Abstract
The immune system is the body’s defense against pathogens, which are complex living organisms found in many parts in the body including organs, tissues, cells, molecules, and proteins. When the immune system works properly, it can recognize and kill the abnormal cells and the infected cells. Otherwise, it can attack the body’s healthy cells even if there is no invader. Many researchers have developed immunotherapy (or cancer vaccines) and have used chemotherapy for cancer treatment that can kill fast-growing cancer cells or at least slow down tumor growth. However, chemotherapy drugs travel throughout the body and tend to kill both healthy cells and cancer cells. In this study, we consider the fact that chemotherapy can kill tumor cells and that the loss of the immune cells may at the same time stir up cancer growth. We present a dynamic time-delay tumor-immune model with the effects of chemotherapy drugs and autoimmune disease. The modeling results can be used to determine the progression of tumor cells in the human body with the effect of chemotherapy, autoimmune diseases, and time delays based on partial differential equations. It can also be used to predict when the tumor viruses’ free state can be reached as time progresses, as well as the state of the body’s healthy cells as time progresses. We also present a few numerical cases that illustrate that the model can be used to monitor the effects of chemotherapy drug treatment and the growth rate of tumor virus-infected cells and the autoimmune disease.
Highlights
Human beings are constantly exposed to germs such as bacteria and viruses that enter the human body and eventually make people sick
The tumor virus-infected counts begin to increase only upto the fourth day and start to decrease until they reach the lowest number of tumor cells at around 23,360, which is at about the 18th day
We have formulated a mathematical model of the immune system with with time-delay effects of the interactions between immune cells and tumor cells with time-delay effects of the interactions between immune cells and tumor cells with autoautoimmune disease incorporating chemotherapy drug treatment, where the amount of immune disease incorporating chemotherapy drug treatment, where the amount of drug drug injected to patients is kept constant using partial differential equations
Summary
Human beings are constantly exposed to germs such as bacteria and viruses that enter the human body and eventually make people sick. One of the tasks of the body’s immune system is to fight off infections, prevent viruses and germs from entering the body, and destroy any infectious microorganisms that do invade the body [1–3]. The skin is a part of the immune system that prevents germs from entering the body [4]. When the body senses danger from a virus or infection, the immune system will respond and attack it. Many researchers have developed immunotherapy and chemotherapy to improve the ability of the immune system and cancer treatment, respectively, to attack cancer cells. When chemotherapy drugs are injected into a person, they travel throughout the body, a process during which they can damage healthy cells. The loss of the immune cells may at the same time stir up cancer growth
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