Introduction
Purpose
The purpose of this mathematical modeling project is to develop a model based on facts known about the spread of the Acquired Immune Deficiency Syndrome (AIDS) virus, and to predict its spread throughout a population that is statistically representative of the average population. This subject was selected due to the fact that AIDS is adversely impacting populations throughout the world. A number of dangerous viruses have been eradicated (i.e. smallpox) in recent history via improved medical technology and treatment; however no cure has yet been discovered for AIDS. Because there is no positive treatment for the cure of AIDS, additional in-depth research will be required in both developed and undeveloped countries. Mathematical modeling can be applied to evaluating multiple aspects involved in exposing a population to the AIDS virus and predicting the spread of AIDS within this population. These mathematical models can be readily converted into a computer project that evaluates effects of the disease and potential spread of the disease.
The spread of this disease was examined by creating a mathematical model, applying the model to numbers obtained from historical statistical data, and then running the model through a computer program to mimic the behavior of the disease[7]. The equation that this program is based on is known as the SI (Susceptible Infected) model which is a mathematical formula that is commonly used to calculate the spread of infectious diseases. The model takes into account the numbers of people with a disease (infected), and people who can still get the disease (susceptible). Using this model the interaction between these two groups can be evaluated by monitoring the infection of those who are susceptible to the disease. Using the SIR (Susceptible-Infected-Recovered) model was considered but HIV/AIDS currently has a recovery rate of zero. The SI model is therefore superior to the SIR model in this case because it more closely models the actual behavior of AIDS and it has all of the basic components for modeling AIDS.
Scope
The scope of this program is limited to developing a mathematical model based on historical data that describes the current health problems associated with AIDS; and creating a set of computer based methods that predict the future behavior of this infectious disease. The program provides a basis for examining the effects of the AIDS virus on a given population and examines the spread of AIDS through a specified population representative of the population of the United States of America. The mathematical models and computer program which were developed by this team to analyze the impact of the AIDS virus in a selected population can also be used, by changing specific input parameters, to predict the behavior of the AIDS virus in other possible situations such as: discovery of a vaccine, a more infectious strain of the virus, or a mutation that causes a part of the population to be immune to AIDS.
Computer Program
This project makes use of the C++ programming language. Before being written in C++, the original SI model was tested in Excel to insure its accuracy and applicability in this situation. C++ is applicable to this situation because of its mathematical capabilities and its simplicity. The computer program was developed by the team and is based on accepted analytical models used to simulate the spread of the AIDS virus. The original SI model used in the program was obtained from a mathematical modeling textbook. This model has been modified as appropriate to accurately represent the threat to a population posed by AIDS for the specified input conditions defined in the document. These modifications, the testing of them, and their final use in this program were accomplished solely by team 80 with input and guidance from the acknowledged sources
