Introduction Cancer is the boundless proliferation of cells [1, 2]. It is one of the most difficult diseases to treat and is one of the main causes of mortality in the world. As a result, immune interactions with tumor cells have developed to manage cancer with the assist of ordinary differential equation models (ODEM). These models have some limitations, so as a solution, the agent based modeling (ABM) was used. Agent based modeling and simulation can lead to a better comprehension of the trend for cancer growth in patients. Agent based modeling consists of agents, environment and framework for simulating agent behaviors and interactions with each other, and also with their environment. Agents are autonomous decision making units with diverse …show more content…
According to Arciero et al [2], “effector cells are assumed to be recruited to a tumor site as a direct result of the presence of tumor cells“. The parameter c in cT/(1+ γS) represents the antigenicity of the tumor that measures the ability of the immune system to recognize tumor cells. Antigenicity was shown to be the main bifurcation parameter in [13] governing equilibrium dynamics. The production of TGF-β has been shown to reduce antigen expression, thereby limiting the level of recruitment, measured by inhibitory parameter γ [12]. The second term represents loss of effector cells due to cell death, and the third term, a proliferation term, asserts effector cell proliferation is dependent upon the presence of the cytokine IL-2 and is decreased when the cytokine TGF-β is present. The Michaelis-Menten forms of components of the proliferation term can be derived by considering the binding of IL-2 and TGF-β to effector cell surface receptors, invoking the law of mass action, and making use of usual quasi-steady state assumptions. Therefore, p1 is the maximum rate of effector cell proliferation in the absence of TGF-β, g1 and q2 are half-saturation constants, and q1 is the maximum rate of anti-proliferative effect of …show more content…
Experimental evidence suggests that TGF-β is produced in very small amounts when tumors are small enough to receive ample nutrient From the surrounding tissue. However, as the tumor population grows sufficiently large, tumor cells suffer from the lack of oxygen and begin to produce TGF-β in order to stimulate angiogenesis and to evade the immune response once tumor growth resumes [15, 6]. This switch in TGF-β production is modeled by the first term in (4). Here, p4 is the maximum rate of TGF-β production and τ_c is the critical tumor cell population at which the switch occurs. The decay rate of TGF-β is represented by μ3. According to this conceptual model we can define Agent-Based Modeling as a discrete probabilistic model. For example in equation (5) first term and second term are presenting the number of effector cell in the tumor site. As it is mentioned the ABM in this paper is based on a discrete probabilistic model that must be achieved the possibility of death or cell growth in each interval. The probability of Increase or decrease a parameter is shown in the following