Stability analysis of a fractional model for the transmission of the cochineal

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dc.citation.epage386
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage379
dc.contributor.affiliationЛабораторія аналізу моделювання та симуляції, Касабланка
dc.contributor.affiliationЛабораторія математики та застосунків, ENS, Касабланка
dc.contributor.affiliationLaboratory of Analysis Modeling and Simulation, Casablanca
dc.contributor.affiliationLaboratory of Mathematics and Applications, ENS, Casablanca
dc.contributor.authorЕль Баз, О.
dc.contributor.authorАйт Ічоу, М.
dc.contributor.authorЛаарабі, Х.
dc.contributor.authorРачік, М.
dc.contributor.authorEl Baz, O.
dc.contributor.authorAit Ichou, M.
dc.contributor.authorLaarabi, H.
dc.contributor.authorRachik, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T10:28:07Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractЛускокрилі — це паразитичні комахи, які уражують багато кімнатних і вуличних рослин, включаючи кактуси та сукуленти. Ці комахи є одними з частих причин захворювань кактусів: вони витривалі, розмножуються за рекордно короткий час і можуть бути згубними для цих рослин, хоча вони і вважаються стійкими. Борошнисті червці живляться соком рослин, висушуючи і знебарвлюючи іх. У цьому дослідженні пропонується та досліджується дробова модель передачі кошенілі. Спершу доводиться додатність і обмеженість розв’язків, щоб переконатися в коректності запропонованої моделі. Встановлюється локальна стійкість рівноваги без захворювання та рівноваги хронічної інфекції. Для підтвердження наших теоретичних результатів подано чисельне моделювання.
dc.description.abstractScale insects are parasitic insects that attack many indoor and outdoor plants, including cacti and succulents. These insects are among the frequent causes of diseases in cacti: for the reason that they are tough, multiply in record time and could be destructive to these plants, although they are considered resistant. Mealybugs feed on the sap of plants, drying them out and discoloring them. In this research, we propose and investigate a fractional model for the transmission of the Cochineal. In the first place, we prove the positivity and boundedness of solutions in order to ensure the well-posedness of the proposed model. The local stability of the disease-free equilibrium and the chronic infection equilibrium is established. Numerical simulations are presented in order to validate our theoretical results.
dc.format.extent379-386
dc.format.pages8
dc.identifier.citationStability analysis of a fractional model for the transmission of the cochineal / O. El Baz, M. Ait Ichou, H. Laarabi, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 379–386.
dc.identifier.citationenStability analysis of a fractional model for the transmission of the cochineal / O. El Baz, M. Ait Ichou, H. Laarabi, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 379–386.
dc.identifier.doi10.23939/mmc2023.02.379
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63400
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 2 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 2 (10), 2023
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dc.relation.references[17] Deng W., Li C., L¨u J. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynamics. 48, 409–416 (2007).
dc.relation.references[18] Delavari H., Baleanu D., Sadati J. Stability analysis of Caputo fractional-order nonlinear systems revisited. Nonlinear Dynamics. 67, 2433–2439 (2012).
dc.relation.references[19] Matouk A. E. Stability conditions, hyperchaos and control in a novel fractional order hyperchaotic system. Physics Letters A. 373 (25), 2166–2173 (2009).
dc.relation.references[20] Zhang R., Liu Y. A new Barbalat’s lemma and Lyapunov stability theorem for fractional order systems. 2017 29th Chinese Control and Decision Conference (CCDC). 3676–3681 (2017).
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dc.relation.referencesen[3] Du M., Wang Z., Hu H. Measuring memory with the order of fractional derivative. Scientific Reports. 3,3431 (2013).
dc.relation.referencesen[4] Ait Ichou M., Bachraoui M., Hattaf K., Yousfi N. Dynamics of a fractional optimal control HBV infection model withcapsids and CTL immune response. Mathematical Modeling and Computing. 10 (1), 239–244 (2023).
dc.relation.referencesen[5] Khajji B., Boujallal L., Elhia M., Balatif O., Rachik M. A fractional-order model for drinking alcohol behaviour leading toroad accidents and violence. Mathematical Modeling and Computing. 9 (3), 501–518 (2022).
dc.relation.referencesen[6] Bounkaicha C., Allali K., Tabit Y., Danane J. Global dynamic of spatio-temporal fractional order SEIR model. Mathematical Modeling and Computing. 10 (2), 299–310 (2023).
dc.relation.referencesen[7] Fadugba S. E., Ali F., Abubakar A. B. Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order. Mathematical Modeling and Computing. 8 (3), 537–548 (2021).
dc.relation.referencesen[8] Pawar D. D., Patil W. D., Raut D. K. Fractional-order mathematical model for analysing impactofquarantine on transmission of COVID-19 in India. Mathematical Modeling and Computing. 8 (2), 253–266 (2021).
dc.relation.referencesen[9] Elkaf M., Allali K. Fractional derivative model for tumor cells and immune systemcompetition. Mathematical Modeling and Computing. 10 (2), 288–298 (2023).
dc.relation.referencesen[10] Diethelm K. A fractional calculus based model for the simulation of an outbreak of dengue fever. Nonlinear Dynamics. 71, 613–619 (2013).
dc.relation.referencesen[11] Toubeish K. H. Simulation num´erique par les ondelettes des mod`eles fractionnaires en ´epid´emiologie. Th`eses de doctorat (2018).
dc.relation.referencesen[12] Petr´aˇs I. Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Springer–Verlag, Berlin, Heidelberg (2011).
dc.relation.referencesen[13] Diethelm K. The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Springer Berlin, Heidelberg (2010).
dc.relation.referencesen[14] Odibat Z. M., Shawagfeh N. T. Generalized Taylor’s formula. Applied Mathematics and Computation. 186 (1), 286–293 (2007).
dc.relation.referencesen[15] Li H.-L., Zhang L., Hu C., Jiang Y.-L., Teng Z. Dynamical analysis of a fractional-order predator-prey model incorporating a prey refuge. Journal of Applied Mathematics and Computing. 54, 435–449 (2017).
dc.relation.referencesen[16] Cong N. D., Tuan H. T. Existence, uniqueness, and exponential boundedness of global solutions to delay fractional differential equations. Mediterranean Journal of Mathematics. 14, 193 (2017).
dc.relation.referencesen[17] Deng W., Li C., L¨u J. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynamics. 48, 409–416 (2007).
dc.relation.referencesen[18] Delavari H., Baleanu D., Sadati J. Stability analysis of Caputo fractional-order nonlinear systems revisited. Nonlinear Dynamics. 67, 2433–2439 (2012).
dc.relation.referencesen[19] Matouk A. E. Stability conditions, hyperchaos and control in a novel fractional order hyperchaotic system. Physics Letters A. 373 (25), 2166–2173 (2009).
dc.relation.referencesen[20] Zhang R., Liu Y. A new Barbalat’s lemma and Lyapunov stability theorem for fractional order systems. 2017 29th Chinese Control and Decision Conference (CCDC). 3676–3681 (2017).
dc.relation.urihttps://www.cotemaison.fr/plantes-fleurs/cochenille-lutter-contre-ce-nuisible_28730.html#:~:text=Qu’est\%2Dce\%20que\%20la,des\%20tas\%20cotonneux\%20et\%20blanch\%C3\%A2tres
dc.relation.urihttps://www.agri-mag.com/2017/06/cactus-cochenille-et-lutte-biologique/#:~:text=Le\%20cactus\%20est\%20pr\%C3\%A9sent\%20dans,\%C3\%A9cosyst\%C3\%A8mes\%20\%C3\%A0\%20travers\%20le\%20monde.&text=Le\%20cactus\%20est\%20pr\%C3\%A9sent\%20au,des\%20maisons\%20et\%20des\%20douars
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectдробові диференціальні рівняння
dc.subjectкошеніль
dc.subjectдробова похідна Капуто
dc.subjectмодель епідемії SIRC
dc.subjectлокальна стійкість
dc.subjectчисельне моделювання
dc.subjectfractional differential equations
dc.subjectcochineal
dc.subjectCaputo fractional derivative
dc.subjectSIRC epidemic model
dc.subjectlocal stability
dc.subjectnumerical simulations
dc.titleStability analysis of a fractional model for the transmission of the cochineal
dc.title.alternativeАналіз стійкості дробової моделі передачі кошенілі
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 2