{"id":1375,"date":"2020-08-31T20:23:27","date_gmt":"2020-08-31T20:23:27","guid":{"rendered":"https:\/\/lorandparajdi.wordpress.com\/?page_id=1375"},"modified":"2023-07-17T15:57:39","modified_gmt":"2023-07-17T15:57:39","slug":"analysis-of-a-planar-differential-system-arising-from-hematology","status":"publish","type":"page","link":"https:\/\/www.cs.ubbcluj.ro\/~lorand\/analysis-of-a-planar-differential-system-arising-from-hematology\/","title":{"rendered":"Article no.2"},"content":{"rendered":"\n

Analysis of a Planar Differential System Arising from HematologyResearch Paper, June 25, 2018 \/ Lorand Gabriel Parajdi<\/span><\/a><\/p>\n\n\n\n

Published in Studia Universitatis Babe\u015f-Bolyai Mathematica, 63(2), 235\u2013244,<\/em> DOI: <\/a>10.24193\/subbmath.2018.2.07<\/span><\/a>, 2018<\/em>.<\/p>\n\n\n\n

\"\"  The full paper is available on the Studia Universitatis Babe\u015f-Bolyai Mathematica website:<\/span><\/strong><\/a>https:\/\/www.cs.ubbcluj.ro\/~studia-m\/index.php\/journal\/article\/view\/352\/pdf<\/span><\/a><\/p>\n\n\n\n

Authors:<\/mark><\/strong> Lorand Gabriel Parajdi1<\/sup> and Radu Precup1<\/sup> <\/p>\n\n\n\n

<\/a>1 <\/sup>Department of Mathematics, “Babe\u015f\u2013Bolyai” University, Cluj-Napoca, Romania<\/p>\n\n\n\n

Abstract:<\/span><\/strong> A complete analysis of a planar dynamic system arising from hematology is provided to confirm the conclusions of computer simulations. Existence and uniqueness for the Cauchy problem, boundedness of solutions and their asymptotic behavior to infinity are established. Particularly, the global asymptotic stability of a steady state is proved in each of the following cases related to leukemia: normal, chronic and accelerated-acute.<\/p>\n\n\n\n

Subject Classification:<\/span><\/strong> 34A34, 34D23, 93D20<\/p>\n\n\n\n

Keywords<\/strong>:<\/mark> Nonlinear dynamic system; Existence and uniqueness; Continuous dependence on data; Boundedness; Global asymptotic stability; Biomathematical model.<\/p>\n\n\n\n

Cite As:<\/span><\/strong>  L.G. Parajdi and R. Precup, Analysis of a planar differential system arising from hematology, Stud. Univ. Babe\u0219-Bolyai Math. 63(2018), No. 2, 235\u2013244. DOI: 10.24193\/subbmath.2018.2.07<\/p>\n\n\n\n

References:<\/span><\/strong>
1.<\/span><\/strong> Barbu, V., Differential Equations<\/em>, Springer, Cham, 2017<\/strong>. [Book]<\/span><\/a>

2<\/span>.<\/strong> Cucuianu, A., Precup, R., A hypothetical-mathematical model of acute myeloid leukemia pathogenesis,<\/em> Comput. Math. Methods Med., 11(2010<\/strong>), 49-65. [Article]<\/span><\/a>

3.<\/span><\/strong> Dingli, D., Michor, F., Successful therapy must eradicate cancer stem cells,<\/em> Stem Cells, 24(2006<\/strong>), 2603-2610. [Article]<\/span><\/a>

4.<\/span><\/strong> Parajdi, L.G., Modeling the treatment of tumor cells in a solid tumor, J. Nonlinear Sci. Appl., 7(2014<\/strong>), 188-195. [Article]<\/span><\/a>

5.<\/span><\/strong> Parajdi, L.G., Precup, R., Bonci, E.-A., Tomuleasa, C.: A mathematical model of the transition from the normal hematopoiesis to the chronic and acceleration-acute stages in myeloid leukemia<\/em>. Mathematics 8(2020<\/strong>), no. 3, 376. [Article]<\/span><\/a>

6<\/span>.<\/strong> Precup, R., Ordinary Differential Equations,<\/em> De Gruyter, Berlin, 2018<\/strong>. [Book]<\/span><\/a>

7.<\/span><\/strong> Precup, R., Arghirescu, S., Cucuianu, A., \u0218erban, M., Mathematical modeling of cell dynamics after allogeneic bone marrow transplantation,<\/em> Int. J. Biomath., 5(2012<\/strong>), no. 2, Article 1250026, 1-18. [Article]<\/span><\/a>

8<\/span>.<\/strong> Precup, R., \u0218erban, M.., Trif, D., Cucuianu, A., A planning algorithm for correction therapies after allogeneic stem cell transplantation,<\/em> J. Math. Model. Algor., 11(2012<\/strong>), 309-323. [Article]<\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Analysis of a Planar Differential System Arising from HematologyResearch Paper, June 25, 2018 \/ Lorand Gabriel Parajdi Published in Studia Universitatis Babe\u015f-Bolyai Mathematica, 63(2), 235\u2013244, DOI: 10.24193\/subbmath.2018.2.07, 2018.   The full paper is available on the Studia Universitatis Babe\u015f-Bolyai Mathematica website:https:\/\/www.cs.ubbcluj.ro\/~studia-m\/index.php\/journal\/article\/view\/352\/pdf Authors: Lorand Gabriel Parajdi1 and Radu Precup1 1 Department of Mathematics, “Babe\u015f\u2013Bolyai” University, Cluj-Napoca, Romania … Continue reading Article no.2<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.cs.ubbcluj.ro\/~lorand\/wp-json\/wp\/v2\/pages\/1375"}],"collection":[{"href":"https:\/\/www.cs.ubbcluj.ro\/~lorand\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.cs.ubbcluj.ro\/~lorand\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.cs.ubbcluj.ro\/~lorand\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cs.ubbcluj.ro\/~lorand\/wp-json\/wp\/v2\/comments?post=1375"}],"version-history":[{"count":19,"href":"https:\/\/www.cs.ubbcluj.ro\/~lorand\/wp-json\/wp\/v2\/pages\/1375\/revisions"}],"predecessor-version":[{"id":5412,"href":"https:\/\/www.cs.ubbcluj.ro\/~lorand\/wp-json\/wp\/v2\/pages\/1375\/revisions\/5412"}],"wp:attachment":[{"href":"https:\/\/www.cs.ubbcluj.ro\/~lorand\/wp-json\/wp\/v2\/media?parent=1375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}