{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T12:46:30Z","timestamp":1763037990076,"version":"3.41.2"},"reference-count":45,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T00:00:00Z","timestamp":1715212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats:p>This research introduces a sophisticated mathematical model for understanding the transmission dynamics of COVID-19, incorporating both integer and fractional derivatives. The model undergoes a rigorous analysis, examining equilibrium points, the reproduction number, and feasibility. The application of fixed point theory establishes the existence of a unique solution, demonstrating stability in the model. To derive approximate solutions, the generalized Adams-Bashforth-Moulton method is employed, further enhancing the study's analytical depth. Through a numerical simulation based on Thailand's data, the research delves into the intricacies of COVID-19 transmission, encompassing thorough data analysis and parameter estimation. The study advocates for a holistic approach, recommending a combined strategy of precautionary measures and home remedies, showcasing their substantial impact on pandemic mitigation. This comprehensive investigation significantly contributes to the broader understanding and effective management of the COVID-19 crisis, providing valuable insights for shaping public health strategies and guiding individual actions.<\/jats:p>","DOI":"10.3389\/fams.2024.1374721","type":"journal-article","created":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T05:09:08Z","timestamp":1715231348000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Understanding COVID-19 propagation: a comprehensive mathematical model with Caputo fractional derivatives for Thailand"],"prefix":"10.3389","volume":"10","author":[{"given":"Shamil","family":"E","sequence":"first","affiliation":[]},{"given":"Sayooj Aby","family":"Jose","sequence":"additional","affiliation":[]},{"given":"Hasan S.","family":"Panigoro","sequence":"additional","affiliation":[]},{"given":"Anuwat","family":"Jirawattanapanit","sequence":"additional","affiliation":[]},{"given":"Benjamin I.","family":"Omede","sequence":"additional","affiliation":[]},{"given":"Zakaria","family":"Yaagoub","sequence":"additional","affiliation":[]}],"member":"1965","published-online":{"date-parts":[[2024,5,9]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"104714","DOI":"10.1016\/j.bspc.2023.104714","article-title":"Mathematical modeling of chickenpox in Phuket: efficacy of precautionary measures and bifurcation analysis","volume":"84","author":"Jose","year":"2023","journal-title":"Biomed Signal Proc Control"},{"key":"B2","doi-asserted-by":"publisher","first-page":"4879","DOI":"10.1007\/s11071-022-08063-5","article-title":"Mathematical modeling on co-infection: transmission dynamics of Zika virus and Dengue fever","volume":"111","author":"Jose","year":"2023","journal-title":"Nonlinear Dyn"},{"key":"B3","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission","volume":"180","author":"Van den Driessche","year":"2002","journal-title":"Math Biosci"},{"key":"B4","doi-asserted-by":"publisher","first-page":"845","DOI":"10.3390\/sym15040845","article-title":"A fractional-order density-dependent mathematical model to find the better strain of wolbachia","volume":"15","author":"Joseph","year":"2023","journal-title":"Symmetry"},{"key":"B5","doi-asserted-by":"publisher","first-page":"5060","DOI":"10.1002\/mma.8818","article-title":"Computational dynamics of a fractional order substance addictions transfer model with Atangana-Baleanu-Caputo derivative","volume":"46","author":"Jose","year":"2023","journal-title":"Math Methods Appl Sci"},{"key":"B6","doi-asserted-by":"publisher","first-page":"2250059","DOI":"10.1142\/S1793524522500590","article-title":"Modeling and analysis of SEIRS epidemic models using homotopy perturbation method: A special outlook to 2019-nCoV in India","volume":"15","author":"Thomas","year":"2022","journal-title":"Int J Biomathem"},{"key":"B7","doi-asserted-by":"publisher","first-page":"842","DOI":"10.1002\/oca.2856","article-title":"Stability analysis and comparative study on different eco-epidemiological models: stage structure for prey and predator concerning impulsive control","volume":"43","author":"Jose","year":"2022","journal-title":"Opt Control Applic Methods"},{"key":"B8","doi-asserted-by":"publisher","first-page":"4140","DOI":"10.1002\/mma.7859","article-title":"Impact of strong determination and awareness on substance addictions: a mathematical modeling approach","volume":"45","author":"Jose","year":"2022","journal-title":"Math Methods Appl Sci"},{"key":"B9","first-page":"1","article-title":"Numerical analysis of fractional order model of HIV-1 infection of CD4+ T-cells","volume":"5","author":"Haq","year":"2017","journal-title":"Comput Methods Differ Equ"},{"key":"B10","doi-asserted-by":"publisher","first-page":"17","DOI":"10.11121\/ijocta.01.2018.00532","article-title":"Analysis of rubella disease model with non-local and non-singular fractional derivatives","volume":"8","author":"Koca","year":"2018","journal-title":"Int J Optimiz Contr"},{"key":"B11","doi-asserted-by":"publisher","first-page":"189","DOI":"10.21608\/jfca.2016.308382","article-title":"Solution of the fractional epidemic model by L-ADM","volume":"7","author":"Rida","year":"2016","journal-title":"J Fract Calc Appl"},{"key":"B12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-017-1404-y","article-title":"Approximate solutions of a sum-type fractional integro-differential equation by using Chebyshev and Legendre polynomials","volume":"2017","author":"Akbari Kojabad","year":"2017","journal-title":"Adv Differ Equat"},{"key":"B13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-020-2517-2","article-title":"On the existence of solutions for a pointwise defined multi-singular integro-differential equation with integral boundary condition","volume":"2020","author":"Talaee","year":"2020","journal-title":"Adv Differ Equat"},{"key":"B14","doi-asserted-by":"publisher","first-page":"109478","DOI":"10.1016\/j.chaos.2019.109478","article-title":"Monotonically decreasing behavior of measles epidemic well captured by Atangana-Baleanu-Caputo fractional operator under real measles data of Pakistan","volume":"131","author":"Qureshi","year":"2020","journal-title":"Chaos, Solit Fract"},{"key":"B15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1140\/epjp\/i2018-11950-y","article-title":"Cancer treatment model with the Caputo-Fabrizio fractional derivative","volume":"133","author":"Ali Dokuyucu","year":"2018","journal-title":"Eur Phys J Plus"},{"key":"B16","doi-asserted-by":"publisher","first-page":"2118","DOI":"10.3934\/dcdss.2023010","article-title":"Optimization of the fractional-order parameter with the error analysis for human immunodeficiency virus under Caputo operator","volume":"16","author":"Jan","year":"2023","journal-title":"Discr Contin Dyn Syst S"},{"key":"B17","doi-asserted-by":"publisher","first-page":"5937420","DOI":"10.1155\/2022\/5937420","article-title":"Dynamical behaviour and chaotic phenomena of HIV infection through fractional calculus","volume":"2022","author":"Jan","year":"2022","journal-title":"Discr Dyn Nat Soc"},{"key":"B18","doi-asserted-by":"publisher","first-page":"2497","DOI":"10.1140\/epjs\/s11734-023-00926-1","article-title":"Dynamical analysis, infections in plants, and preventive policies utilizing the theory of fractional calculus","volume":"232","author":"Jan","year":"2023","journal-title":"Eur Phys J Special Topics"},{"key":"B19","doi-asserted-by":"publisher","first-page":"2240266","DOI":"10.1142\/S0218348X22402666","article-title":"Mathematical modeling and stability analysis of the dynamics of monkeypox via fractional-calculus","volume":"30","author":"Alharbi","year":"2022","journal-title":"Fractals"},{"key":"B20","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.35378\/gujs.857099","article-title":"Prediction of breast cancer through tolerance-based intuitionistic fuzzy-rough set feature selection and artificial neural network","volume":"34","author":"Lanbaran","year":"2021","journal-title":"Gazi University J Sci"},{"key":"B21","first-page":"49","article-title":"Analyzing a novel coronavirus model (COVID-19) in the sense of Caputo-Fabrizio fractional operator","volume":"20","author":"Dokuyucu","year":"2021","journal-title":"Appl Comput Mathem"},{"key":"B22","doi-asserted-by":"publisher","first-page":"8113760","DOI":"10.1155\/2022\/8113760","article-title":"Chaotic phenomena and oscillations in dynamical behaviour of financial system via fractional calculus","volume":"2022","author":"Shah","year":"2022","journal-title":"Complexity"},{"key":"B23","doi-asserted-by":"publisher","first-page":"105001","DOI":"10.1088\/1572-9494\/ac7e2b","article-title":"Fractional-calculus analysis of human immunodeficiency virus and CD4+ T-cells with control interventions","volume":"74","author":"Jan","year":"2022","journal-title":"Commun Theor Phys"},{"key":"B24","doi-asserted-by":"publisher","first-page":"7893570","DOI":"10.1155\/2022\/7893570","article-title":"Qualitative analysis of the transmission dynamics of dengue with the effect of memory, reinfection, and vaccination","volume":"2022","author":"Tang","year":"2022","journal-title":"Comput Math Methods Med"},{"key":"B25","doi-asserted-by":"publisher","first-page":"361","DOI":"10.3390\/fractalfract7050361","article-title":"In vivo HIV dynamics, modeling the interaction of HIV and immune system via non-integer derivatives","volume":"7","author":"Jan","year":"2023","journal-title":"Fract Fract"},{"key":"B26","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.aej.2023.10.036","article-title":"Fractional perspective evaluation of chikungunya infection with saturated incidence functions","volume":"83","author":"Jan","year":"2023","journal-title":"Alexandr Eng J"},{"key":"B27","doi-asserted-by":"publisher","first-page":"2440012","DOI":"10.1142\/S0218348X24400127","article-title":"Fractional dynamics of chronic lymphocytic leukemia with the effect of chemoimmunotherapy treatment","volume":"15","author":"Jan","year":"2024","journal-title":"Fractals"},{"key":"B28","doi-asserted-by":"publisher","first-page":"106489","DOI":"10.1016\/j.rinp.2023.106489","article-title":"A predator-prey model with additive Allee effect and intraspecific competition on predator involving Atangana-Baleanu-Caputo derivative","volume":"49","author":"Anggriani","year":"2023","journal-title":"Results in Physics"},{"key":"B29","doi-asserted-by":"publisher","first-page":"73","DOI":"10.12785\/pfda\/010201","article-title":"A new definition of fractional derivative without singular kernel","volume":"1","author":"Caputo","year":"2015","journal-title":"Progr Fract Different Applic"},{"key":"B30","doi-asserted-by":"publisher","first-page":"115","DOI":"10.2478\/ijmce-2023-0009","article-title":"Dynamical analysis of a Tumor Growth model under the effect of fractal fractional Caputo-Fabrizio derivative","volume":"1","author":"Singh","year":"2023","journal-title":"Int J Math Comput Eng"},{"key":"B31","doi-asserted-by":"publisher","first-page":"763","DOI":"10.2298\/TSCI160111018A","article-title":"New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model","volume":"20","author":"Atangana","year":"2016","journal-title":"Therm Sci"},{"key":"B32","doi-asserted-by":"publisher","first-page":"396","DOI":"10.11648\/j.acm.20150406.12","article-title":"mathematical model for control and elimination of the transmission dynamics of measles","volume":"4","author":"Edward","year":"2015","journal-title":"Appl Comput Mathem"},{"key":"B33","doi-asserted-by":"publisher","first-page":"398","DOI":"10.3390\/vaccines9040398","article-title":"On a discrete SEIR epidemic model with two-doses delayed feedback vaccination control on the susceptible","volume":"9","author":"De la Sen","year":"2021","journal-title":"Vaccines"},{"key":"B34","doi-asserted-by":"publisher","first-page":"111063","DOI":"10.1016\/j.jtbi.2022.111063","article-title":"Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold","volume":"540","author":"Gomes","year":"2022","journal-title":"J Theor Biol"},{"key":"B35","doi-asserted-by":"publisher","first-page":"110072","DOI":"10.1016\/j.chaos.2020.110072","article-title":"Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia","volume":"139","author":"Annas","year":"2020","journal-title":"Chaos, Solit Fract"},{"key":"B36","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1016\/S1473-3099(21)00143-2","article-title":"Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study","volume":"21","author":"Moore","year":"2021","journal-title":"Lancet Infect Dis"},{"key":"B37","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1080\/10255842.2023.2197542","article-title":"On a two-strain epidemic mathematical model with vaccination","volume":"27","author":"Yaagoub","year":"2024","journal-title":"Comput Methods Biomech Biomed Engin"},{"key":"B38","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1023\/A:1016592219341","article-title":"A predictor-corrector approach for the numerical solution of fractional differential equations","volume":"29","author":"Diethelm","year":"2002","journal-title":"Nonlinear Dyn"},{"key":"B39","doi-asserted-by":"publisher","first-page":"97","DOI":"10.2478\/ijmce-2024-0008","article-title":"Some fractional calculus findings associated with the product of incomplete \u2135-function and Srivastava polynomials","volume":"2","author":"Nishant","year":"2024","journal-title":"Int J Math Comput Eng"},{"key":"B40","doi-asserted-by":"publisher","first-page":"105","DOI":"10.2478\/ijmce-2023-0008","article-title":"Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method","volume":"1","author":"Abdulazeez","year":"2023","journal-title":"Int J Math Comput Eng"},{"key":"B41","unstructured":""},{"key":"B42","unstructured":""},{"key":"B43","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/s40435-022-00982-w","article-title":"Third wave of COVID-19: mathematical model with optimal control strategy for reducing the disease burden in Nigeria","volume":"11","author":"Omede","year":"2023","journal-title":"Int J Dyn Control"},{"key":"B44","doi-asserted-by":"publisher","first-page":"102433","DOI":"10.1016\/j.jaut.2020.102433","article-title":"The epidemiology and pathogenesis of coronavirus disease (COVID-19) outbreak","volume":"109","author":"Rothan","year":"2020","journal-title":"J Autoimmun"},{"key":"B45","doi-asserted-by":"publisher","first-page":"110032","DOI":"10.1016\/j.chaos.2020.110032","article-title":"Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria","volume":"139","author":"Okuonghae","year":"2020","journal-title":"Chaos, Solit Fract"}],"container-title":["Frontiers in Applied Mathematics and Statistics"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2024.1374721\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T05:09:13Z","timestamp":1715231353000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2024.1374721\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,9]]},"references-count":45,"alternative-id":["10.3389\/fams.2024.1374721"],"URL":"https:\/\/doi.org\/10.3389\/fams.2024.1374721","relation":{},"ISSN":["2297-4687"],"issn-type":[{"type":"electronic","value":"2297-4687"}],"subject":[],"published":{"date-parts":[[2024,5,9]]},"article-number":"1374721"}}