Hiv and Dynamical Systems

Throughout the semester we have used mathematical modeling to simulate many processes throughout the body—including caffeine/alcohol elimination and the breakdown of several drugs in the body. For our next unit we will use math modeling to help get a better understanding of HIV. Before beginning, it is useful to discuss the virus and its effects on the body. For our purpose, it is required to know that within the blood there are two kinds of white-blood cells that are associated with HIV. The CD-8 cells (killer-t cells) attack foreign invaders of the body such as infection and disease while the CD-4 cells (helper-t cells) authorize the CD-8 cells to attack these foreign invaders. What HIV does is infiltrate the CD-4 cell and replicates very quickly until the cell becomes overwhelmed and dies. Once this happens, HIV particles are released and spread to other CD-4 cells. The timeline of HIV is also useful when trying to wrap one’s mind around the virus. In the first two weeks of infection, the number of HIV particles in the blood spikes then levels off. Over a period of 5-10 years, the number of CD-4 cells slowly decreases until a certain point. Once the number of CD-4 cells reaches below 200 per mL of blood, the person is said to have AIDS. At this point the days are numbered because the patient will soon be unable to fight off even the most common illnesses. Having said all of this, it is time to start using math modeling to simulate this timeline as well as other scenarios such as when medication is used.