Concepts in Infectious Disease Epidemiology: Models & Prediction

1. Concepts in Infectious Disease Epidemiology: Models & Prediction David Vlahov, Ph. D.

10. Log Normal - Epidemic Curve Exposure Median - Organism - Time of Exposure - Distribution of Cases

11. Sartwell’s Law: • The distribution of the incubation period for an infectious disease is log normal. • In a point source epidemic, the log normal distribution of cases reflects the incubation period.

12. Normal Curve and the Mean

13. -3 -2 -1 0 1 2 3 Normal Curve: Corresponding Z Scores

14. -3 -2 -1 0 Normal Curve: Area Under the Curve

15. -3 -2 -1 0 Normal Curve: Area Under the Curve

16. Z Cumulative p Scale Probability Under Curve p x 104 - 3.0 0.0013 0.0013 13 - 2.5 0.0062 0.0049 49 - 2.0 0.0228 0.0166 166 - 1.5 0.0668 0.0440 440 - 1.0 0.1587 0.0919 919 - 0.5 0.3085 0.1498 1498 0 0.5000 0.1915 1915 +0.5 0.6915 0.1915 1915 +1.0 0.7413 0.1498 1498 ...

17. 13 49 166 440 919 1498 1915 1915 Z: -2.0 -1.5 -1.0 0 -3 -2.5 -0.5 Normal Curve: Z score, probabilities and Area Under the Curve

18. Histogram with Corresponding Area Under the Curve Identified

19. Cases First Ratio Second Ratio 13 49 3.388 0.782 166 2.651 0.788 440 2.087 0.781 919 1.630 0.784 1498 1.278 0.782 1915 1.000 0.782 1498 0.782 0.784 919 0.613 0.781 440 0.479 0.787 166 0.377 0.783 49 0.295 13

20. Ro = cD Ro= Reproductive Rate (# 20 infections/infected case)  = average probability susceptible partner will be infected over duration of relationship c= average rate of acquiring new partners D = average duration of infectiousness -Anderson & May, 1988

21. To Sustain an Epidemic: Ro > 1; but also  > 0: (transmission must be possible) can block with barriers c > 0: (new susceptibles) can reduce contacts D >0: (maintain infectiousness) can treat infection

22. Deadly Public Policy Martin T. Schechter Michael V. O’Shaughnessy University of British Columbia BC Centre for Excellence in HIV/AIDS CHÉOS St. Paul’s Hospital

23. 59 years • Life expectancy of men in the DTES (1992) • Canada 1930

24. Proportion of all new HIV infections in injecting drug users: 1998-1999 100 90 80 70 60 Percentage 50 40 30 20 10 0 Canada China Latvia Malaysia Moldova Russian Ukraine Viet Nam Federation Source: National AIDS Programmes

25. 1995 1985 1993 1987 1989 1991 1983 1983 1983 1985 1985 1987 1987 1989 1989 1991 1991 1993 1993 1995 1995 Explosive HIV spread among IDUsprevalence quickly rising to 40% or more 80 Myanmar HIVprevalence (%) 60 Manipur&Yunnan Edinburgh 40 Ho Chi Minh City Bangkok 20 Odessa

26. 1995 1997 1985 1993 1983 1983 1983 1985 1985 1987 1987 1987 1989 1989 1989 1991 1991 1991 1993 1993 1995 1995 Explosive HIV spread among IDUsprevalence quickly rising to 40% or more 80 Myanmar HIVprevalence (%) 60 Manipur&Yunnan Edinburgh Vancouver 40 Ho Chi Minh City Bangkok 20 Odessa

27. Injection Drug Users (Vancouver) Long standing pattern - low incidence - stable prevalence

28. IDUs in Vancouver - explosive outbreak - annual rates as high as 19%

29. What fuels these HIV epidemics?

30. Viral Load (primary vs. latent)Vancouver Data seroconverter study seroincident VIDUS seroprevalent VIDUS 5.73 4.93 3.83

31. Implications • first 3 months = 100 x infectious

32. Implications • first 3 months = 100 x infectious • can infect as many people in first 3 months as in 25 later years

33. Implications • first 3 months = 100 x infectious • can infect as many people in first 3 months as in 25 later years • explosive epidemic behaves like an acute infectious outbreak

34. Concurrency (sterile syringes)

35. Concurrency (monogamy)

36. Concurrency (2-core)

37. Concurrency Simulations increasing concurrency Morris M, Kretzschmar M. Concurrent partnerships and the spread of HIV. AIDS 1997; 11:641-8.

38. What fuels these HIV epidemics? • primary infection (first 3 months) • concurrent networks • their interaction

39. IDU Simulations - Vancouver N = 100,000 ßa = 0.1 ßb = 0.002 c = 2.5 Da = 3 mos monthly incidence

40. IDU Simulations N = 100,000 ßa = 0.1 ßb = 0.002 c = 2.5 » 4.5 Da = 3 mos

41. IDU Simulations N = 100,000 ßa = 0.1 ßb = 0.002 c = 2.5 » 4.5 Da = 3 mos incidence

42. How to create an explosive HIV epidemic • Embark on public policies which: • promote concurrent networks • compress the population geographically so that the 2-core network is large • Wait for a spark to light the fuse and ignite an outbreak (primary infection)

43. Blueprint for an EpidemicDeadly Public Policy

44. Blueprint for an Epidemic - 1 • concentration of IDUs in small geographical area

45. Blueprint for an Epidemic - 1 • concentratation of IDUs in small geographical area • inadequate housing • use of SROs

46. Social Housing Starts per Year (Vancouver)

47. Blueprint for an Epidemic - 1 • concentratation of IDUs in small geographical area • inadequate housing • use of SROs • nightly exit fees (still in effect)

48. Blueprint for an Epidemic - 1 • concentratation of IDUs in small geographical area • inadequate housing • use of SROs • nightly exit fees (still in effect) • de facto shooting galleries

49. Blueprint for an Epidemic - 1 • concentratation of IDUs in small geographical area • inadequate housing • use of SROs • nightly exit fees • de facto shooting galleries • war on drugs • police crackdowns • force addicts into hideaways

50. Blueprint for an Epidemic - 2 • de-institutionalization of mentally ill • without community services