Abstract
Thyroid cancer is the most prevalent endocrine neoplasia in the world. The use of mathematical models on the development of tumors has yielded numerous results in this field and modeling with differential equations is present in many papers on cancer. In order to know the use of mathematical models with differential equations or similar in the study of thyroid cancer, studies since 2006 to date was reviewed. Systems with ordinary or partial differential equations were the means most frequently adopted by the authors. The models deal with tumor growth, effective half-life of radioiodine applied after thyroidectomy, the treatment with iodine-131, thyroid volume before thyroidectomy, and others. The variables usually employed in the models includes tumor volume, thyroid volume, amount of iodine, thyroglobulin and thyroxine hormone, radioiodine activity, and physical characteristics such as pressure, density, and displacement of the thyroid molecules. In conclusion, the mathematical models used so far with differential equations approach several aspects of thyroid cancer, including participation in methods of execution or follow-up of treatments. With the development of new models, an increase in the current understanding of the detection, evolution, and treatment of diseases is a step that should be considered.