Over the past semester I have studied the classic SIR endemic and epidemic models and contemplated how they may be applied to analyse the spread and control of contagious diseases. By investigating the dynamics of a non-fatal endemic disease I have discovered the requirements for a disease to become an endemic, or for the disease to be eradicated. This rests upon the critical value of the basic reproductive number and the critical vaccination number, which is also used to determine the fraction of a population that needs to be vaccinated to eradicate an endemic disease. By understanding the transmission characteristics of an infectious disease, we can obtain a better solution to diminish the transmission of these diseases.
Alcoholism is a problem that many people face not only in Australia, but also all over the world. Recent statistics taken by the ABS (Australian Bureau of Statistics) show that in 2004-5, 13.4% (approximately 2 million) of Australians could be classed as alcoholics. The survey showed that since 1995 there has been a 5% increase in the amount of alcoholics within Australian society. Furthermore, a 2001 survey conducted in the US found that in that year 100,000 people died as a result of alcoholism.
Many treatment programs, such as Alcoholics Anonymous and medications, have been introduced to try and combat the spread of alcoholism. However, these treatments do little to contribute to the understanding of how alcoholism comes about and how treatment should be administered.
How can we understand the way in which alcoholism spreads? Most people would not think of mathematics as a way in which this can be done. However, by applying the classic SIR endemic it is possible to do just that.
The goal of doing this is to facilitate methods by which alcoholism can be controlled and limited in a population. This will also lead to methods by which treatment can be effectively administered in order to ensure that no relapses occur and minimize the amount of alcoholics in society.
In this project, chapters 1-3 examine the original epidemiological models, which include the classic SIR endemic and epidemic model. Chapter 4 uses the mathematical skills examined in Chapters 1-3 to analyse the most recent model of alcoholism discussed in the article "Drinking as an Epidemic (2007)" by Sanchez et al.