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RESEARCH

Refining Sigal et al.’s Model of Cancer Treatments and Heterogeneous Tumor Growth in “Mathematical Modeling of Cancer Stem Cell-Targeted Immunotherapy” to Exhibit Gompertzian Growth

CATHERINE FENG, Harvard College '27

THURJ Volume 15 | Issue 1

Abstract

Tumors are typically heterogeneous, consisting of multiple cell types. A small but aggressive subset are cancer stem cells (CSCs), which are closely related to tumor growth and resistance, making them critical targets for therapeutic intervention. Traditional therapies like chemotherapy often fail to eradicate CSCs, necessitating targeted treatments like immunotherapy. While the interactions of different types of cancer and immune cells, immunotherapy, and chemotherapy have been studied experimentally, mathematical models are needed to better understand why certain treatments fail and how to improve cancer treatment. In this manuscript, I replicate and expand upon a mathematical model developed by Sigal et al. (2019) that employs a system of seven ordinary differential equations (ODEs) to simulate the effects of immunotherapy and chemotherapy on tumors containing both CSCs and non-CSCs (nCSCs). The model incorporates two types of immune cells involved in promising immunotherapies and antitumor response: dendritic cells (DCs) and cytotoxic T-cells (CTCs). I modify the original model by introducing a Gompertzian growth term to better capture long-term tumor growth as the tumor approaches its carrying capacity, addressing the model’s current limitations. Future work includes refining parameter values and extending the model to account for tumors composed solely of CSCs or nCSCs. This modified model has the potential to provide valuable insights into the potential efficacy and optimal timing of cancer treatments.

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