Title | Mathematical modeling of tumor cells metastasis dynamics |
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Authors | A. B. Goncharova^{1}, E. P. Kolpak^{1}, M. Y. Vil^{1}^{1}St. Petersburg State University |

Annotation | The process of tumor spread through the affected organ is an interference competition of tumor and healthy cells and takes into account the angiogenesis of the tumor. An extension of the constructed model based on compartment modeling, which simulates the ability of malignant tumors to metastasize and form new lesions, is presented. It is assumed that secondary tumors have the same properties as the primary lesion. In the metastasis model, two treatment delivery options are considered: the implementation of continuous continuous treatment and the implementation of discrete drug delivery using repeated or scheduled doses. In both treatment models, it is assumed that drugs are used only to suppress malignant cells, and their side effects are neglected. The results of simulation with metastasis were carried out in the MATLAB SimBiology Model Analyzer application. |

Keywords | cancer, angiogenesis, metastases, treatment model, MATLAB SimBiology, mathematical modeling, compartment model |

Citation | Goncharova A. B., Kolpak E. P., Vil M. Y. ''Mathematical modeling of tumor cells metastasis dynamics'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 39-47. Available at: https://conf.svmo.ru/files/2023/papers/paper05.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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