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Tropical Medicine
Eveline M. Bunge et al.
PLoS Neglected Tropical Diseases
(2022)
Article
Mathematics, Interdisciplinary Applications
Anwarud Din et al.
Summary: This paper investigates a newly constructed system of equations for Hepatitis B disease using the concept of fractional order derivative. By applying well-known results of fixed point theory, the stability and qualitative analysis of the candidate solution are obtained. The results show that LADM is an efficient method for solving nonlinear problems.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Infectious Diseases
Najmul Haider et al.
Summary: The study discusses the research gaps in the epidemiology of Monkeypox virus (MPX) in endemic countries and proposes hypotheses for the recent increase in MPX cases in West Africa, suggesting a possible explanation for the ongoing epidemic in Europe, America, and Australia. The authors highlight the epidemic potential of MPX in humans and emphasize the need for a better understanding of the burden of MPX in West and Central Africa, as well as the unknown diversity and extent of the animal reservoir. They hypothesize that increased human-rodent interactions and a larger immune-naive population may have contributed to the recent surge in MPX cases. The study emphasizes the importance of national, regional, and international collaborations to address the research gaps related to MPX outbreaks.
INTERNATIONAL JOURNAL OF INFECTIOUS DISEASES
(2022)
Article
Engineering, Multidisciplinary
P. Veeresha et al.
Summary: This study analyzed the susceptible-infected-recovered (SIR) epidemic model of childhood disease using the q-homotopy analysis transform method (q-HATM), presenting two distinct explanatory cases and demonstrating simulations for different order values. The research illustrates the significant role of both derivatives and techniques in the analysis, revealing the behavior of diverse mathematical models described with differential equations in human disease.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Multidisciplinary
Andrew Omame et al.
Summary: A new mathematical model for dual variants of COVID-19 and HIV co infection has been presented and analyzed. The impact of different variants and vaccination on virus dynamics was studied using methods including fractional derivatives. Simulation results showed a significant decrease in co-infected populations as vaccination rate increased.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Physics, Multidisciplinary
Mohammad Izadi et al.
Summary: This paper aims to develop accurate novel collocation techniques for solving a fractional fractional-order Lotka-Volterra predator-prey model. The study introduces Morgan-Voyce polynomials and two new techniques, demonstrating their high accuracy and feasibility through experiments and comparisons.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Mathematics
Ndolane Sene
Summary: This paper introduces a modified chaotic system under the fractional operator with singularity, focusing on the influence of parameters and fractional order. The study uses bifurcation diagrams, Lyapunov exponents, and numerical schemes to analyze the chaotic behaviors and stability of the model's equilibrium points, proposing an adaptive control to correct instability. Initial conditions are found to significantly impact the system's behavior, with coexisting attractors illustrating this influence.
JOURNAL OF MATHEMATICS
(2021)
Article
Engineering, Multidisciplinary
Isa Abdullahi Baba et al.
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
Harendra Singh et al.
Summary: The study examines a non-integer order smoking model using an iterative scheme, discussing the stability of the model and the efficiency of the iterative scheme used. The proposed technique is found to have high accuracy and low computational cost, with figures showing the fractional time behavior of the solution.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Materials Science, Multidisciplinary
Harendra Singh et al.
Summary: The study aims to investigate the dynamics of a fractional-order Covid-19 model using an efficient computational method based on domain discretization and memory principle. The proposed method demonstrates stability and effectiveness in reducing computational cost for long-time behavior. Numerical results support the efficiency of the method with low computational cost and graphical simulation.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Abderrazak Nabti et al.
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
Mathematics, Applied
Weiqiu Pan et al.
Summary: This paper studies the fractional-order Ebola system and utilizes the GMMP and MGAM methods to obtain numerical solutions and parameters, finding that the fractional-order model fits the real data better. Additionally, the study investigates fractional-order Ebola systems with different orders.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Harendra Singh
Summary: This paper explores a fractional order model for HIV infection of CD4(+) T-cells with the impact of drug treatment, proposing an iterative scheme based on domain discretization for numerical solution. The scheme shows efficiency and accuracy, validated through comparison with various other numerical methods, and is effective over long time periods. Graphical results depict the behavior of cell densities and the impact of drug therapy.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Sania Qureshi et al.
Summary: A new epidemiological model considering both integer and fractional order operators was developed to study the transmission dynamics of measles. Stability analysis and parameter sensitivity were discussed, with optimization of the fractional order parameter chi. Various simulations were conducted to observe the effects of parameters on the dynamics of the epidemic.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Ali Akgul et al.
Summary: This article analyzes the fractional order computer epidemic model, extending a classical model using the Atangana-Baleanu fractional differential operator. The regularity condition and existence of solutions in the Banach space are described, with stability at steady states studied using the Jacobian matrix method. The significance of the basic reproduction number on stability analysis is highlighted, with numerical designs and graphical solutions presented through computer simulations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Chernet Tuge Deressa et al.
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
Materials Science, Multidisciplinary
Faiz Muhammad Khan et al.
Summary: A mosquito-borne viral disease (Dengue) is becoming endemic worldwide, causing severe illness and death in various Asian and Latin American countries. Proper management by researchers and medical professionals is essential. The current research aims to prevent/reduce such deadly diseases by addressing mathematical proofs related to existence and stability, utilizing mathematical modeling techniques. The study establishes existence results for the proposed model using the Atangana-Baleanu derivative in Caputo sense (ABC) with fractional order, and also demonstrates deterministic stability. Finally, a new numerical approximation framework for the ABC fractional derivative is used to conduct numerical simulations of the obtained results.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
A. M. R. Elsonbaty et al.
Summary: A discrete fractional SITRS model is presented for simulating the COVID-19 pandemic, with modifications to account for reinfection and unequal infection rates of different population groups. Equilibrium points and stability analysis were discussed, with numerical simulations providing insights into disease spread and parameter influences, along with comparisons with clinical data.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Immunology
Phi-Yen Nguyen et al.
Summary: The monkeypox outbreak in Nigeria from 2017 to 2020 serves as a case study for emerging zoonoses, with declining immunity contributing to the substantial resurgence of the disease. Factors such as population growth, accumulation of unvaccinated cohorts, and decline in smallpox vaccine immunity were identified as key drivers for the renewed outbreak.
EMERGING INFECTIOUS DISEASES
(2021)
Review
Virology
Hermann Meyer et al.
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Mathematics, Interdisciplinary Applications
Piu Samui et al.
CHAOS SOLITONS & FRACTALS
(2020)
Article
Mathematics, Interdisciplinary Applications
Harendra Singh
CHAOS SOLITONS & FRACTALS
(2020)
Review
Virology
Emmanuel Alakunle et al.
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Public, Environmental & Occupational Health
Kara N. Durski et al.
MMWR-MORBIDITY AND MORTALITY WEEKLY REPORT
(2018)
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Review
Virology
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Harendra Singh et al.
CHAOS SOLITONS & FRACTALS
(2017)
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Mathematics, Applied
Thabet Abdeljawad
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2015)
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Mathematics, Applied
Thabet Abdeljawad
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2011)
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Multidisciplinary Sciences
O. Diekmann et al.
JOURNAL OF THE ROYAL SOCIETY INTERFACE
(2010)
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Multidisciplinary Sciences
Anne W. Rimoin et al.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2010)
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Mathematics, Applied
Shatter Momani et al.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2008)
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Mathematics, Applied
K Diethelm et al.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2002)
