1. What can modelling tell us about HIV and TB that we don’t already know?

2. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know [God’s] thoughts, the rest are details. Albert Einstein

3. Nature only uses the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry. Richard Feynman

4. 1.Why is there so much HIV in southern Africa and so little in India and Latin America? 2.Can we control TB without controlling AIDS? 3.Why does survival after infection with HIV vary from months to decades? 4.Is migration important in determining the spread of HIV. Questions for Einstein

5. 1.Is the prevalence of HIV in Harare really declining at 10% per year? 2.Are CD4 counts a useful measure of immune status for people with HIV? 3.Of TB cases in HIV+ people, what proportion are new and what proportion are reactivations? 4.What is the duration of TB disease in HIV+ and HIV- people? Questions for Feynman

6. Theories and models A model is the expression of a theory 1.Models should be as simple as possible but no simpler. 2.Always start from what is known. 3.Only add complexity as the data or the questions demand it.

7. 15 – 40 5 – 15 1 – 5 0.5 – 1 0.1 – 0.5 0.0 – 0.1 No data Prevalence of HIV among adults (%)

8. Highest per capita TB incidence in Africa 25 to 49 50 to 99 100 to 299 < 10 10 to 24 300 or more No Estimate per 100 000 population The boundaries and names shown and the designations used on this map do not imply the expression of any opinion whatsoever on the part of the World Health Organization concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. Dotted lines on maps represent approximate border lines for which there may not yet be full agreement. © WHO 2002

9. Prevalence of HIV in adults (2005) North India: 0.2% South India: 1.5% Brazil: 0.7% West Africa: 3% East Africa: 5% South Africa: 21% (Median values in Africa)

10. Kinds of models 1.Dimensional models 2.Analytical models 3.Simple compartmental models 4.Complex compartmental models 5.Stochastic models 6.Micro-simulation models 7.Network models

11. Risk factors for HIV infection Behavioural Number of sexual partners, condom use Biological Other sexually transmitted infections, gender Cultural Male circumcision, premarital sex Economic Poverty and commercial sex work Social Peer pressure and gender violence Occupational Truck drivers and mine workers

12. Risk factors for TB Behavioural Alcoholism, smoking Biological Gender, possibly race, age, HIV Economic Poverty, crowding, indoor solid fuel Occupational Silica exposure

13. Three key concepts R 0 : how many people does one person infect? Generation time T 0 : How long does it take? Steady state P 0 : Where does it settle down?

14. Doubling time = 15 months R 0 = 120/15 = 8

15. 1. Grosskurth, H., et al., Impact of improved treatment of sexually transmitted diseases on HIV infection in rural Tanzania: randomised controlled trial. Lancet, 1995. 346: p. 530-6. 2. Laga, M. STD control for HIV prevention--it works! Lancet, 1995. 346: p. 518-9. Syndromic management of sexually transmitted diseases, Mwanza, Tanzania Prevalence of STIs ~ 10% Curable STIs increase transmission ~ 5 times STIs increase HIV incidence by 0.1  5+0.9  1 = 1.4 times Measured incidence in two groups of villages Control: 0.9%/yr Intervention: 0.6%/yr Ratio: 1.6 (1.2–2.2) 1 It works! 2

16. Mwanza: Grosskurth, H., et al., Lancet, 1995 Rakai: Wawer, M.J., et al., Lancet, 1999 Masaka: Kamali, A., et al., Lancet, 2003 Control Interv. Ratio Mwanza (SM)0.90.61.61 (1.18–2.22) Rakai (MT)1.51.51.03 (0.86–1.23) Masaka (IEC+SM)0.80.81.00 (0.63–1.59) SM: syndromic management; MT: mass treatment; IEC: information, education and counselling. Three trials

17. STDSim: Micro-simulation model Individual based Stochastic Health care STI natural history and transmission Sexual behaviour Demography Interventions

18. Richard White’s conclusion …in widely disseminated HIV epidemics … STI treatment may [not be an] effective HIV prevention strategy. In less advanced … HIV epidemics [it may be an] effective … strategy, and it remains useful … in sub-populations with very high rates of STIs, such as sex workers, their clients and regular partners. Richard White Variability in the effectiveness of STI treatment interventions to prevent HIV transmission in Eastern and Southern Africa, Ph.D. Thesis. LSHTM, 2006

20.  = birth rate N = S + I = rate at which new infections occur  = mortality  S I I  N S I /N  I S  The basic model

21. R 0 = 3.3

22.  = birth rate N = S + I = infection rate  I = Weibull mortality  S I I  N S I /N  I S Normal (Weibull 2) Exponential (Weibull 1)

24.  = birth rate N = population = e –  P  I = Weibull mort. ~ ~  S I I  N S I /N  I S  –P–P e Heterogeneity in sexual behaviour

26. ~  S I I  N S I /N  I S ~  = birth rate N = population = C(t)  I = mortality ~ ~ C(t)C(t) Including control

28. ~  S I I  N S I /N  I S *  = birth rate N = population = e  I = mortality ~ * –M–M –M–M e Mortality leads to behaviour change

30. Nairobi 6 yr Nunn P et al. Tuberculosis control in the era of HIV. Nat Rev Immunol. 2005 Oct;5(10):819-26.

31. TB incidence among gold miners in SA Corbett EL Stable incidence rates of tuberculosis (TB) among human immunodeficiency virus (HIV)-negative South African gold miners during a decade of epidemic HIV-associated TB. J Infect Dis. 2003;188: 1156-63.

32. SS+ Tuberculosis Prevalence Incidence Disease Duration (%) (%/yr) (yr) HIV+ 0.44 (0.02-1.05)2.87 (1.94-4.25)0.15 (0.05-0.48) HIV-0.55 (0.14–0.95)0.48 (0.27-0.84)1.15 (0.48-1.13) DDR = 0.13 (0.09–0.20) Gold miners in South Africa We define disease duration as prevalence divided by incidence

33. Repeat the model 4 times, once for each stage of HIV. Use time series of HIV prevalence to determine incidence. Incidence gives rate at which people enter first stage; overall (Weibull) survival determines rate at which people move to next stage. TB-HIV model Williams BG et al. The impact of HIV/AIDS on the control of tuberculosis in India. PNAS 2005 102: 9619-9624.

34. Impact of interventions on TB cases in Kenya TB incidence/100k/yr 800 600 400 200 0. Baseline ARV 80% TLTI (6 m) TLTI (life) ARV 100% TB detect. TB cure HIV incid Base line: CDR = 50% CR = 70% Interventions: 1% increase 1980 2000 2020 2040 Year Currie, C. et al. Cost, affordability and cost-effectiveness of strategies to control tuberculosis in countries with high HIV prevalence. BMC, 2005. 5: 130.

35. Percent HIV positive HIV negative Williams BG et al. HIV Infection, Antiretroviral Therapy, and CD4+ Cell Count Distributions in African Populations. J Infect Dis, 2006 194: 1450-8.

36. 1,000 2,000 10 20 Time to death (yrs) Initial CD4/  L Time to death (yrs) 1,000 2,000 10 20 Initial CD4/  L Model 1 CD4 decline independent of starting value Survival determined by pre- infection CD4 Model 2 Survival independent of starting value CD4 decline determine entirely by starting value and survival distribution 

37. Spatial Epidemiology of HIV Doubling time = 1 year Life expectancy = 10 years Number of partners = 4 Proportion of random partners chosen at random = 0 (left hand set) or 10% (right hand set) in the following slides. Note that in this model migrants have exactly the same sexual behaviour and individual risk as non-migrants.

44. 1.Can we combine spatial/network models with our more conventional continuous time models of HIV? 2.Can we get a better understanding of the host-viral interaction? 3.What are the population level implications of 2? 4.Do we have enough data to explore fully the joint dynamics of TB and HIV? Questions for all of us

45. Advice to young epidemiologists Never make a calculation until you know the answer. Make an estimate before every calculation, try a simple biological argument (R 0, generation time, selection, survival, control). Guess the answer to every puzzle. Courage: no one else needs to know what the guess is. Therefore, make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case, life as an epidemiologist, however long, is more fun. Plagiarised from E.F. Taylor and J.A. Wheeler Space-time Physics 1963