Exploring the Landscape of Fractional-Order Models in Epidemiology: A Comparative Simulation Study

被引:1
作者
Agarwal, Ritu [1 ]
Airan, Pooja [1 ]
Agarwal, Ravi P. [2 ]
机构
[1] Malaviya Natl Inst Technol, Dept Math, Jaipur 302017, India
[2] Florida Inst Technol, Dept Math & Syst Engn, Melbourne, FL 32901 USA
关键词
epidemics; transmission dynamics; fractional calculus; numerical simulation; mathematical modeling; A-PRIORI PATHOMETRY; GLOBAL STABILITY; NONLINEAR INCIDENCE; SEIR MODEL; DYNAMICAL BEHAVIOR; LYAPUNOV FUNCTIONS; HEPATITIS-B; SIR; INFECTION; DISEASES;
D O I
10.3390/axioms13080545
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many researchers have discussed various types of epidemiological models, including deterministic, stochastic, and fractional order models, for this purpose. This article presents a comprehensive review and comparative study of the transmission dynamics of fractional order in epidemiological modeling. A significant portion of the paper is dedicated to the graphical simulation of these models, providing a visual representation of their behavior and characteristics. The article further embarks on a comparative analysis of fractional-order models with their integer-order counterparts. This comparison sheds light on the nuances and subtleties that differentiate these models, thereby offering valuable insights into their respective strengths and limitations. The paper also explores time delay models, non-linear incidence rate models, and stochastic models, explaining their use and significance in epidemiology. It includes studies and models that focus on the transmission dynamics of diseases using fractional order models, as well as comparisons with integer-order models. The findings from this study contribute to the broader understanding of epidemiological modeling, paving the way for more accurate and effective strategies in disease control and prevention.
引用
收藏
页数:49
相关论文
共 137 条
[1]  
Agarwal R., 2023, Mathematical Methods in Medical and Biological Sciences
[2]  
Agarwal R., 2024, J. Comput. Anal. Appl, V33, P289
[3]  
Agarwal R., 2020, Mathematical Modeling and Soft Computing in Epidemiology, P273
[4]   Numerical and graphical simulation of the non-linear fractional dynamical system of bone mineralization [J].
Agarwal R. ;
Airan P. ;
Sajid M. .
Mathematical Biosciences and Engineering, 2024, 21 (04) :5138-5163
[5]   Numerical and bifurcation analysis of SIQR model [J].
Ahmed, Nauman ;
Raza, Ali ;
Rafiq, Muhammad ;
Ahmadian, Ali ;
Batool, Namra ;
Salahshour, Soheil .
CHAOS SOLITONS & FRACTALS, 2021, 150
[6]   Fractional stochastic sir model [J].
Alkahtani, Badr Saad T. ;
Koca, Ilknur .
RESULTS IN PHYSICS, 2021, 24
[7]  
Allen L.J., 2015, Math. Biosci. Lect. Ser. Stochastics Biol. Syst, V1, P120
[8]  
Allen Linda J S, 2017, Infect Dis Model, V2, P128, DOI 10.1016/j.idm.2017.03.001
[9]  
Almeida R., 2019, Int. J. Dyn. Control, V7, P776, DOI [10.1007/s40435-018-0492-1, DOI 10.1007/S40435-018-0492-1]
[10]   Analysis of a fractional SEIR model with treatment [J].
Almeida, Ricardo .
APPLIED MATHEMATICS LETTERS, 2018, 84 :56-62