.
One of the issues in numerical solution analysis is the non-linear distributed-order fractional Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. We solve the problem by proposing a numerical solution based on the shifted Legendre Gauss–Lobatto (SL-GL) collocation technique. The solution of the DO-FBTE is approximated by a truncated series of shifted Legendre polynomials, and the SL-GL collocation points are employed as interpolation nodes. At the SL-GL quadrature points, the residuals are computed. The DO-FBTE is transformed into a system of algebraic equations that can be solved using any conventional method. A set of numerical examples is used to verify the proposed scheme’s accuracy and compare it to existing findings. Full article
(This article belongs to the Special Issue Recent Developments on Mathematical Models of Deadly Disease)
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22 pages, 700 KiB  
Article
Mathematical Identification Analysis of a Fractional-Order Delayed Model for Tuberculosis
by Slavi Georgiev
Fractal Fract. 2023, 7(7), 538; https://doi.org/10.3390/fractalfract7070538 - 12 Jul 2023
Cited by 1 | Viewed by 908
Abstract
Extensive research was conducted on the transmission dynamics of tuberculosis epidemics during its reemergence from the 1980s to the early 1990s, but this global problem of investigating tuberculosis spread dynamics remains of paramount importance. Our study utilized a fractional-order delay differential model to [...] Read more.
Extensive research was conducted on the transmission dynamics of tuberculosis epidemics during its reemergence from the 1980s to the early 1990s, but this global problem of investigating tuberculosis spread dynamics remains of paramount importance. Our study utilized a fractional-order delay differential model to study tuberculosis transmission, where the time delay in the model was attributed to the disease’s latent period. What is more, this model accounts for endogenous reactivation, exogenous reinfection, and treatment of tuberculosis. The model qualitative properties and the basic reproduction number were analyzed. The primary goal of the study was to recover the important dynamic parameters of tuberculosis. Our understanding of these complex processes leverages the efficacy of efforts for controlling the disease, forecasting future dynamics, and applying further appropriate strategies to prevent its spread.The calibration itself was carried out via minimization of a quadratic cost functional. Computational simulations demonstrated that the algorithm is capable of working with noisy real data. Full article
(This article belongs to the Special Issue Recent Developments on Mathematical Models of Deadly Disease)
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26 pages, 1158 KiB  
Article
Study Models of COVID-19 in Discrete-Time and Fractional-Order
by Kamel Djeddi, Tahar Bouali, Ahmed H. Msmali, Abdullah Ali H. Ahmadini and Ali N. A. Koam
Fractal Fract. 2023, 7(6), 446; https://doi.org/10.3390/fractalfract7060446 - 31 May 2023
Cited by 1 | Viewed by 969
Abstract
The novel coronavirus disease (SARS-CoV-2) has caused many infections and deaths throughout the world; the spread of the coronavirus pandemic is still ongoing and continues to affect healthcare systems and economies of countries worldwide. Mathematical models are used in many applications for infectious [...] Read more.
The novel coronavirus disease (SARS-CoV-2) has caused many infections and deaths throughout the world; the spread of the coronavirus pandemic is still ongoing and continues to affect healthcare systems and economies of countries worldwide. Mathematical models are used in many applications for infectious diseases, including forecasting outbreaks and designing containment strategies. In this paper, we study two types of SIR and SEIR models for the coronavirus. This study focuses on the discrete-time and fractional-order of these models; we study the stability of the fixed points and orbits using the Jacobian matrix and the eigenvalues and eigenvectors of each case; moreover, we estimate the parameters of the two systems in fractional order. We present a statistical study of the coronavirus model in two countries: Saudi Arabia, which has successfully recovered from the SARS-CoV-2 pandemic, and China, where the number of infections remains significantly high. Full article
(This article belongs to the Special Issue Recent Developments on Mathematical Models of Deadly Disease)
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20 pages, 2902 KiB  
Article
Investigation of Fractional Order Dynamics of Tuberculosis under Caputo Operator
by Ihsan Ullah, Saeed Ahmad, Muhammad Arfan and Manuel De la Sen
Fractal Fract. 2023, 7(4), 300; https://doi.org/10.3390/fractalfract7040300 - 29 Mar 2023
Cited by 2 | Viewed by 861
Abstract
In this article, a new deterministic disease system is constructed to study the influence of treatment adherence as well as awareness on the spread of tuberculosis (TB). The suggested model is composed of six various classes, whose dynamics are discussed in the sense [...] Read more.
In this article, a new deterministic disease system is constructed to study the influence of treatment adherence as well as awareness on the spread of tuberculosis (TB). The suggested model is composed of six various classes, whose dynamics are discussed in the sense of the Caputo fractional operator. Firstly the model existence of a solution along with a unique solution is checked to determine whether the system has a solution or not. The stability of a solution is also important, so we use the Ulam–Hyers concept of stability. The approximate solution analysis is checked by the technique of Laplace transformation using the Adomian decomposition concept. Such a solution is in series form which is decomposed into smaller terms and the next term is obtained from the previous one. The numerical simulation is established for the obtained schemes using different fractional orders along with a comparison of classical derivatives. Such an analysis will be helpful for testing more dynamics instead of only one type of integer order discussion. Full article
(This article belongs to the Special Issue Recent Developments on Mathematical Models of Deadly Disease)
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20 pages, 4393 KiB  
Article
Fuzzy Analysis of Artificial Drug Transmission Model with Optimal Control
by B. S. N. Murthy, José Luis Díaz Palencia, V. Madhusudanan, M. N. Srinivas, Nadia Gul and Anwar Zeb
Fractal Fract. 2023, 7(1), 10; https://doi.org/10.3390/fractalfract7010010 - 23 Dec 2022
Viewed by 1129
Abstract
This article presents an artificial drug abusers system consolidating the impact of treatment with psychological and physiological addicts under fuzzy parameters. In the fuzzy model, all of the parameters are considered to be triangular fuzzy numbers to represent the uncertainty that pervaded the [...] Read more.
This article presents an artificial drug abusers system consolidating the impact of treatment with psychological and physiological addicts under fuzzy parameters. In the fuzzy model, all of the parameters are considered to be triangular fuzzy numbers to represent the uncertainty that pervaded the dynamics. To handle the arrangements while avoiding problems, the fuzzy model is turned into a defuzzified model using the utility function method. The fuzzy model’s positivity and boundedness are carefully explored, and an equilibrium analysis is also completed. Both the drug-addict equilibrium and the drug-free equilibrium have established stability analyses. This article explains fuzzy optimum control using Pontryagin’s maximum principle. Finally, it is shown that the treatment alongside counselling and conducting awareness programs is more fruitful and drug-related controlling is more viable in the fuzzy nature. Likewise, we plot the 3D associations with fuzzy parameters which show the inventiveness and appropriateness of the results. Full article
(This article belongs to the Special Issue Recent Developments on Mathematical Models of Deadly Disease)
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