ANALYSIS OF TUMOR GROWTH AND IMMUNE SYSTEM INTERACTION MODEL NOR AZIRAN AWANG a & NORMAH MAAN b 1 a,b Department of Mathematical Sciences, Faculty of Science Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia Corresponding email: normahmaan@utm.my naziran283@gmail.com Abstract. Immune system plays a vital role in controlling the tumor growth. Therefore, this paper proposes a new mathematical model that describes tumor-immune interaction, focusing on the role of natural killer (NK) cell and CD8 + T cell. The tumor population is subdivided into two different phases, namely interphase and mitosis. This model used Ordinary Differential Equations (ODEs) and the functions involved in the model represents tumor-immune growth, responses and interaction between the cells. The stability and analysis of the model are carried out. From the analysis, it shown that the stability curve limits tumor growth region. The curve from the model lie below the curve of the model with single immune response (CD8 + T cell). This result concluded that the proposed model with involvement of NK cell suppression will lower the tumor growth region. Keywords: tumor growth; natural killer (NK); CD8 + T cell. PACS: Replace this text with PACS numbers; choose from this list: http://www.aip.org/pacs/index.html INTRODUCTION Tumor represents a real crisis for public health system worldwide. Primary tumor growth is a complex process, involving many interaction between the tumor and surrounding tissues. Treatments traditionally used to fight against tumor are surgery, radiotherapy and chemotherapy. Unfortunately, these treatments kill normal cells as well as tumor cells. Then, immunotherapy is introduced [1-6]. It is based on the generally-accepted hypothesis that the immune system is the best tool humans have for fighting disease [3,10-13]. In recent years, there is evidence that immune system is capable of recognizing and eliminating tumor cells. Therefore, some researchers intensively continue to develop and investigate the interaction between growing tumor and immune system [1-13]. Majority of the research on immune cells focused on NK cell, T cell and macrophages [3,5-7,10]. The experimental result have shown that these immune cells are associated with good tumor prognosis and also being involved in the lysis of tumor cells [10]. Each of them uses a different mechanism and plays a different role in cell lysis. NK cells are lymphocytes in innate immunity that have ability to kill tumor cells directly without activation [14-16]. It also play key role by destroying abnormal cells before they replicate and grow [10]. By contrast, T cells are part of the adoptive immune system and also have capability to fight the tumor cells. Both innate and adoptive immune cells actively prevent neoplastic development in a process called ‘cancer immunesurveillance’. So, the effectors of the adaptive and innate immunity need to actively cooperate in order to reject tumor cells [7]. Early 1990s, Kuznetsor [17] proposed a mathematical model of the cytotoxic T lymphocyte response to the tumor growth. The model described the kinetic growth and regression of lymphoma. They found that the cytotoxic effector cells are responsible for the lysis of tumor cells. In 1998, Kirschner and Panetta define an ODE model for three main population: effector cell, tumor cell and concentration IL-2. Effector cell or also called as immune-system cell are stimulated to grow based on two terms: recruitment term and proliferation term. Logistic growth function is used as the growth term in this model. de Pillis [10] found that the combination effect of the NK cells and T cells can eliminate larger tumors compared to individual effect of immune cell (the depletion of NK cells have different impact to depletion of T cell). Most of the tumor-immune models are using logistic function, gompertz and exponential function as the growth term [10,17-18]. Gompertz have a serious limitation which is not appropriate in describing the dynamics of very small tumors [19-20] while exponential function only fixed for small population of tumor cells [17]. Then, Villasana [11] come out with the mitosis as the growth term in tumor population. She introduced tumor-immune system model which involved cell-cycle. The population of tumor take placed during interphase and mitosis (M phase). However, Villasana only consider T cell as the immune cell that can fight tumor cells. The system is simple and does not contain many importance interactions. A followed up study of Villasana’s model was recently conducted by Liu [12]. 1 Sila gariskan nama pembentang. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Universiti Teknologi Malaysia Institutional Repository