We are constrained by widespread cancerous diseases to improve treatment methods which save patients and provide better living conditions during and after the treatment period. Because of the complexity of the treatment process, mathematical models need to be used in order to have a better understanding of the process. However, deriving an adequate complex model that can capture the disease pattern which could be confirmed by simulations and experiments has its own barriers. In this paper, a new mathematical model is developed concerning immune system effect on cancer. The model is introduced using nonlinear ordinary differential equations. Also, the qualitative behavior of the proposed system is studied in order to examine the extent of the model with respect to the nature of tumor evolution. Thus, number and status of equilibria points in line with the existence of limit cycles are obtained for sub-systems and the whole system. Meanwhile, possible bifurcations are mentioned, and the consequent evolutions are described. It is shown that the model conforms well to natural possibilities, cancer growth or remission. Thus, the model would be fit for further studies for prediction and contemplating treatment method, especially for immune stimulating drugs and immunotherapy.

中文翻译：

---

考虑免疫系统作用的肿瘤非线性数学模型的动力学行为的开发和研究

我们受到广泛癌症疾病的限制，以改进治疗方法，以挽救患者并在治疗期间和治疗后提供更好的生活条件。由于处理过程的复杂性，需要使用数学模型以便更好地理解该过程。然而，推导出一个可以捕捉可以通过模拟和实验确认的疾病模式的足够复杂的模型有其自身的障碍。在本文中，建立了一个关于免疫系统对癌症影响的新数学模型。该模型是使用非线性常微分方程引入的。此外，研究了所提出系统的定性行为，以检查模型在肿瘤进化性质方面的范围。因此，得到子系统和整个系统与极限环存在一致的平衡点的数量和状态。同时，提到了可能的分叉，并描述了随之而来的演变。结果表明，该模型很好地符合自然可能性、癌症生长或缓解。因此，该模型将适用于预测和考虑治疗方法的进一步研究，特别是免疫刺激药物和免疫治疗。