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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