1. 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

2. Adults and children estimated to be living with HIV/AIDS as of end 1999 Western Europe 520 000 North Africa & Middle East 220 000 sub-Saharan Africa 24.5 million Eastern Europe & Central Asia 420 000 South 5.6 million & South-East Asia 5.6 million Australia & New Zealand 15 000 North America 900 000 Caribbean 360 000 Latin America 1.3 million Total: 34.3 million East Asia & Pacific 530 000

3. A global view of HIV infection 33 million adults living with HIV/AIDS as 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

4. Estimated adult and child deaths from HIV/AIDS during 1999 Western Europe 6 800 North Africa & Middle East 13 000 sub-Saharan Africa 2.2 million Eastern Europe & Central Asia 8 500 East Asia & Pacific 18 000 South & South-East Asia 460 000 Australia & New Zealand < 200 North America 20 000 Caribbean 30 000 Latin America 48 000 Total: 2.8 million

5. Reserved for figures on life expectancy

6. Estimated number of adults and children newly infected with HIV during 1999 Western Europe 30 000 North Africa & Middle East 20 000 sub-Saharan Africa 4.0 million Eastern Europe & Central Asia 130 000 East Asia & Pacific 120 000 South & South-East Asia 800 000 Australia & New Zealand500 North America 45 000 Caribbean 60 000 Latin America 150 000 Total: 5.4 million

7. 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

8. Spread of HIV over time in 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

16. HealthyHIV+AIDS Death    

21. 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)

22. Implications In 1970 we must have had a few hundred HIV+cases; assume we had 1000=10 3 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.

23. 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)

24. NRR of HIV The rate of growth of HIV must be (approx) r HIV = CBR HIV -CDR HIV =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)

25. Then, it follows that… NRR HIV = exp (r HIV * (1/δ)) and, assuming r HIV is small, NRR HIV = (c* ι)/ δ