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
Mathematics, Interdisciplinary Applications
Hasib Khan, Muhammad Ibrahim, Abdel-Haleem Abdel-Aty, M. Motawi Khashan, Farhat Ali Khan, Aziz Khan
Summary: In this article, the fractional-order COVID-19 model is studied for analytical and computational aspects. The computational study shows that the spread will continue for a long time and recovery reduces the infection rate. The numerical scheme is based on Lagrange's interpolation polynomial and the results are similar to the integer order, demonstrating the applicability of the numerical scheme and effectiveness of the fractional order derivative.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Multidisciplinary
W. E. Raslan
Summary: In this study, the concept of fractional derivatives was utilized to enhance a mathematical model for predicting the transmission of COVID-19 in Egypt. Results showed good agreement with actual data, and highlighted the importance of precautionary measures in influencing model behavior, emphasizing the need for an extended quarantine period.
AIN SHAMS ENGINEERING JOURNAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Hasib Khan, Farooq Ahmad, Osman Tunc, Muhammad Idrees
Summary: In this article, a mathematical model for Covid-19 in the fractal-fractional sense of operators is studied, focusing on the existence of solution, Hyers-Ulam stability, and computational results. The model is qualitatively analyzed by converting it to an integral form and using iterative convergent sequence and fixed point approach. For the computational aspect, a numerical scheme based on Lagrange's interpolation is developed for the fractal-fractional waterborne model, and interesting results are obtained through a case study.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
P. Tamilalagan, B. Krithika, P. Manivannan, S. Karthiga
Summary: Serological studies indicate that there is a non-zero chance of reinfection with SARS-CoV2, despite the presence of suitable antibodies in infected individuals or those who are vaccinated. This article examines the impact of reinfection on the transmission dynamics of COVID-19 using a six-compartment mathematical model. The study considers the waves of COVID-19 in India during the spread of the SARS-CoV-2, delta variant, and Omicron variant, and estimates the parameters of the model corresponding to these situations. The results show that even a finite value of reinfection can significantly affect the number of infected individuals and explain secondary rises in COVID-19 cases.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
P. Chellamani, K. Julietraja, Ammar Alsinai, Hanan Ahmed
Summary: In this paper, a novel coronavirus SIDARTHE epidemic model system is constructed using a Caputo-type fuzzy fractional differential equation. The fuzzy concept is applied to the model for finding the transmission of the coronavirus. The dynamic behavior of COVID-19 is understood by applying numerical results and a combination of fuzzy Laplace and Adomian decomposition transform.
Article
Materials Science, Multidisciplinary
Prashant Pandey, Yu-Ming Chu, J. F. Gomez-Aguilar, Hadi Jahanshahi, Ayman A. Aly
Summary: This paper investigates the fractional epidemic mathematical model and dynamics of COVID-19, analyzing the conditions and parameters for slowing the spread of the coronavirus. The effects of various parameters of the corona virus are studied using the fractional mathematical model with utilization of the Laguerre collocation technique for numerical analysis. Experimental data from Maharashtra state, India are collected to study the dynamics of the novel corona virus.
RESULTS IN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Sadia Arshad, Imran Siddique, Fariha Nawaz, Aqila Shaheen, Hina Khurshid
Summary: To immediately halt the spread of COVID-19, understanding the virus's dynamic behavior and replication level is crucial. Mathematical models can assist in comprehending the primary components involved in the spreading of the disease by integrating them with accessible disease data. Fractional derivative modeling is an essential technique for analyzing real-world issues and making accurate assessments of situations.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Immunology
Isa Abdullahi Baba, Usa Wannasingha Humphries, Fathalla A. A. Rihan
Summary: In this paper, a fractional-order mathematical model in the Caputo sense is proposed to investigate the significance of vaccines in controlling COVID-19. The existence and uniqueness of the solution are proven using the Banach contraction mapping principle. Based on the basic reproduction number, the model reveals two stable equilibrium solutions, which are locally stable under different conditions. Numerical simulations demonstrate the significance of vaccines and the effects of varying the fractional order (alpha). The model is validated by fitting it to four months of real COVID-19 infection data in Thailand, and provides good predictions for a longer period.
Article
Mathematics, Applied
Abderrazak Nabti, Behzad Ghanbari
Summary: This paper discusses interventions for epidemics using a fractional-order SVEIR model, verifying the well-posedness and stability of the model. The stability of disease-free and endemic equilibria are analyzed, and the basic reproduction number index corresponding to the model is investigated for describing global dynamics. Numerical simulations provide evidence for the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Materials Science, Multidisciplinary
Sara Salem Alzaid, Badr Saad T. Alkahtani
Summary: This paper investigates a fractional mathematical model of the novel coronavirus and analyzes the transmission mechanism using fixed point theory and iterative numerical solutions. The study compares compartment quantities and stability under different fractional orders, finding faster stability at lower fractional orders.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Laecio Carvalho de Barros, Michele Martins Lopes, Francielle Santo Pedro, Estevao Esmi, Jose Paulo Carvalho dos Santos, Daniel Eduardo Sanchez
Summary: This study explores how hysteresis phenomenon in biological systems can be treated through fractional calculus using a statistical approach, and analyzes the impact of historical values on the evaluation of fractional operators. Additionally, the efficiency of non-integer order calculus is illustrated through the analysis of the dynamics of the spread of COVID-19 in some countries using the SIR compartmental model with and without memory.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Andrew Omame, Ifeoma P. Onyenegecha, Aeshah A. Raezah, Fathalla A. Rihan
Summary: In this study, 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. The existence and stability of the new model are investigated using fixed point theory results. The COVID-19 and viral hepatitis B thresholds are estimated using the model fitting and the effect of non-integer derivatives on the solution paths and trajectory diagram are examined numerically.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Rahat Zarin, Amir Khan, Abdullahi Yusuf, Sayed Abdel-Khalek, Mustafa Inc
Summary: This article analyzes the fractional COVID-19 epidemic model with a convex incidence rate using the noninteger Caputo derivative. The existence and uniqueness of solutions, as well as local and global stability, are studied. Sensitivity analysis and numerical simulations are also conducted to investigate the impact of parameter changes on the system's dynamical behavior.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
V Padmapriya, M. Kaliyappan
Summary: In this paper, a mathematical model with a Caputo fractional derivative under fuzzy sense is developed for COVID-19 prediction, and numerical results for the USA, India, and Italy are presented. The model is used to estimate future outbreaks, evaluate the effectiveness of preventive measures, and explore control strategies. A comparative study with Ahmadian's fuzzy fractional mathematical model is provided, showing that the proposed model gives a closer forecast to the actual data. The study confirms the efficiency and applicability of the fractional derivative under uncertainty conditions in mathematical epidemiology.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2022)
Article
Mathematics, Applied
Joao P. S. Mauricio de Carvalho, Alexandre A. Rodrigues
Summary: This study analyzed a multiparameter periodically-forced dynamical system inspired by the SIR endemic model, and found that R-0 < 1 is not sufficient to eliminate infectious individuals. The study also proposed a new attractor theory approach.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Mathematics, Applied
Joao P. S. Mauricio de Carvalho, Alexandre A. A. Rodrigues
Summary: This article examines bifurcations of an SIR model where the susceptible population grows logistically and is subject to constant vaccination. The authors explicitly prove that the endemic equilibrium is a codimension two singularity in the parameter space, and demonstrate various bifurcation curves unfolding the singularity. The study provides useful insights on the proportion of vaccinated individuals required to eliminate the disease and the impact of vaccination on the epidemic outcome.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
