{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:14:06Z","timestamp":1753884846804,"version":"3.41.2"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"Key Program of the National Nature Science Foundation of China","award":["11831015"],"award-info":[{"award-number":["11831015"]}]},{"DOI":"10.13039\/501100004519","name":"Tian Yuan Mathematical Foundation","doi-asserted-by":"publisher","award":["12126355"],"award-info":[{"award-number":["12126355"]}],"id":[{"id":"10.13039\/501100004519","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004519","name":"Tian Yuan Mathematical Foundation","doi-asserted-by":"publisher","award":["12126363"],"award-info":[{"award-number":["12126363"]}],"id":[{"id":"10.13039\/501100004519","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,1]]},"abstract":"<jats:p> It is of critical importance to comprehend the biological environment and core tumor populations when trying to design successful therapeutic solutions for fighting cancers. In several diseases, G9a has been recognized as a novel epigenetic therapeutic target, and its blockage can shift tumor cells (TCs) toward tumor propagating cells (TPCs). This study combines mathematical modeling based on ordinary differential equations and dynamical analysis to quantitatively and qualitatively understand the interactions among G9a, TCs, and TPCs, denoted as G9a-TC-TPC. We propose four different dynamical systems with the impact of the strong Allee effect, named the Hill\u2013Hill system, Logistic\u2013Logistic system, Hill\u2013Logistic system and Logistic\u2013Hill system, to simulate different biological processes through the Hill functions and the Logistic functions that are often used in the models of biological systems. Based on theoretical analysis of these models, including the positivity, boundedness and stability of equilibria, we find that the Hill\u2013Logistic system can display bistable states that correspond to the wild-type tumors and the aggressive tumors. Consequently, we use bifurcation analysis and numerical simulations to illustrate the complicated dynamical behavior of this system. It has been shown that under a specific therapy that changes the relative apoptotic rate of TCs (G9a suppresses the apoptosis of TCs), which can affect the bistability and instability of the system, the wide-type state can be obtained. We also discover that the relative handling time of TCs and TPCs can cooperatively enhance bistability, whereas the cooperative coefficient of feedback can contribute to all tumor cells moving from high-level monostability to bistable states in a restricted region, then to low-level stable states. These results offer new insights for more precisely understanding epigenetic therapy treatments with G9a. <\/jats:p>","DOI":"10.1142\/s0218127423500062","type":"journal-article","created":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T09:47:44Z","timestamp":1676022464000},"source":"Crossref","is-referenced-by-count":2,"title":["Mathematical Modeling and Dynamical Analysis for Tumor Cells and Tumor Propagating Cells Controlled by G9a Inhibitors"],"prefix":"10.1142","volume":"33","author":[{"given":"Juan","family":"Shen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhihao","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4710-2325","authenticated-orcid":false,"given":"Xuewen","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650504, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5294-0764","authenticated-orcid":false,"given":"Xiufen","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. 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