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Fractal Fract
Special Issues
Fractional Epidemic and Disease Ecology Models: Theory and Applications
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Fractional Epidemic and Disease Ecology Models: Theory and Applications

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 (31 December 2023) | Viewed by 4283

Special Issue Editors

Dr. Kayode Oshinubi

E-Mail Website
Guest Editor
School of Informatics, Computing, and Cyber Systems, Northern Arizona University, Flagstaff, AZ, USA
Interests: computational epidemiology; biostatistics; disease ecology
Special Issues, Collections and Topics in MDPI journals
Dr. Olumuyiwa James Peter

E-Mail Website
Guest Editor
Department Mathematical and Computer Sciences, University of Medical Sciences, Ondo, Nigeria
Interests: fractional calculus; infectious disease modeling; mathematical biology; mathematical epidemiology

Special Issue Information

Dear Colleagues,

This Special Issue will contain a collection of original research papers and reviews written by academics and researchers on the theory and application of fractional derivatives to emerging epidemics and disease ecology. The world is yet to recover from the exponential spread of the new coronavirus that ravaged the socioeconomic and health infrastructures of many countries, hence the need to suggest accurate models that can properly help public health experts and decision makers to be properly prepared for any future epidemics in order to know how and when to deploy interventions. Fractional derivatives are one of the tools that can help in this research direction which has recently been applied to COVID-19 disease. Additionally, some researchers have proposed new theories to better model infectious diseases in the fractional sense.

We encourage ecologists, public health data researchers, infectious disease modelers, and applied mathematicians to consider publishing their recent work on this topic.

Research areas may include (but are not limited to) the following:

Fractional derivatives applied to epidemiology;

Applications of fractional derivatives and optimal control for emerging infectious diseases; 

Disease ecology: mobility, geographical locations and socioeconomic factors that influence the spread of infectious diseases;

Solution of fractional order deterministic models as a tool for predictive modeling; 

Fractional order infection models with Caputo–Fabrizio operator.

Dr. Kayode Oshinubi
Dr. Olumuyiwa James Peter
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 order
  • epidemics
  • disease ecology
  • predictive modeling
  • Caputo–Fabrizio fractional derivative
  • numerical simulation

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

Published Papers (3 papers)

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Research

15 pages, 6951 KiB  
Article
Numerical Performance of the Fractional Direct Spreading Cholera Disease Model: An Artificial Neural Network Approach
by Saadia Malik
Fractal Fract. 2024, 8(7), 432; https://doi.org/10.3390/fractalfract8070432 - 22 Jul 2024
Viewed by 770
Abstract
The current investigation examines the numerical performance of the fractional-order endemic disease model based on the direct spreading of cholera by applying the neuro-computing Bayesian regularization (BR) neural network process. The purpose is to present the numerical solutions of the fractional-order model, which [...] Read more.
The current investigation examines the numerical performance of the fractional-order endemic disease model based on the direct spreading of cholera by applying the neuro-computing Bayesian regularization (BR) neural network process. The purpose is to present the numerical solutions of the fractional-order model, which provides more precise solutions as compared to the integer-order one. Real values based on the parameters can be obtained and one can achieve better results by utilizing these values. The mathematical form of the fractional direct spreading cholera disease is categorized as susceptible, infected, treatment, and recovered, which represents a nonlinear model. The construction of the dataset is performed through the implicit Runge–Kutta method, which is used to lessen the mean square error by taking 74% of the data for training, while 8% is used for both validation and testing. Twenty-two neurons and the log-sigmoid fitness function in the hidden layer are used in the stochastic neural network process. The optimization of BR is performed in order to solve the direct spreading cholera disease problem. The accuracy of the stochastic process is authenticated through the valuation of the outputs, whereas the negligible calculated absolute error values demonstrate the approach’s correctness. Furthermore, the statistical operator performance establishes the reliability of the proposed scheme. Full article
(This article belongs to the Special Issue Fractional Epidemic and Disease Ecology Models: Theory and Applications)
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21 pages, 608 KiB  
Article
Understanding the Role of Intraspecific Disease Transmission and Quarantine on the Dynamics of Eco-Epidemiological Fractional Order Model
by Hasan S. Panigoro, Nursanti Anggriani and Emli Rahmi
Fractal Fract. 2023, 7(8), 610; https://doi.org/10.3390/fractalfract7080610 - 8 Aug 2023
Cited by 2 | Viewed by 1432
Abstract
An eco-epidemiological model involving competition regarding the predator and quarantine on infected prey is studied. The prey is divided into three compartments, namely susceptible, infected, and quarantine prey, while the predator only attacks the infected prey due to its weak condition caused by [...] Read more.
An eco-epidemiological model involving competition regarding the predator and quarantine on infected prey is studied. The prey is divided into three compartments, namely susceptible, infected, and quarantine prey, while the predator only attacks the infected prey due to its weak condition caused by disease. To include the memory effect, the Caputo fractional derivative is employed. The model is validated by showing the existence, uniqueness, non-negativity, and boundedness of the solution. Three equilibrium points are obtained, namely predator-disease-free, predator-free-endemic, and predator-endemic points, which, respectively, represent the extinction of both predator and disease, the extinction of predator only, and the existence of all compartments. The local and global stability properties are investigated using the Matignon condition and the Lyapunov direct method. The numerical simulations using a predictor–corrector scheme are provided not only to confirm the analytical findings but also to explore more the dynamical behaviors, such as the impact of intraspecific competition, memory effect, and the occurrence of bifurcations. Full article
(This article belongs to the Special Issue Fractional Epidemic and Disease Ecology Models: Theory and Applications)
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23 pages, 2085 KiB  
Article
Dynamics of Age-Structure Smoking Models with Government Intervention Coverage under Fractal-Fractional Order Derivatives
by Emmanuel Addai, Adejimi Adeniji, Olumuyiwa J. Peter, Janet O. Agbaje and Kayode Oshinubi
Fractal Fract. 2023, 7(5), 370; https://doi.org/10.3390/fractalfract7050370 - 29 Apr 2023
Cited by 15 | Viewed by 1445
Abstract
The rising tide of smoking-related diseases has irreparably damaged the health of both young and old people, according to the World Health Organization. This study explores the dynamics of the age-structure smoking model under fractal-fractional (F-F) derivatives with government intervention coverage. We present [...] Read more.
The rising tide of smoking-related diseases has irreparably damaged the health of both young and old people, according to the World Health Organization. This study explores the dynamics of the age-structure smoking model under fractal-fractional (F-F) derivatives with government intervention coverage. We present a new fractal-fractional model for two-age structure smokers in the Caputo–Fabrizio framework to emphasize the potential of this operator. For the existence-uniqueness criterion of the given model, successive iterative sequences are defined with limit points that are the solutions of our proposed age-structure smoking model. We also use the functional technique to demonstrate the proposed model stability under the Ulam–Hyers condition. The two age-structure smoking models are numerically characterized using the Newton polynomial. We observe that in Groups 1 and 2, a change in the fractal-fractional orders has a direct effect on the dynamics of the smoking epidemic. Moreover, testing the inherent effectiveness of government interventions shows a considerable impact on potential, occasional, and temporary smokers when the fractal-fractional order is 0.95. It is the view that this study will contribute to the applicability of the schemes, the rich dynamics of the fractal, and the fractional perspective of future predictions. Full article
(This article belongs to the Special Issue Fractional Epidemic and Disease Ecology Models: Theory and Applications)
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