Deterministic, stochastic and fractional mathematical approaches applied to AMR
In this work, we study the qualitative properties of a simple mathematical model that can be applied to the reversal of antimicrobial resistance. In particular, we analyze the model from three perspectives: ordinary differential equations (ODEs), stochastic differential equations (SDEs) driven by Br...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2025015 |
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| author | Sebastian Builes Jhoana P. Romero-Leiton Leon A. Valencia |
| author_facet | Sebastian Builes Jhoana P. Romero-Leiton Leon A. Valencia |
| author_sort | Sebastian Builes |
| collection | DOAJ |
| description | In this work, we study the qualitative properties of a simple mathematical model that can be applied to the reversal of antimicrobial resistance. In particular, we analyze the model from three perspectives: ordinary differential equations (ODEs), stochastic differential equations (SDEs) driven by Brownian motion, and fractional differential equations (FDEs) with Caputo temporal derivatives. Finally, we address the case of Escherichia coli exposed to colistin using parameters from the literature in order to assess the validity of the qualitative properties of the model. |
| format | Article |
| id | doaj-art-5bba7aadc865462fb663da9c5d3edb5a |
| institution | OA Journals |
| issn | 1551-0018 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5bba7aadc865462fb663da9c5d3edb5a2025-08-20T01:54:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182025-02-0122238941410.3934/mbe.2025015Deterministic, stochastic and fractional mathematical approaches applied to AMRSebastian Builes0Jhoana P. Romero-Leiton1Leon A. Valencia2Institute of Mathematics, University of Antioquia, Medellin, ColombiaDepartment of Mathematical Sciences, University of Puerto Rico at Mayagüez, Puerto Rico, USAInstitute of Mathematics, University of Antioquia, Medellin, ColombiaIn this work, we study the qualitative properties of a simple mathematical model that can be applied to the reversal of antimicrobial resistance. In particular, we analyze the model from three perspectives: ordinary differential equations (ODEs), stochastic differential equations (SDEs) driven by Brownian motion, and fractional differential equations (FDEs) with Caputo temporal derivatives. Finally, we address the case of Escherichia coli exposed to colistin using parameters from the literature in order to assess the validity of the qualitative properties of the model.https://www.aimspress.com/article/doi/10.3934/mbe.2025015ordinary differential equationstochastic differential equationfractional differential equationcaputo derivativebrownian motionstabilityqualitative properties |
| spellingShingle | Sebastian Builes Jhoana P. Romero-Leiton Leon A. Valencia Deterministic, stochastic and fractional mathematical approaches applied to AMR Mathematical Biosciences and Engineering ordinary differential equation stochastic differential equation fractional differential equation caputo derivative brownian motion stability qualitative properties |
| title | Deterministic, stochastic and fractional mathematical approaches applied to AMR |
| title_full | Deterministic, stochastic and fractional mathematical approaches applied to AMR |
| title_fullStr | Deterministic, stochastic and fractional mathematical approaches applied to AMR |
| title_full_unstemmed | Deterministic, stochastic and fractional mathematical approaches applied to AMR |
| title_short | Deterministic, stochastic and fractional mathematical approaches applied to AMR |
| title_sort | deterministic stochastic and fractional mathematical approaches applied to amr |
| topic | ordinary differential equation stochastic differential equation fractional differential equation caputo derivative brownian motion stability qualitative properties |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2025015 |
| work_keys_str_mv | AT sebastianbuiles deterministicstochasticandfractionalmathematicalapproachesappliedtoamr AT jhoanapromeroleiton deterministicstochasticandfractionalmathematicalapproachesappliedtoamr AT leonavalencia deterministicstochasticandfractionalmathematicalapproachesappliedtoamr |