Statistical Modeling of The AIDS Virus


An excursion into the modeling of infectious diseases

Executive Summary

Introduction

Project Proposal

Analytical Methodology

Results

Conclusions

Future Work

References

Appendix 1
Understanding The Model


Appendix 2
Code, and Computations


Appendix 3
History of the AIDS Virus

Appendix 3

History, Transmission, and Behavior of the AIDS Virus

AIDS (Acquired Immunodeficiency Syndrome) is a worldwide pandemic that has been growing rapidly since its recognition in the early 1980's. It is only recently that treatment has been developed that has allowed people to live with AIDS for up to 10-20 years. It is estimated that as of the end of 2004, 37.2 million adults and 2.2 million children worldwide were living with AIDS. During 2004, an estimated 4.9 million people contracted AIDS, and 3.1 million died of the disease[6].

AIDS is caused by a virus known as HIV (Human Immunodeficiency Virus). HIV is abundant in the bodily fluids of people affected with AIDS, and is usually spread through them. The most common forms of HIV infection are through sexual contact, and through the sharing of needles in intravenous drug use. The virus can also be transmitted from mother to child during childbirth or breast-feeding, though transmission seldom occurs in the womb[7]. Before much was know about AIDS and HIV, another common form of transmission was blood transfusions. After someone has been infected with HIV they are called HIV+, or HIV positive[8].

HIV causes infection by attacking the CD4+ T cells that are supposed to coordinate the body's immune system to fight off infection. After being infected with HIV a person may experience various flu-like symptoms (this is called seroconversion illness), but many people do not show any symptoms[8]. Soon, all newly infected people become symptom-free. During this time the HIV particle count in the patient’s body increases by billions every day, and the CD4+ T cell count decreases, with varying speeds. Because the virus specifically attacks the cells of the immune system, the antibody response is low or nonexistent, and the virus is allowed to spread unchecked. Typically, once a person’s CD4 cell count is below 200 per cubic millimeter, they are considered to have AIDS[8]. The time from being infected with HIV and being diagnosed with AIDS varies; some have been diagnosed with aids only months after becoming HIV+, and some have remained symptom-free for as long as 20 years. The typical time from infection to AIDS is 8 to 10 years[7].

AIDS is closely related to the simian immunodeficiency viruses (SIV). SIV is endemic to many African monkeys and apes, though most of them do not show symptoms of the virus. Scientists speculate that SIV was transferred to humans through one of many various methods, such as the consumption of raw flesh [9]. The exact location and time where the transference took place is still unknown, but the earliest known fluid sample known to contain HIV was taken in 1959, from a British sailor who had apparently contracted it in what is now known as the Democratic Republic of the Congo[8].

AIDS became officially recognized in 1981, when the American Centers for Disease Control put out a press release, which described five cases of a rare respiratory disease that people with healthy immune systems were seldom affected with. Afterwards several cases of a form of skin cancer were reported, which was also seldom seen in people with healthy immune systems. Both of these diseases were later classified as opportunistic infections, because they are commonly found in patients suffering from AIDS[7]. Other tests performed on these people also found that they were suffering from several other diseases that were also later classified as opportunistic infections. The patients also had a much lower than average CD4+ T cell count. Because most of the original sufferers of the virus were homosexual men, the syndrome was originally referred to by doctors as GRID (Gay-Related Immune Deficiency), but after it was discovered that other sufferers included Haitian immigrants, intravenous drug users, blood transfusion recipients, and heterosexual women, the virus was officially renamed AIDS in 1982[9].

It wasn’t until 1984 that researchers were able to isolate the virus that causes AIDS. The two men who discovered the virus, Robert Gallo and Jean Luc Montagnier, agreed to share credit after a long dispute. In 1986 it was officially given the name HIV. This discovery allowed for the development of an antibody test, which allowed people to know if they were infected and at risk of developing AIDS[8].

Currently, there is no cure for AIDS, though in recent years combinations of drugs, known as "cocktails", have allowed people with AIDS to have a much longer lifespan than previously expected. Most of these treatments usually consist of combinations of two or more anti-retroviral agents. Such treatment has caused patients to repeatedly test negative for HIV, though if the treatment was discontinued the viral loads quickly increased. These treatments are not perfect, however, and there is concern that drug resistance will develop[8]. Also, as these treatments are inevitably very expensive, they are not availiable to the vast majority of people living with AIDS.



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