{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T20:14:24Z","timestamp":1723580064131},"reference-count":54,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2021,4]]},"abstract":"In this paper, we study two fractional models in the Caputo\u2013Fabrizio sense and Atangana\u2013Baleanu sense, in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered. Using Lyapunov theory, we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model, and the fractional models, whenever the basic reproduction number [Formula: see text] is greater than one. By using fixed point theory, we prove existence, and conditions of the uniqueness of solutions, as well as the stability and convergence of numerical schemes. Numerical simulations for both models, using fractional Euler method and Adams\u2013Bashforth method, respectively, are provided to confirm the effectiveness of used approximation methods for different values of the fractional-order [Formula: see text].<\/jats:p>","DOI":"10.1142\/s1793962321500136","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T05:56:20Z","timestamp":1604296580000},"page":"2150013","source":"Crossref","is-referenced-by-count":30,"title":["A malaria model with Caputo\u2013Fabrizio and Atangana\u2013Baleanu derivatives"],"prefix":"10.1142","volume":"12","author":[{"given":"Hamadjam","family":"Abboubakar","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, University Institute of Technology, University of Ngaound\u00e9r\u00e9, P.O. Box 455, Ngaound\u00e9r\u00e9, Cameroon"}]},{"given":"Pushpendra","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab-151001, India"}]},{"given":"Norodin A.","family":"Rangaig","sequence":"additional","affiliation":[{"name":"Department of Physics, Mindanao State University-Main Campus, Marawi City 9700, Philippines"}]},{"given":"Sachin","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab-151001, India"}]}],"member":"219","published-online":{"date-parts":[[2021,1,5]]},"reference":[{"key":"S1793962321500136BIB002","doi-asserted-by":"publisher","DOI":"10.1186\/1475-2875-13-424"},{"key":"S1793962321500136BIB003","doi-asserted-by":"publisher","DOI":"10.1186\/s12936-015-0587-5"},{"key":"S1793962321500136BIB004","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1999.0839"},{"key":"S1793962321500136BIB005","doi-asserted-by":"publisher","DOI":"10.1093\/beheco\/13.6.816"},{"key":"S1793962321500136BIB006","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1998.0358"},{"key":"S1793962321500136BIB007","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pbio.0030298"},{"key":"S1793962321500136BIB008","doi-asserted-by":"publisher","DOI":"10.1038\/087466a0"},{"key":"S1793962321500136BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s11587-016-0293-9"},{"key":"S1793962321500136BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(88)90076-4"},{"key":"S1793962321500136BIB011","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524515500771"},{"key":"S1793962321500136BIB012","doi-asserted-by":"publisher","DOI":"10.1137\/050638941"},{"key":"S1793962321500136BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.05.016"},{"key":"S1793962321500136BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(00)00169-2"},{"key":"S1793962321500136BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2018.12.043"},{"key":"S1793962321500136BIB016","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2012.0921"},{"key":"S1793962321500136BIB017","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pmed.1000324"},{"key":"S1793962321500136BIB018","doi-asserted-by":"publisher","DOI":"10.1017\/S0031182008000371"},{"key":"S1793962321500136BIB019","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-017-08526-5"},{"key":"S1793962321500136BIB020","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-019-2199-9"},{"issue":"14","key":"S1793962321500136BIB021","first-page":"1","volume":"2","author":"Okyere E.","year":"2016","journal-title":"J. Adv. Math. Comput. Sci."},{"key":"S1793962321500136BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2012.11.017"},{"key":"S1793962321500136BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.109929"},{"key":"S1793962321500136BIB024","volume-title":"Theory and Applications of Fractional Differential Equations","volume":"204","author":"Kilbas Anatoli\u00e4\u0142 Aleksandrovich","year":"2006"},{"key":"S1793962321500136BIB025","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Miller K. S.","year":"1993"},{"key":"S1793962321500136BIB026","volume-title":"The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order","author":"Oldham K.","year":"1974"},{"key":"S1793962321500136BIB027","volume-title":"Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applications","author":"Podlubny I.","year":"1998"},{"key":"S1793962321500136BIB028","volume-title":"Applications of Fractional Calculus in Physics","author":"Rudolf H.","year":"2000"},{"key":"S1793962321500136BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2020.04.015"},{"key":"S1793962321500136BIB030","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.02.007"},{"key":"S1793962321500136BIB031","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2019.03.020"},{"key":"S1793962321500136BIB032","doi-asserted-by":"publisher","DOI":"10.3390\/e21030303"},{"key":"S1793962321500136BIB033","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1016\/j.amc.2011.03.017","volume":"218","author":"Rivero M.","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"S1793962321500136BIB034","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5511"},{"key":"S1793962321500136BIB035","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-020-00400-0"},{"key":"S1793962321500136BIB036","first-page":"144","volume":"46","author":"Ganji R. M.","year":"2020","journal-title":"Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb."},{"key":"S1793962321500136BIB037","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.109736"},{"key":"S1793962321500136BIB038","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2019.109405"},{"key":"S1793962321500136BIB039","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13661-016-0733-1","volume":"2017","author":"Baleanu D.","year":"2017","journal-title":"Bound. Val. Problem."},{"key":"S1793962321500136BIB040","volume-title":"Abstract and Applied Analysis","volume":"2013","author":"Atangana A.","year":"2013"},{"key":"S1793962321500136BIB041","doi-asserted-by":"publisher","DOI":"10.1051\/mmnp\/2018010"},{"key":"S1793962321500136BIB042","doi-asserted-by":"publisher","DOI":"10.1007\/BF00879562"},{"key":"S1793962321500136BIB043","doi-asserted-by":"publisher","DOI":"10.1017\/S002211200400789X"},{"key":"S1793962321500136BIB044","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2006.02.048"},{"key":"S1793962321500136BIB045","doi-asserted-by":"publisher","DOI":"10.1007\/s10773-010-0249-x"},{"key":"S1793962321500136BIB046","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2008.12.012"},{"key":"S1793962321500136BIB047","first-page":"1","volume":"1","author":"Caputo M.","year":"2015","journal-title":"Progr. Fract. Differ. Appl."},{"key":"S1793962321500136BIB048","first-page":"87","volume":"1","author":"Losada J.","year":"2015","journal-title":"Progr. Fract. Differ. Appl."},{"key":"S1793962321500136BIB049","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.06.009"},{"key":"S1793962321500136BIB050","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2012.706673"},{"key":"S1793962321500136BIB051","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970432"},{"key":"S1793962321500136BIB052","doi-asserted-by":"publisher","DOI":"10.3390\/math7020200"},{"key":"S1793962321500136BIB053","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.110224"},{"key":"S1793962321500136BIB054","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0493(1991)119<0702:TTOABM>2.0.CO;2"},{"key":"S1793962321500136BIB055","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.10.020"}],"container-title":["International Journal of Modeling, Simulation, and Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793962321500136","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T09:36:59Z","timestamp":1698313019000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793962321500136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,5]]},"references-count":54,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["10.1142\/S1793962321500136"],"URL":"https:\/\/doi.org\/10.1142\/s1793962321500136","relation":{},"ISSN":["1793-9623","1793-9615"],"issn-type":[{"value":"1793-9623","type":"print"},{"value":"1793-9615","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,5]]}}}