Fractional Dynamics in Epidemic Models: Theoretical Approaches and Applications

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Life Science, Biophysics".

Deadline for manuscript submissions: 15 January 2026 | Viewed by 742

Special Issue Editors


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Guest Editor
Department of Mathematics, Guangzhou University, Guangzhou, China
Interests: fractional calculus; fractals; differential equations; analytical methods
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Mathematics, Sun Yat-sen University, Guangzhou 510000, China
Interests: fractal fractional-based epidemic model; applied mathematics; probability analysis; stochastic modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue explores the intersection of fractional dynamics and epidemiological modeling, focusing on advanced theoretical approaches and their practical applications in understanding and controlling infectious diseases. The integration of stochastic models and non-linear dynamics provides a robust framework for capturing the inherent randomness and complexity of epidemic spread, while fractional calculus offers a powerful tool to model memory effects and long-range dependencies in disease transmission. By treating epidemics as complex systems, this Special Issue highlights the interplay between individual behaviors, environmental factors, and population-level dynamics. Contributions in this collection emphasize the role of dynamical systems theory in analyzing stability, bifurcations, and control strategies for epidemic models.

The Special Issue also addresses real-world challenges, such as parameter estimation, uncertainty quantification, and the impact of interventions, using cutting-edge mathematical and computational techniques. By bridging theoretical advancements with practical applications, this Special Issue aims to provide insights into the design of effective public health policies and foster interdisciplinary collaborations among mathematicians, epidemiologists, and public health experts. Researchers and practitioners will find this collection a valuable resource for understanding the complexities of epidemic dynamics and developing innovative solutions to mitigate future outbreaks.

Dr. Qura Tul Ain
Dr. Anwarud Din
Guest Editors

Manuscript Submission Information

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Keywords

  • fractional calculus
  • fractional stochastic models
  • fractional dynamics
  • fractional-order epidemic models
  • epidemiological modeling
  • fractional models

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Published Papers (1 paper)

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Research

18 pages, 1319 KiB  
Article
The Influence of Lévy Noise and Independent Jumps on the Dynamics of a Stochastic COVID-19 Model with Immune Response and Intracellular Transmission
by Yuqin Song, Peijiang Liu and Anwarud Din
Fractal Fract. 2025, 9(5), 306; https://doi.org/10.3390/fractalfract9050306 - 8 May 2025
Viewed by 150
Abstract
The coronavirus (COVID-19) expanded rapidly and affected almost the whole world since December 2019. COVID-19 has an unusual ability to spread quickly through airborne viruses and substances. Taking into account the disease’s natural progression, this study considers that viral spread is unpredictable rather [...] Read more.
The coronavirus (COVID-19) expanded rapidly and affected almost the whole world since December 2019. COVID-19 has an unusual ability to spread quickly through airborne viruses and substances. Taking into account the disease’s natural progression, this study considers that viral spread is unpredictable rather than deterministic. The continuous time Markov chain (CTMC) stochastic model technique has been used to anticipate upcoming states using random variables. The suggested study focuses on a model with five distinct compartments. The first class contains Lévy noise-based infection rates (termed as vulnerable people), while the second class refers to the infectious compartment having similar perturbation incidence as the others. We demonstrate the existence and uniqueness of the positive solution of the model. Subsequently, we define a stochastic threshold as a requisite condition for the extinction and durability of the disease’s mean. By assuming that the threshold value R0D is smaller than one, it is demonstrated that the solution trajectories oscillate around the disease-free state (DFS) of the corresponding deterministic model. The solution curves of the SDE model fluctuate in the neighborhood of the endemic state of the base ODE system, when R0P>1 elucidates the definitive persistence theory of the suggested model. Ultimately, numerical simulations are provided to confirm our theoretical findings. Moreover, the results indicate that stochastic environmental disturbances might influence the propagation of infectious diseases. Significantly, increased noise levels could hinder the transmission of epidemics within the community. Full article
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