{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:12:38Z","timestamp":1760238758793,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,2]],"date-time":"2020-09-02T00:00:00Z","timestamp":1599004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007480","name":"Universidad de Castilla-La Mancha","doi-asserted-by":"publisher","award":["2020-GRIN-29225"],"award-info":[{"award-number":["2020-GRIN-29225"]}],"id":[{"id":"10.13039\/501100007480","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018-097198-B-I00"],"award-info":[{"award-number":["PGC2018-097198-B-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a discrete-time model for Babesiosis disease, given by means of nonstandard finite difference (NSFD) schemes, is first provided and analyzed. Mathematical analyses show that the provided NSFD schemes preserve the essential (qualitative) dynamical properties of the continuous-time model, namely, positivity and boundedness of the solutions, equilibria, and their stability properties. In particular, the global stability of the disease free equilibrium point is proved by using an appropriate Lyapunov function. As a relevant consequence, we get the dynamic consistency of NSFD schemes in relation to the continuous-time model. Numerical simulations are presented to support the validity of the established theoretical results.<\/jats:p>","DOI":"10.3390\/sym12091447","type":"journal-article","created":{"date-parts":[[2020,9,2]],"date-time":"2020-09-02T11:07:14Z","timestamp":1599044834000},"page":"1447","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Nonstandard Finite Difference Schemes for the Study of the Dynamics of the Babesiosis Disease"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6386-7347","authenticated-orcid":false,"given":"Quang A.","family":"Dang","sequence":"first","affiliation":[{"name":"Center for Informatics and Computing, Vietnam Academy of Science and Technology (VAST), 18 Hoang Quoc Viet, Cau Giay, Hanoi 100000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6089-3451","authenticated-orcid":false,"given":"Manh T.","family":"Hoang","sequence":"additional","affiliation":[{"name":"Institute of Information Technology, Vietnam Academy of Science and Technology (VAST), 18 Hoang Quoc Viet, Cau Giay, Hanoi 100000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7586-9091","authenticated-orcid":false,"given":"Deccy Y.","family":"Trejos","sequence":"additional","affiliation":[{"name":"Faculty of Science and Education, Universidad Distrital Francisco Jos\u00e9 de Caldas, Carrera 3 No. 26A - 40, Bogot\u00e1 11021-110231588, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3214-9606","authenticated-orcid":false,"given":"Jose C.","family":"Valverde","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Castilla-La Mancha, Avda. de Espana, s\/n, 02071 Albacete, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,2]]},"reference":[{"key":"ref_1","first-page":"37","article-title":"Epidemiology of bovine babesiosis. 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