Modelling Human Immune Response to Virus Infectious Diseases

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JUNE 2011
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This study is aimed at modelling human immune response to virus infectious diseases. The issue of humans’ defense against viral infections and the reaction of immune system to these infections are the main problems in practical immunology. In addition to antiviral defense, the human immune system plays a decisive role in compatibility reactions such as autoimmune diseases and other allergies. Four systems of differential equations have been developed, analyzed and the numerical solutions found. These systems have been used to model different stages of the human immune response to viral infection. The first three differential equations describe the behaviour of lymphocytes in the absence of virus cells. The next two differential equations also describe the first line of defense in the innate immune response stage. The overlapping stage of innate and adaptive immune responses comprises a system of four differential equations. The last three equations describe the adaptive immune response which is the final stage of combating viral infection. The steady states and their stability for these differential models are deduced. Each of the models permits the existence of two types of stationary states. There is the state of no infection, with no virus cells while the other is the state of coexistence where a virus cell persists against the background of immune response. The state of no infection is asymptotically stable and a state of infection is unstable. It was found from the study that the state of no infection represents the immune state.
A Thesis Submitted In Partial Fulfillment of the Requirements for the Degree OF Master OF Philosophy in Industrial Mathematics DEPARTMENT OF MATHEMATICS, SCHOOL OF GRADUATE STUDIES. INSTITUTE OF DISTANCE LEARNING,