The incidence of thyroid cancer is rising all over the world, and the papillary subtype (PTC) is the primary factor for this increase. The presence of thyroid tumors is commonly associated with increased levels of cytokines, such as interleukin 6 (IL-6). Considering PTC patients treated with thyroidectomy and radioactive iodine [Formula: see text]I (RAI), we propose an ordinary differential system using four variables: the RAI activity, the number of cancer cells and the serum concentrations of IL-6 and thyroglobulin (Tg). Our objective is to study the efficacy of different therapeutic doses of RAI in the treatment of thyroid cancer. The Allee effect is taken into account when modeling cancer cells growth under the influence of IL-6. From the results obtained, the main factors and conditions correlated with successful treatment, such as the RAI activity used and the tumor response are addressed. The detection of minimal doses of RAI that can cause tumor extinction is performed, though this has also meant longer periods for tumor cell elimination. The critical number of tumor cells due to the Allee effect is analyzed and linked to the immune system or biological factors that can slow the progression of the tumor but are insufficient after thyroid resection surgery.

中文翻译：

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利用等位基因效应治疗甲状腺乳头状癌的数学模型

全世界甲状腺癌的发病率都在上升，而乳头状亚型（PTC）是这一上升的主要因素。甲状腺肿瘤的存在通常与细胞因子水平升高有关，例如白细胞介素 6 (IL-6)。考虑接受甲状腺切除术和放射性碘治疗的PTC患者[公式：见正文]I（RAI），我们提出了一个普通的分类系统，使用四个变量：RAI活性、癌细胞数量和血清IL-6和甲状腺球蛋白浓度（ Tg)。我们的目标是研究不同治疗剂量的 RAI 在治疗甲状腺癌中的疗效。在对受 IL-6 影响的癌细胞生长进行建模时，考虑了 Allee 效应。从获得的结果来看，与成功治疗相关的主要因素和条件，例如使用的 RAI 活性和肿瘤反应得到解决。进行了可导致肿瘤消退的最小剂量 RAI 的检测，尽管这也意味着肿瘤细胞消除的时间更长。分析了由于 Allee 效应导致的肿瘤细胞临界数量，并将其与免疫系统或可以减缓肿瘤进展但在甲状腺切除手术后不足的生物因素相关联。