Article
Engineering, Mechanical
Lihua Dai, Xianning Liu, Yuming Chen
Summary: This paper proposes and analyzes a fractional-order SIS model with a generalized transmission function and media coverage. The existence, uniqueness, and non-negativeness of solutions are obtained. The basic reproduction number R0 is calculated using the next generation matrix method, serving as a threshold parameter. Numerical simulations demonstrate the main theoretical results and reveal the impact of media coverage on disease transmission.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics
Meghadri Das, Guruprasad Samanta, Manuel De la sen
Summary: The study proposed a fractional-order synthetic drugs transmission model with psychological addicts and psychological treatment. The model's local and global stability, existence and uniqueness criteria, positivity and boundedness of solutions were analyzed, as well as sensitivity of parameters. An optimal control problem controlling psychological addiction was formulated and analyzed with Pontryagin maximum principle, validated by numerical simulations.
Article
Mathematics
Tingting Xue, Xiaolin Fan, Yan Xu
Summary: The article introduces a fractional-order calculus model to describe real-world problems with non-local and memory genetic effects. It presents a fractional hepatitis B epidemic model with a general incidence rate and studies its solutions, equilibrium points, stability, and optimal control. The optimal control strategy includes isolating infected and non-infected individuals, treating patients, and vaccinating susceptible people to minimize the number of hepatitis B patients and ultimately eliminate the virus transmission.
Article
Mathematics, Applied
Beyza Billur Iskender Eroglu, Dilara Yapiskan
Summary: In this article, the fractional optimal control strategy of computer virus propagation in a heterogeneous network is examined. A generalized SLBS model is introduced using the Caputo derivative to model the relations of the computers in the network consistent with power-law. Different control strategies are studied using antivirus programs installed in separate compartments of the model. Stability analysis, calculation of basic reproduction number, and the application of Pontryagin's maximum principle are performed to investigate the optimal control. The numerical solution and plot of comparative results are obtained using the Adams-type predictor-corrector method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Emmanuel Addaia, Lingling Zhangb, Joshua K. K. Asamoahc, John Fiifi Esseld
Summary: This paper presents a nonlinear fractional mathematical model for the smoke epidemic that includes two age groups. The Atangana-Baleanu-Caputo fractional derivative is used to solve the smoke epidemic. The Banach and Krasnoselskii type fixed point theorem is used to determine existence and uniqueness. The model's stability is explored using the Hyers-Ulam form of stability. The behaviour of the smoke epidemic of the 2-age group model is generated using Lagrange interpolation. The numerical simulation shows that the model has potential for both groups, and age-specific interventions can be used to reduce smoking rates in the general population.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Physics, Multidisciplinary
A. El-Mesady, Waleed Adel, A. A. Elsadany, Amr Elsonbaty
Summary: In this study, a novel Caputo fractional order monkeypox epidemic model is used to investigate the spread of the monkeypox virus. The model considers the interaction between human and rodent populations and the effects of control signals established through optimal control strategy. The influence of memory is also examined by varying fractional order parameters in the model. The theoretical findings are verified through numerical experiments, and the optimal control scheme is shown to reduce the infected, quarantined, and exposed categories while increasing the susceptible and recovered categories.
Article
Engineering, Multidisciplinary
Isa Abdullahi Baba, Bashir Ahmad Nasidi
Summary: This research investigates the transmissibility of Covid-19 using a mathematical model, where bats are considered the origin of the virus. The model analyzes the transmission dynamics and equilibrium solutions, obtaining key parameters and conducting global stability analysis. Numerical simulations demonstrate the importance of fractional order differential equations in describing biological systems.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Computer Science, Information Systems
Sara Soulaimani, Abdelilah Kaddar
Summary: In this article, an analysis and optimal control investigation of a fractional order SEIR epidemic model with General Incidence and Vaccination are presented. The utilization of fractional calculus enhances the model's ability to capture real-world complexities by accounting for memory effects and non-local interactions in the disease transmission process. The existence, uniqueness, and stability of equilibrium points are investigated, and the impact of vaccination on the disease dynamics is considered. Additionally, an optimal control strategy is developed to minimize the number of infected individuals by optimizing the vaccination rate.
Article
Mathematics, Applied
Chernet Tuge Deressa, Gemechis File Duressa
Summary: The study on a SEAIR epidemic model with Atangana-Baleanu fractional-order derivative showed that reducing the fractional order can slow down the spread of the epidemic.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Hegagi Mohamed Ali, Ismail Gad Ameen
Summary: In this research, the transmission dynamics of maize streak virus disease in agriculture is studied using fractional calculus. A fractional-order model (FOM) with fractional differential equations within Caputo fractional derivative (CFD) is developed. Mathematical analysis of this FOM is conducted, including the computation of control reproduction number (7z.c), examination of local and global stability, and sensitivity analysis. A fractional optimal control problem (FOCP), with three control efforts for prevention, quarantine, and insecticide chemical, is formulated based on the suggested FOM. The FOCP is studied analytically to derive the fractional necessary optimality conditions (NOCs) using Pontryagin's maximum principle.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yanyan He, Zhen Wang
Summary: This paper develops a fractional model for the transmission dynamics of cholera and shows that the optimal strategy for controlling the disease is a combination of treatment and awareness programs, through numerical simulations and cost-effectiveness analysis.
FRACTAL AND FRACTIONAL
(2022)
Article
Engineering, Multidisciplinary
Waleed Adel, Amr Elsonbaty, A. Aldurayhim, A. El-Mesady
Summary: In this paper, a novel fractional-order monkeypox epidemic model is proposed, which applies fractional-order derivatives in order to achieve more realistic results. The model consists of a 14-dimensional system of fractional-order differential equations, representing the transmission and spread of monkeypox between humans and rodents. The existence, uniqueness, non-negativity, and boundedness of the solution to the model are proven, and the next-generation matrix approach is used to determine the control monkeypox reproduction number and the equilibrium points. The effect of the main parameters and optimal control strategies on the dynamics of the model are investigated.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Computer Science, Interdisciplinary Applications
Shiv Mangal, O. P. Misra, Joydip Dhar
Summary: This paper presents a deterministic fractional-order epidemic model (FOEM) to study the transmission dynamics of HIV and AIDS. The model highlights the role of undetected and unaware HIV-infected individuals in spreading the disease. Control strategies and their impact on disease persistence or elimination are analyzed using actual HIV data from Mexico and India. The results show that the disease will persist in Mexico but eventually die out in India after a long time, based on the derived basic reproduction number R0 alpha and its implications on disease dynamics.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Abiodun Ezekiel Owoyemi, Ibrahim Mohammed Sulaiman, Pushpendra Kumar, Venkatesan Govindaraj, Mustafa Mamat
Summary: This research analyzes the fractional-order model of Covid-19 and demonstrates its effectiveness compared to integer-order dynamics through graph visualization.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Madasamy Vellappandi, Venkatesan Govindaraj
Summary: This paper investigates the fractional optimal control problem with a single delay in the state using the operator theoretic approach. It establishes the existence of an optimal pair for the abstract system by reducing the delay fractional dynamical system into an equivalent operator equation and providing sufficient conditions to the operators. The optimality system for the quadratic cost functional is derived using the Frechet derivative and related to the Hamiltonian system of Pontryagin's minimum principle. The article demonstrates the existence of an optimal pair for the fractional-order delay dynamical system and provides numerical examples to support the theoretical findings.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
