Iqra Batool

• Cancer, a complex and multifaceted disease, continues to challenge the boundaries of biomedical research. In this dissertation, we explore the complexity of cancer genesis, employing multiscale modeling, abstract mathematical concepts such as stability analysis, and numerical simulations as powerful tools to decipher its underlying mechanisms. Through a series of comprehensive studies, we mainly investigate the cell cycle dynamics, the delicate balance between quiescence and proliferation, the impact of mutations, and the co-evolution of healthy and cancer stem cell lineages. The introductory chapter provides a comprehensive overview of cancer and the critical importance of understanding its underlying mechanisms. Additionally, it establishes the foundation by elucidating key definitions and presenting various modeling perspectives to address the cancer genesis. Next, cell cycle dynamics have been explored, revealing the temporal oscillatory dynamics that govern the progression of cells through the cell cycle. The first half of the thesis investigates the cell cycle dynamics and evolution of cancer stem cell lineages by incorporating feedback regulation mechanisms. Thereby, the pivotal role of feedback loops in driving the expansion of cancer stem cells has been thoroughly studied, offering new perspectives on cancer progression. Furthermore, the mathematical rigor of the model has been addressed by deriving wellposedness conditions, thereby strengthening the reliability of our findings and conclusions. Then, expanding our modeling scope, we explore the interplay between quiescent and proliferating cell populations, shedding light on the importance of their equilibrium in cancer biology. The models developed in this context offer potential avenues for targeted cancer therapies, addressing perspective cell populations critical for cancer progression. The second half of the thesis focuses on multiscale modeling of proliferating and quiescent cell populations incorporating cell cycle dynamics and the extension thereof with mutation acquisition. Following rigorous mathematical analysis, the wellposedness of the proposed modeling frameworks have been studied along with steady-state solutions and stability criteria. In a nutshell, this thesis represents a significant stride in our understanding of cancer genesis, providing a comprehensive view of the complex interplay between cell cycle dynamics, quiescence, proliferation, mutation acquisition, and cancer stem cells. The journey towards conquering cancer is far from over. However, this research provides valuable insights and directions for future investigation, bringing us closer to the ultimate goal of mitigating the impact of this formidable disease.