{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T18:14:34Z","timestamp":1778782474439,"version":"3.51.4"},"reference-count":78,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:00:00Z","timestamp":1778716800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"\n Breast cancer treatment optimization is hindered by heterogeneity, resistance development, and differences among individuals. Most of the existing traditional mathematical models generally do not consider memory effects in biological systems. This may somewhat limit their predictive capability. Therefore, this study develops a fractional-order computational framework to capture tumor dynamics, immune responses, resistance mechanisms, and effects of thermal therapy regarding memory effects concerning their significance to treatment predictions. We considered the values of fractional order parameter (\n \n \n \n \n \n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ) which varied from 0.75 to 1.0 across five treatment protocols, and the analysis also included four patient populations. Efficacy was highest (32.26) with Continuous protocols at\n \n \n \n \n \n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = 0.75. Specifically-optimized, patient-specific input yielded context-dependent patterns: Younger patients realized the maximum benefit (32.38) with Continuous therapy at\n \n \n \n \n \n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = 0.80, while compromised patients had an optimum response (32.36) to Adaptive treatment performed at\n \n \n \n \n \n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = 0.75. For older patients, the better result (31.82) was achieved using Continuous protocols at\n \n \n \n \n \n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = 0.93. Parameter sensitivity analyses show that immune cytotoxic killing rate is the most effective parameter. In addition, treatment resistance parameters are among the five most sensitive. While aggregate differences between fractional-order and integer-order models remain small, context-specific improvements witnessed in certain patient-protocol combinations were as much as 3.68%. Fractional-order modeling thus creates a framework for investigating memory effects in cancer treatment, while actual clinical validation must establish whether such theoretical improvements indeed create a discernible increase in predictive accuracy in practice.\n <\/jats:p>","DOI":"10.1371\/journal.pone.0347160","type":"journal-article","created":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T17:37:13Z","timestamp":1778780233000},"page":"e0347160","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimizing breast cancer treatment strategies through fractional-order dynamics: A computational modeling approach"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7855-6892","authenticated-orcid":true,"given":"Irshad Sikandar","family":"Jamadar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krishna","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ambareen","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0942-6621","authenticated-orcid":true,"given":"Sher Afghan","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmad Aziz","family":"Alahmadi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mamdooh","family":"Alwetaishi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liew Tze","family":"Hui","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2026,5,14]]},"reference":[{"issue":"3","key":"pone.0347160.ref001","first-page":"209","article-title":"Global cancer statistics 2020: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries","volume":"71","author":"H Sung","year":"2021","journal-title":"CA: A Cancer Journal for Clinicians"},{"issue":"12","key":"pone.0347160.ref002","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1038\/nrc4029","article-title":"The mathematics of cancer: integrating quantitative models","volume":"15","author":"PM Altrock","year":"2015","journal-title":"Nature Reviews Cancer"},{"issue":"4","key":"pone.0347160.ref003","doi-asserted-by":"crossref","first-page":"041005","DOI":"10.1088\/1478-3975\/ab1a09","article-title":"The 2019 mathematical oncology roadmap","volume":"16","author":"RC Rockne","year":"2019","journal-title":"Physical biology"},{"issue":"30","key":"pone.0347160.ref004","doi-asserted-by":"crossref","first-page":"4934","DOI":"10.2174\/1381612819666131125150434","article-title":"Mathematical modeling of tumor growth and treatment","volume":"20","author":"H Enderling","year":"2014","journal-title":"Current pharmaceutical design"},{"issue":"6348","key":"pone.0347160.ref005","doi-asserted-by":"crossref","DOI":"10.1126\/science.aal2380","article-title":"Epigenetic plasticity and the hallmarks of cancer","volume":"357","author":"WA Flavahan","year":"2017","journal-title":"Science"},{"issue":"11","key":"pone.0347160.ref006","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1038\/nm.3394","article-title":"Microenvironmental regulation of tumor progression and metastasis","volume":"19","author":"DF Quail","year":"2013","journal-title":"Nature Medicine"},{"issue":"6382","key":"pone.0347160.ref007","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1126\/science.aar4060","article-title":"Cancer immunotherapy using checkpoint blockade","volume":"359","author":"A Ribas","year":"2018","journal-title":"Science"},{"key":"pone.0347160.ref008","volume-title":"Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. 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