Abstract
Over the last few decades, there have been significant developments in theoretical, experimental, and clinical approaches to understand the dynamics of cancer cells and their interactions with the immune system. These have led to the development of important methods for cancer therapy including virotherapy, immunotherapy, chemotherapy, targeted drug therapy, and many others. Along with this, there have also been some developments on analytical and computational models to help provide insights into clinical observations. This work develops a new mathematical model that combines important interactions between tumor cells and cells in the immune systems including natural killer cells, dendritic cells, and cytotoxic CD8+ T cells combined with drug delivery to these cell sites. These interactions are described via a system of ordinary differential equations that are solved numerically. A stability analysis of this model is also performed to determine conditions for tumor-free equilibrium to be stable. We also study the influence of proliferation rates and drug interventions in the dynamics of all the cells involved. Another contribution is the development of a novel parameter estimation methodology to determine optimal parameters in the model that can reproduce a given dataset. Our results seem to suggest that the model employed is a robust candidate for studying the dynamics of tumor cells and it helps to provide the dynamic interactions between the tumor cells, immune system, and drug-response systems.
Highlights
Cancer is one of the leading causes of death in the world today
We will consider a model that consists of four main cell populations including tumor cells (T(t)), natural killer cells (N(t)), dendritic cells (D(t)), and cytotoxic CD8+ T cells denoted by (L(t)). e dynamics of these cells will include interactions between each other as well as dynamics generated by interaction with chemotherapy as well immunotherapy drug concentrations in the blood stream
We developed a mathematical model that incorporated the dynamics of four coupled cell populations including tumor cells, natural killer cells, dendritic cells, and cytotoxic CD8+ T cells that in uence the growth of tumors
Summary
Cancer is one of the leading causes of death in the world today. By 2030, over 13 million are estimated to harbor some form of the disease. Ese equations include nonlinear interactions and do not often admit an exact solution and require computational methods to solve them While these mathematical models have provided useful information regarding the importance of the immune system in controlling tumor growth, there is still a great need to continue to enhance existing models to incorporate new clinical developments and biological discoveries. E focus of this paper is to enhance existing models of tumor growth that incorporate tumor dynamics in conjunction with the immune system response and study the effect of additional interventions including antitumor vaccination and immunotherapies along with chemotherapy. Is paper attempts to make a new contribution in this direction by developing a coupled mathematical model that incorporates tumor dynamics and interactions between the dendritic cells, natural killer cells, and CD8+ T cells. A new parameter estimation technique is proposed that helps to estimate parameters optimally for a given extrapolated dataset
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