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The first internet site I looked into deeply was:

http://www1.ocdsb.edu.on.ca/srbhweb/math/Data%20Management/Charleen/Charleen%20on%20Aids.htm

www.assa.org.za/downloads/aids/summarystats.htm

I was not quite sure yet what my project was going to look at directly so I just poked around to see what I could find. They had a lot of data and I printed it all so I could get a better understanding of what they had looked at. They had made graphs already for their statistics but I also made my own in Microsoft Excel.

The first graph I made was that of the entire population of Africa for the next fifteen years. This was estimated by the Actuarial Society of South Africa, the author of the website. I was unable to find an exact date that the information from the website was last updated, but it does say in the statistics that all were estimated from the year 2000 and forward. Therefore all of the statistics from this website are only approximations based on the trends from previous years. This could skew my data because the statistics are not necessarily perfect and cannot be reliable since they are only estimates.

I can’t necessarily make any concrete conclusions from this graph but as can be seen, experts estimate that the population will be increasing rapidly until about 2007. Then it begins to descend at a rapid rate but the slope is not as steep as the increase in population prior to 2007.

The second graph I made represented the number of HIV infections in Africa. This data was also collected from the same website and the statistics are again, only approximations calculated by the Actuarial Society of South Africa. I wanted to see if there was any relationship between the increase and decrease patterns of the population and the number of HIV infections. It could be expected that with an increase of population there would be an increase in HIV infections and I would expect it to be the same with a decrease in population as well.

The fact that these statistics are approximations the graphs will generally look the same because the trends may have been the same in the past but they may not be that way in the future. It is impossible to create a perfect estimate of future trends because it is exactly that, the future. We do not know what will happen in Africa in the next ten years that could affect the population or the number of HIV infections. We can see however that based on these graphs there is a correlation between the two. Both graphs are steadily increasing until about 2007 where both begin to decrease at a little slower rate. We can also see in the graph of HIV infections that the trend-line is a close fit because the line has a very high r-squared value. To get the closest fitting trendline using Excel, I went to Insert and went to Add Trend-line. I tried all of the different types of trendlines to find the one with the highest correlation co-efficient, which ended up being the polynomial line. This line shows the increase, the eventual peak in 2007 and then the decrease of the number of HIV infections over the 15 years estimated.

At this point I am still not sure what exactly I am looking for in my data so I continue to make graphs and see if there are relationships between them. I decided now to begin to look at the orphan statistics that I gathered. The website from my previous two graphs had the information needed on it so I made a graph in Excel from those statistics. Once again they are only estimates from 2000 to 2015.

The graph shows a very rapid increase in the number of AIDS orphans throughout the fifteen years. I did not really understand why there would still be such a rapid increase in the number of AIDS orphans because of the previous graph that showed a peak in 2007 and then a decrease in the number of HIV infections. I was wondering why this could happen and decided that this should be my thesis question.

Therefore my thesis question is: Why do experts predict an ongoing increase for the number of AIDS orphans in South Africa over the next fifteen years?

My hypothesis is: Experts predict this increase because there are still a number of South Africans living with the disease who are going to leave children behind when they die in the future. Another factor affecting their estimate is the age a child is considered an orphan until.

I wanted to look into the definitions of an AIDS orphan first so I went back to my first search using the "Google" search engine and decided to check out another website at:

http://trochim.human.cornell.edu/gallery/Ruiz/home.html

The title for this website was "What is your definition of orphan?" I found this interesting because the age of a defined ‘AIDS orphan’ may show a relation to the graph. They included two definitions in their report. The first was the definition from the Merriam-Webster Dictionary and it said: "(1) a child deprived by death of one or usually both parents; (2) a young animal that has lost its mother, and (3) one deprived of some protection or advantage." (http://trochim.human.cornell.edu/gallery/Ruiz/monica5.htm) The website also states that the definition used for AIDS orphan. " The definition of ‘AIDS orphan’ used by UNAIDS, WHO [World Health Organization] and UNICEF is of a child who loses his/her mother to AIDS before reaching the age of 15 years. Some of these children have also lost, or will later lose, their father to AIDS." (http://trochim.human.cornell.edu/gallery/Ruiz/monica5.htm)

I wanted to relate this back to the graph of the number of AIDS orphans to prove that there is a correlation between the age of a defined ‘AIDS orphan’ and the increase in their number. Since the age a child is considered an orphan until is age 15 years, this could be linked to my thesis. Because the data is estimated for the next fifteen years, a child who loses their mother or both parents to AIDS in the year 2000, will still be included in the estimates until 2015. I found this very interesting because it would explain why there is an increasing number. The number of children who become AIDS orphans and the number of children who already are AIDS orphans are not calculated separately. Therefore I wanted to attempt to make those calculations myself. I made another spreadsheet in Excel and to calculate the additional orphans for each year, I subtracted the number of AIDS orphans from the previous years from the total accumulated AIDS orphans. For each of the cells I entered: =(C3-B3) for example and came up with the differences for each year. This is the spreadsheet.

I also made a graph for the new calculations I made and this is what it looks like.

I noticed that the trend in this graph looked similar to the trends in the graphs for the total number of HIV infections, the number of AIDS deaths and the general population graph. I wanted to compare all of these graphs so I compiled them all into one line graph in Excel to observe the trends.

Obviously, this first graph does not clearly represent the data because of the difference in the numbers on the y-axis. So I decided to try the graph again but not use the population data because those numbers are the highest and farthest away.

Once again, the graph did not clearly represent my data or show the trends I was hoping for. This is when I decided to do the same thing with the HIV infections as I did with the AIDS orphans. Since the data given was for the accumulating number of HIV infections, I calculated the number of new HIV infections for each year. This is the spreadsheet from Excel and I calculated the numbers using the same method I used for the new AIDS orphans calculations.

This graph did not work either because of the negative values I was getting for the number of new HIV infections after the year 2007. I think the experts are expecting there to be no new reported cases of HIV after 2007 and because of the number of deaths, the number of HIV infections will go down. I realised that this is not necessarily realistic since there is no known cure for HIV or AIDS yet. This made me think why there would be the negative values for those years. I looked back at the number of deaths for those years and figured that the number of deaths from AIDS was greater than the number of new HIV infections and that is why there are negative values. This means that from these calculations I cannot calculate the number of new HIV infections per year without knowing the amount of AIDS deaths for that year alone. I could attempt to calculate this but this is not an essential part of proving my thesis so I did not want to concentrate on it too much. I did make a graph comparing the number of AIDS deaths with the number of new AIDS orphans because I knew there must be some correlation between the two. I figured this because as the number of people who are dying from AIDS decreases, the number of children who are orphaned by AIDS must decrease. This is the graph on the next page.

By stretching this graph vertically, I can see the trend I wanted to. The increase and decrease seem to occur at almost the same time and the overall graphs look the same. This can prove that the number of new orphans is decreasing with the number of deaths caused by AIDS which is one possible answer to my thesis question.

I also made a relationship with another factor of the definition of an AIDS orphan. The fact that to be considered an orphan the child must only lose their mother, which is still a substantial loss, might have an effect on the graph. I thought that maybe the decrease in the number of infections reflected a very high decrease in the number of infected males but the number of infected females was still on the rise. This could explain the third graph because even if there was a decrease of infections in the overall population, more women may still be dying. This would therefore cause a continued increase in the number of AIDS orphans. This new idea led me to research about the differences between males and females and their infection rates over the next 15 years. I now wanted to prove that there may be a decrease in the number of infected males but an increase in the number of infected females.

The calculations I made for the number of new orphans can help prove the first part of my hypothesis also. The graph of the number of new AIDS orphans and the number of AIDS deaths shows that there is some correlation but I was not satisfied with the strength of that correlation. So I decided to make the same calculations I made with the AIDS orphans and the number of HIV infections for the number of AIDS deaths. I thought that if there was a strong enough correlation and a relatively small difference in numbers of these two factors, my hypothesis would be right. I said a small difference in numbers because there should be close to the same amount of new AIDS orphans as there are new AIDS deaths. The fact that some parents who die from AIDS may have more than one child may be the reason for any difference in numbers. As I was writing that last sentence, I also came up with something that might skew my data. For the data I am using an AIDS orphan is only defined as a child who loses their mother to AIDS, therefore after I graph the deaths for both genders I will find the information for female deaths from AIDS and compare those numbers as well. This should prove to be an even stronger correlation.

This graph shows a lot of correlation but not enough to make a strong conclusion about. Therefore I went back to the ‘Google’ search engine to find the data for women dying from AIDS until 2015. I went back to the site with the information for almost all the calculations I have made so far and found prevalence rates for women ages 20 to 65 years old. This data was in percentage form and I was not quite sure if that number was a percentage of the total population or of the population infected with HIV. I decided to look for more reliable data and ended up looking at the United Nations website. The website is: www.unstats.un.org. The only statistic on females living with AIDS was once again a percentage for the prevalence of HIV/AIDS among adult women. This was not what I was looking for because I needed the number of deaths of females due to AIDS. I went back to the website www.assa.org.za/downloads/aids/summarystats.htm where the total number of AIDS deaths were but did not find any information for the number of female deaths from AIDS. Therefore I could not make my conclusion based on that fact, but the graph for both genders does show there is some relationship between the number of new AIDS orphans and the number of new AIDS deaths each year. Unfortunately, the data was not available but I think if it was the correlation would prove my hypothesis.