Predicting

HIV Effects Model

Courtney Larson

South Africa

Description & HIV/AIDS Prevalence

Description of South Africa

South Africa, the southernmost country on the African continent, renowned for its varied topography, great natural beauty, and cultural diversity, all of which have made the country a favoured destination for travelers since the legal ending of apartheid (Afrikaans: “apartness,” or racial separation) in 1994.

(South Africa, Encyclopaedia Britannica)

(Gonzalez, Arturo Lavin, South African Roads)

(Viseux, Christophe, South African Girl At Mandela's Funeral)

HIV/AIDS In South Africa

HIV/AIDS is responsible for South Africa’s average life expectancy plunging to less than 43 years in 2008; it has rebounded to 63 years as of 2017. HIV/AIDS continues to be a serious public health threat, although awareness-raising campaigns and the wider availability of antiretroviral drugs is stabilizing the number of new cases, enabling infected individuals to live longer, healthier lives, and reducing mother-child transmissions.

(AFRICA::SOUTH AFRICA, Central Intelligence Agency)

(Aids Symptoms, Google)

Estimating Change In Personal Income

Average Income Of Someone With(out) Aids/Hiv Over The Next 10 Years

Averages

Average Income In South Africa:

$12,260

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Average Annual Income Increase:

1.5%

Average Income In South Africa Over The Next 10 Years:

$145,527.04

Average Annual Income Decrease With AIDS/HIV:

-1.1%

Average Income With AIDS/HIV In South Africa Over The Next 10 years:

$127,720.24

Income Growth/Decay Equations

Average income of person without aids equation:

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y = 12260e^0.015x

Average income of person with aids equation:

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y = 12260e^-0.011x

Variables:

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y: Income

x: years after 2018

Chart of Income Growth/Decay Equations

Graph of Income Growth/Decay Equations

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y = 12260e^0.015x

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y = 12260e^-0.011x

Estimating The Value of Eradicating HIV/AIDS

Calculating The Total Income Gained By Eradicating Hiv/Aids Over A 10 Year Period

Income Without HIV/AIDS

Total Income Of A Person Without Aids Over 10 Years In South Africa:�$145,527.04 =

12260 + 12445.29 + 12633.37 + 12824.3 + 13018.12 + 13214.86 + 13414.57 + 13617.31 + 13823.11 + 14032.02 + 14244.09 �Average Total Income Of South Africa Without Aids Over 10 Years:�$8.14E+12 =

145527.04 * 55910000�

Income With HIV/AIDS

Total Income Of A Person With Aids Over 10 Years:�$127,720.24 =

12260 + 12125.88 + 11993.23 + 11862.02 + 11732.26 + 11603.91 + 11476.96 + 11351.41 + 11227.23 + 11104.41 + 10982.93 �Average Total Income Of South Africa With Hiv Prevalence

(18.90% In South Africa)

$7.95E+12 =

(127720.24 * 10566990) + (145527.04 * 45343010)

Income Loss With HIV/AIDS

Average Total Amount Lost Over 10 Year Period Without Change In Aids/Hiv Prevalence:

$188,164,300,000 =

8136416800000 - 7948252500000

Reflection

Effects On Income Growth, Influence On Public Policy, Calculation Surprises, Sources of Error, Related Questions

Why might wide-spread diseases like HIV affect personal income growth in the country?

South Africa is a third-world country and as such personal income is miniscule and not supportive of a healthy or progressive lifestyle. People who contract HIV/AIDS face a degenerative disease that requires lifelong care and medical watch. Without care the disease slowly destroys the body disabling its ability to work. Due to low incomes within South Africa many can’t receive care and therefore become too weak to work. This lays the duty of income upon the children in the family, making them work long hours for even smaller pay then their parents because of little to no laws regarding child labor. With having a substantial amount of children available for employment, businesses start to choose children over healthy adults when hiring because they work for less and often for longer. This pressures adults to lower their salary expectations in order to find a job, and therefore causes competition between children and adults to see who will work for the smallest amount paid. Over time this decreases GDP within a country and familial/personal income growth for its population.

How could your calculation influence public policy in your country?

With the prevalence of HIV/AIDS so high in South Africa it has already attracted grand attention worldwide. In an effort to slow and prevent further extension of this epidemic many projects including free sex education, free health care, free antiretroviral treatments, and free screenings, have moved to South Africa. The HIV/AIDS prevalence rate hasn’t started to decrease because of inheritance of the disease, but more people every year are receiving treatment, diagnosis, and education.

What surprised you about your calculations?

The thing that surprised me the most from my calculations was how much money was lost from the average income of a person with aids/hiv in South Africa. They on average lose $17,806.8 over a 10 year period working jobs that already have poor wages. I think this number expresses how damaging AIDS/HIV is not only to the economy of a country, but to its individual people as well.

What are some sources of error?

The main source of error in my calculations was that annual income was an averaged number, found by dividing the income of the country by the population of the country. Many people make less or more than this value, which disables it from being representative of the whole country.

What related mathematical questions could you ask about these scenarios?

• How much money will be spent for medical purposes over 10 years as aids/hiv health care become more readily available in South Africa?
• At its current rate of progression, how long will it take for every person aids/hiv positive in South Africa to gain access to antiretroviral therapy?
• What is the expected income of South Africa in 10 years given that hiv/aids prevalence is decreasing?
• How long will it take South Africa’s economy to develop into that of a first world nation’s?
• What is the progression of the CD4 count in the blood over the 1st year of acquiring the disease?�

Extension

Zombie Virus

Situation

A zombie virus starts to exponentially spread amongst the population of the United states at a rate of 25% per month. How many years will it take before everyone is a decaying meat bag given you can’t have less than 1 human alive ?

(Zombie Apocalypse Wallpaper, Wallpaper Abyss)

Equation

Population of United States:

325,700,000

(U.S. and World Population Clock, United States Census Bureau)

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Equation:

y = 325700000e^-0.25x

Question We Need to Solve:

What is the value of x(number of months since start of apocalypse) when y(number of humans still alive) is less than one.

1 = 325700000e^-0.25x

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(Zombie Apocalypse Wallpaper, Wallpaper Abyss)

Graph

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(Zombie Apocalypse Wallpaper, Wallpaper Abyss)

Solve

1. y = 325700000e^-0.25x
2. 1 = 325700000e^-0.25x
3. 1/325700000 = e^-0.25x
4. ln 1/325700000 = ln e^-0.25x
5. ln 1/325700000 = -0.25x * lne

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6. ln 1/325700000 = -0.25x�7. ln 1/325700000 / -0.25 = x�8. x = 78.40594908�9. 78.41 months / 12 months = 10. x > 6.53 years�

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(Zombie Apocalypse Wallpaper, Wallpaper Abyss)

Answer

A zombie virus starts to exponentially spread amongst the population of the United States at a rate of 25% per month. It will take 6.53 years before everyone is a decaying meat bag given you can’t have less than 1 human alive.

(Zombie Apocalypse Wallpaper, Wallpaper Abyss)

THANKS!

Any questions?

You can find me at

court_larso588@ahschools.us

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Works Cited

Aids Symptoms. Google, www.google.com/search?q=aids&rlz=1C1CHBF_enUS767US768&oq=aids&aqs=chrome.0.69i59j69i60j69i61l2j0l2.621j0j7&sourceid=chrome&ie=UTF-8&safe=active&ssui=on.

“Zombie Apocalypse Wallpaper.” Wallpaper Abyss, Alpha Coders, wall.alphacoders.com/by_sub_category.php?id=176274&name=Zombie Apocalypse Wallpapers.

“AFRICA :: SOUTH AFRICA.” Central Intelligence Agency, www.cia.gov/library/publications/the-world-factbook/geos/sf.html.

Gonzalez, Arturo Lavin. “South African Roads.” Digital Photography School, Digital Photography School, digital-photography-school.com/travel-photography-inspiration-project-south-africa/.

“South Africa.” Encyclopaedia Britannica , Encyclopaedia Britannica, Incorporation , 26 May 1999, www.britannica.com/place/South-Africa.

“U.S. and World Population Clock.” United States Census Bureau, U.S Department of Commerce, www.census.gov/popclock/?intcmp=w_200x402.

Viseux, Christophe. “South African Girl At Mandela's Funeral.” Christophe Viseux Freelance Photographer, Christophe Viseux, 17 Dec. 2013, www.christophephoto.com/2013/12/mandela-funeral-documentary-photography-africa/.