**1. Introduction**

Lifestyle has changed significantly in recent decades due to rapid development in every sphere of life. Consequently, the rate of noncommunicable diseases (NCDs), such as cardiovascular disease, cancer, chronic respiratory disease, and diabetes, has dramatically increased. In 2016, the World Health Organization (WHO) reported that 71% of all deaths worldwide occurred as a result of NCDs. According to the report, the highest mortality figures were those related to cardiovascular disease, representing 44% of deaths from the four main NCDs. The second most deadly disease was cancer, accounting for approximately 22% of deaths from the four main NCDs; while chronic respiratory disease and diabetes reached around 9% and 4%, respectively. In addition, gender variation in NCDs is another important factor. Research found that adult men are more likely to be affected than adult women, with 22% of men and 15% of women being affected [1]. According to a recent study, cancer is more common in certain countries; for example, Australia reported the highest percentage of cancer, with 4680 people per 100,000 having the disease. New Zealand registered 4381 people per 100,000. The number of cancer cases has been estimated as 3522 per 100,000 in the USA, compared with 3192 registered cases per 100,000 in the United Kingdom [2]. The tissues and organs of the human body are formed from 10<sup>13</sup> tiny cells. There is a one-to-one correspondence between cells and human body growth. The more increased the number of cells, the more tissue grows. The cells between conception and adulthood divide and grow very quickly [3]. Yet, the functions of these cells vary, and as a result the division and growth of the cells depend on their functions. For example, blood and skin cells divide continuously, while some cells have particular functions in the body and do not usually multiply. Concerning the multiplication of cells, it is possible for them to multiply as many as 60 times before dying, as a result of the signals that control cellular growth and death [4,5]. On the other hand, they can become damaged during the process of division, which can lead to self-elimination. This process is known as apoptosis and it protects the human body from cancer. Conversely, cell division is sometimes abnormal when there is damage during cell division, with very unique characteristics [3–5]. In such cases, the immune system reacts to protect the human body by preventing these cells from growing into a tumor [3–5]. Assessing modern lifestyles is the key to understanding the causes of the increasing rates of cancer. One of the disadvantages of the development of society is that dietary habits have changed to encompass more fast and processed foods. These types of foods have a higher calorie count, contain more protein, and have lower amounts of fiber and carbohydrates than healthy foods, which are rich in natural sources of vitamins and minerals and high in fiber and carbohydrates [6]. Studies have shown the increase in death rate associated with a diet based on animal products and a high intake of carbohydrates, and contrarily, how a vegetable-based diet and a low carbohydrate intake reduces the mortality rate. Furthermore, malnutrition debilitates the immune system and increases the mortality rate as well as elevating the risk of contracting NDCs [7]. It has been shown that only 5–10% of cancers occur as a result of internal factors such as inherited mutations, hormones, and immune conditions, and that 90–95% of cancers are due to lifestyle and environmental factors [8]. Dietary habits are one of the main factors related to the weakening of the immune system and the risk of cancer [9–12]. From 1994, mathematical researchers started to formulate tumor–immune interaction models using the function of Michaelis–Menten [13,14]. In 1995, Mayer and others proposed a basic mathematical model of the immune response by using two ordinary differential equations to describe the interaction between the immune system and a pathogen, such as a tumor cell or virus. Their model succeeded in illustrating that the combination of a few proposed nonlinear interaction rules between the immune system and pathogens is able to generate a considerable variety of immune responses, with many of them being observed both experimentally and clinically. Hence, the process of the interaction of the immune system with pathogens can be described dynamically [15]. In 2003, Magda Galach used the simplified model of Kuznetsov–Taylor and changed the Michaelis–Menten function using the Lotka–Volterra form [16]. Many models have used ordinary differential equations, partial differential equations, and delay differential equations to illustrate the growth of tumors and their treatments [17–19]. In the last few years, mathematical researchers have dynamically examined cancer risk factors and ye<sup>t</sup> still have a grea<sup>t</sup> deal to uncover. Estrogen has been studied as a breast cancer risk [20]; furthermore, Green and others studied the relationship between body mass index, menopausal status, estrogen replacement therapy and the risk of breast cancer [21]. In 2016, Roberto and others proposed an obesity–cancer model using ordinary differential equations to illustrate the association between obesity and cancer risk [22]. Additionally, they presented the effects of obesity on the optimal control program of chemotherapy. This model differs from that of De Pillis and Radunskaya [23] by adding a dynamic equation related to stored fat [24]. Other studies have presented models regarding drug therapy which contribute to decision making and early cancer treatment [25]. In 2018, Alharbi and Rambely suggested dynamically that switching back to a healthy lifestyle boosted the immune system in terms of inhibiting or eliminating a moderately abnormal cell [26]. Hence, the immune system has the ability to protect the human body from developing cancer.

In 1618, Thomas Adams stated that "Prevention is so much better than healing because it saves the labour of being sick" [27]. In this work, we propose and simulate the immune–healthy diet model (IHDM) based on the models of references [15,26] using ordinary differential equations to study the behavior of the immune system when responding to the appearance of abnormal cells which fail to eliminate themselves. Usually, these types of cells do not need to be treated clinically. However, the appearance of abnormal cells in the tissue is considered as an emergency situation, with any progression being able to trigger the formation of tumor cells and the development of cancer. Therefore, most cancers develop as a consequence of multiple abnormalities, which accumulate over many years [5]. For instance, colon cancer has increased more than tenfold between the ages of 30 and 50, and tenfold again between 50 and 70 [28].

We aim to enhance understanding of the symmetry and antisymmetry of the relationship between diet habits and the function of the immune system, raise awareness of healthy habits and promote healthy eating habits. In doing so, we hope that the results of this paper contribute to increasing awareness of cancer risk.

This paper is organized as follows. In Section 2, we present the IHDM and analyze the equilibrium points of the model and stability cases. In Section 3, we analyze the stability of the equilibrium points for the immune–unhealthy diet model (IUNHDM). The numerical simulation of the IHDM and IUNHDM are presented in Section 4. The conclusion is presented in Section 5.
