The mysterious emergence of HIV/AIDS

• Malthus’s ghost: is this a XXth century ‘positive’ check? Where does it come from?

• Runs counter to the idea that health improvements are irreversible: nasty consequences endure after we learned to reach expectancies at birth of 80 yrs

• The global magnitude of the epidemic

Adults and children estimated to be Adults and children estimated to be living living

with HIV/AIDS as of end 1999with HIV/AIDS as of end 1999Western Europe

520 000520 000North Africa & Middle East

220 000220 000sub-Saharan

Africa

24.5 24.5 millionmillion

Eastern Europe & Central Asia

420 000420 000

South & South-East Asia 5.6 million5.6 million

Australia & New Zealand

15 00015 000

North America

900 000900 000Caribbean

360 000360 000

Latin America

1.3 1.3 millionmillion

Total: 34.3 Total: 34.3 millionmillion

East Asia & Pacific

530 000530 000

A global view of HIV infectionA global view of HIV infection 33 million adults living with HIV/AIDS 33 million adults living with HIV/AIDS

as of end 1999as of end 1999

Adult prevalence rate

15.0% – 36.0% 5.0% – 15.0% 1.0% – 5.0% 0.5% – 1.0% 0.1% – 0.5% 0.0% – 0.1% not available

Estimated adult and child deaths Estimated adult and child deaths from HIV/AIDS during 1999from HIV/AIDS during 1999

Western Europe

6 8006 800North Africa & Middle East

13 00013 000sub-Saharan

Africa

2.2 2.2 millionmillion

Eastern Europe &Central Asia

8 5008 500East Asia & Pacific

18 00018 000South & South-East Asia

460 000460 000

Australia & New Zealand

< 200< 200

North America

20 00020 000Caribbean

30 00030 000

Latin America

48 00048 000

Total: 2.8 Total: 2.8 millionmillion

Reserved for figures on life expectancy

Estimated number of adults and Estimated number of adults and childrenchildren

newly infected with HIV during newly infected with HIV during 19991999

Western Europe

30 00030 000North Africa & Middle East

20 00020 000sub-Saharan

Africa

4.0 4.0 millionmillion

Eastern Europe &Central Asia

130 000130 000East Asia & Pacific

120 000120 000South & South-East Asia

800 000800 000

Australia & New Zealand

500500

North America

45 00045 000Caribbean

60 00060 000

Latin America

150 000150 000

Total: 5.4 Total: 5.4 millionmillion

Puzzling features

• Geographic contours: different patterns of the disease (infectivity, incubation, mortality)

• Perplexing geographic distribution in continental Africa: the East vs West and North vs South cleavage

Spread of HIV over timeSpread of HIV over timein sub-Saharan Africa, 1984 to 1999in sub-Saharan Africa, 1984 to 1999

Estimated percentage of adults

(15–49) infected with HIV 20.0% – 36.0%10.0% – 20.0% 5.0% – 10.0% 1.0% – 5.0% 0.0% – 1.0%trend data unavailable

outside region

Healthy HIV+ AIDS

Death

A simple framework to understand the diffusion of HIV/AIDS

• Initially, the epidemic may grow exponentially;

• This can be expressed as:

• HIV(t)=HIV(0)*exp(rt)

Implications

In 1970 we must have had a few hundred HIV+cases; assume we had 1000=103 cases. In 2000 itis estimated we will have between 30 and 40 million cases.

This means that:

(a) the rate of increase of HIV cases is approximately .35 per year and

(b) the doubling time is about 2.0 years.

CBR and CDR of HIV• CBR must depend

on :

• No of susceptible contacts per infected person

• Conditional probability of infection

• CDR must depend on

• Rate of attrition of HIV individuals

• Equivalent to rate of incubation (if mortality as AIDS is very high)

NRR of HIV• The rate of growth of HIV must be (approx)

• r HIV = CBRHIV-CDRHIV=ι*c – δ

• The first parameter, ι, is the infectivity per effective contact

• The second parameter, c, is the average number of partners per person per year

• The is the rate of incubation (see assumptions in lecture)

Then, it follows that…

• NRRHIV= exp (rHIV* (1/δ))

• and, assuming rHIV is small,

• NRRHIV= (c* ι)/ δ