Abstract
The immune system is a complex interconnected network consisting of many parts including organs, tissues, cells, molecules and proteins that work together to protect the body from illness when germs enter the body. An autoimmune disease is a disease in which the body’s immune system attacks healthy cells. It is known that when the immune system is working properly, it can clearly recognize and kill the abnormal cells and virus-infected cells. But when it doesn’t work properly, the human body will not be able to recognize the virus-infected cells and, therefore, it can attack the body’s healthy cells when there is no invader or does not stop an attack after the invader has been killed, resulting in autoimmune disease.; This paper presents a mathematical modeling of the virus-infected development in the body’s immune system considering the multiple time-delay interactions between the immune cells and virus-infected cells with autoimmune disease. The proposed model aims to determine the dynamic progression of virus-infected cell growth in the immune system. The patterns of how the virus-infected cells spread and the development of the body’s immune cells with respect to time delays will be derived in the form of a system of delay partial differential equations. The model can be used to determine whether the virus-infected free state can be reached or not as time progresses. It also can be used to predict the number of the body’s immune cells at any given time. Several numerical examples are discussed to illustrate the proposed model. The model can provide a real understanding of the transmission dynamics and other significant factors of the virus-infected disease and the body’s immune system subject to the time delay, including approaches to reduce the growth rate of virus-infected cell and the autoimmune disease as well as to enhance the immune effector cells.
Highlights
Human beings are constantly exposed to germs such as bacteria, viruses and toxins that enter into the human body that make-up the infections and diseases that will eventually make people sick
Developing mathematical models to predict the growth of tumors, virus-infected cells and immune cells have been of interest in the area of cancer epidemiology research [7,8,9,10] and infectious disease epidemiology [11,12] in the past few decades
We develop a new mathematical model considering the multiple timedelay interactions between the immune cells and virus-infected cells with an autoimmune disease in the form of delay partial differential equations
Summary
Human beings are constantly exposed to germs such as bacteria, viruses and toxins (chemicals produced by microbes) that enter into the human body that make-up the infections and diseases that will eventually make people sick. Developing mathematical models to predict the growth of tumors, virus-infected cells and immune cells have been of interest in the area of cancer epidemiology research [7,8,9,10] and infectious disease epidemiology [11,12] in the past few decades. We develop a new mathematical model considering the multiple timedelay interactions between the immune cells and virus-infected cells with an autoimmune disease in the form of delay partial differential equations. We discuss a new virus-immune time-delay model of the body’s immune system with considerations of the multiple interactions between the virus-infected cells and body’s immune cells with an autoimmune disease.
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