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Fractal Fract
Special Issues
Novel and Innovative Methods for Fractional-Order Epidemic Model
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Novel and Innovative Methods for Fractional-Order Epidemic Model

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Numerical and Computational Methods".

Deadline for manuscript submissions: closed (15 November 2023) | Viewed by 3648

Special Issue Editors

Dr. Anwarud Din

E-Mail Website
Guest Editor
Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
Interests: fractal fractional-based epidemic model; applied mathematics; probability analysis; stochastic modeling
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yongjin Li

E-Mail Website
Guest Editor
Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
Interests: functional analysis; functional differential equations; ordinary differential equation; fuzzy logic
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The field of mathematical modeling has witnessed significant advancements in recent years, particularly in the realm of fractional calculus. Fractional calculus, despite its long-standing history, has seen a resurgence in interest due to its wide-ranging applications across diverse areas, particularly in modeling epidemic diseases. The use of fractional-order epidemic models offers a novel and innovative approach to understanding the complex dynamics of disease spread. These models incorporate long-term memory effects and spatial heterogeneity, providing a more realistic representation of real-world scenarios than traditional integer-order models. They are powerful tools in our theoretical arsenal for tackling pressing public health problems.

In this Special Issue, we invite researchers from across the globe to contribute their innovative work in the field of fractional-order epidemic modeling. We are particularly interested in studies that explore and apply novel methods, develop new theoretical insights, or significantly advance our understanding of epidemic dynamics using fractional calculus. We invite novel theoretical results involving integral inequalities in the context of fractional-order epidemic models.

We look forward to your contributions in pushing the boundaries of our understanding of epidemic dynamics using fractional calculus. Topics of interest include, but are not limited to:

  • development and analysis of fractional-order epidemic models
  • utilization of fractional integral and differential operators in modeling disease spread
  • novel theoretical results involving integral inequalities in the context of fractional-order epidemic models
  • the application of fractional optimal control theory
  • theoretical, computational, and realistic nature of infectious disease models
  • review of effect of new fractal differential and integral operators for modeling infectious diseases
  • modeling diseases with fuzzy differential equations
  • stochastic fractional-order epidemic models.

Dr. Anwarud Din
Prof. Dr. Yongjin Li
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

  • differential equations
  • stochastic differential equations
  • fractional differential equations
  • deterministic and stochastic models of infectious diseases
  • fractional models of infectious diseases

Published Papers (3 papers)

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Research

15 pages, 3262 KiB  
Article
Dynamics and Event-Triggered Impulsive Control of a Fractional-Order Epidemic Model with Time Delay
by Na Liu, Jia Wang, Qixun Lan and Wei Deng
Fractal Fract. 2024, 8(1), 22; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract8010022 - 27 Dec 2023
Viewed by 1027
Abstract
Due to the lack of timely protection measures against infectious diseases, or based on the particularity of the transmission of some infectious diseases and the time-varying connections between people, the transmission dynamics of infectious diseases in the information society are becoming more and [...] Read more.
Due to the lack of timely protection measures against infectious diseases, or based on the particularity of the transmission of some infectious diseases and the time-varying connections between people, the transmission dynamics of infectious diseases in the information society are becoming more and more complex and changeable. A fractional-order epidemic mathematical model with network weighting and latency is proposed in this paper, and the stability near the disease-free equilibrium point and endemic equilibrium point are discussed separately. Subsequently, an event-triggered impulsive control strategy based on an infection rate threshold is put forward. By selecting the appropriate control gain, the Zeno phenomenon can be eliminated on the premise of ensuring the stability of the control error system. Finally, the theoretical results were validated numerically and some conclusions are presented. These findings contribute to future research on the limited-time event-triggered impulsive control of infectious diseases. Full article
(This article belongs to the Special Issue Novel and Innovative Methods for Fractional-Order Epidemic Model)
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17 pages, 1139 KiB  
Article
Dynamical Analysis of Rubella Disease Model in the Context of Fractional Piecewise Derivative: Simulations with Real Statistical Data
by Badr Saad T. Alkahtani
Fractal Fract. 2023, 7(10), 746; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract7100746 - 10 Oct 2023
Cited by 1 | Viewed by 931
Abstract
Rubella is a viral disease that can lead to severe health complications, especially in pregnant women and their unborn babies. Understanding the dynamics of the Rubella disease model is crucial for developing effective strategies to control its spread. This paper introduces a major [...] Read more.
Rubella is a viral disease that can lead to severe health complications, especially in pregnant women and their unborn babies. Understanding the dynamics of the Rubella disease model is crucial for developing effective strategies to control its spread. This paper introduces a major innovation by employing a novel piecewise approach that incorporates two different kernels. This innovative approach significantly enhances the accuracy of modeling Rubella disease dynamics. In the first interval, the Caputo operator is employed to address initial conditions, while the Atangana–Baleanu derivative is utilized in the second interval to account for anomalous diffusion processes. A thorough theoretical analysis of the piecewise derivative for the problem is provided, discussing mathematical properties, stability, and convergence. To solve the proposed problem effectively, the piecewise numerical Newton polynomial technique is employed and the numerical scheme for both kernels is established. Through extensive numerical simulations with various fractional orders, the paper demonstrates the approach’s effectiveness and flexibility in modeling the spread of the Rubella virus. Furthermore, to validate the findings, the simulated results are compared with real data obtained from Rubella outbreaks in Uganda and Tanzania, confirming the practical relevance and accuracy of this innovative model. Full article
(This article belongs to the Special Issue Novel and Innovative Methods for Fractional-Order Epidemic Model)
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21 pages, 1285 KiB  
Article
Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of Vaccination
by Andrew Omame, Ifeoma P. Onyenegecha, Aeshah A. Raezah and Fathalla A. Rihan
Fractal Fract. 2023, 7(7), 544; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract7070544 - 14 Jul 2023
Cited by 3 | Viewed by 1126
Abstract
The modeling of biological processes has increasingly been based on fractional calculus. In this paper, a novel fractional-order model is used to investigate the epidemiological impact of vaccination measures on the co-dynamics of viral hepatitis B and COVID-19. To investigate the existence and [...] Read more.
The modeling of biological processes has increasingly been based on fractional calculus. In this paper, a novel fractional-order model is used to investigate the epidemiological impact of vaccination measures on the co-dynamics of viral hepatitis B and COVID-19. To investigate the existence and stability of the new model, we use some fixed point theory results. The COVID-19 and viral hepatitis B thresholds are estimated using the model fitting. The vaccine parameters are plotted against transmission coefficients. The effect of non-integer derivatives on the solution paths for each epidemiological state and the trajectory diagram for infected classes are also examined numerically. An infection-free steady state and an infection-present equilibrium are achieved when R0<1 and R0>1, respectively. Similarly, phase portraits confirm the behaviour of the infected components, showing that, regardless of the order of the fractional derivative, the trajectories of the disease classes always converge toward infection-free steady states over time, no matter what initial conditions are assumed for the diseases. The model has been verified using real observations. Full article
(This article belongs to the Special Issue Novel and Innovative Methods for Fractional-Order Epidemic Model)
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