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

10. Log Normal - Epidemic Curve ExposureMedian - 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. Normal Curve: Corresponding Z Scores -3-20123

14. Normal Curve: Area Under the Curve -3-20

15. Normal Curve: Area Under the Curve -3-20

16. Z Cumulative p Scale Probability Under Curve p x 10 4 - 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. Normal Curve: Z score, probabilities and Area Under the Curve 1915 14989194401664913 -3-2.5 -2.0-1.5 -0.5 0Z:

18. Histogram with Corresponding Area Under the Curve Identified

19. Cases First Ratio Second Ratio 13 49 3.3880.782 166 2.6510.788 440 2.0870.781 919 1.6300.784 1498 1.2780.782 1915 1.0000.782 1498 0.7820.784 919 0.6130.781 440 0.4790.787 166 0.3770.783 49 0.295 13

20. R o =  cD R o = Reproductive Rate (# 2 0 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: R o > 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 Michael V. O’Shaughnessy University of British Columbia BC Centre for Excellence in HIV/AIDS CHÉOS St. Paul’s Hospital Martin T. Schechter Michael 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 Life expectancy of men in the DTES (1992) Canada 1930

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

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

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

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 4.93 5.73 3.83 seroprevalentVIDUS seroincidentVIDUS seroconverterstudy

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 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 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 primary infection (first 3 months) concurrent networks their interaction

39. IDU Simulations - Vancouver N = 100,000 ß a = 0.1 ß b = 0.002 c = 2.5 D a = 3 mos N = 100,000 ß a = 0.1 ß b = 0.002 c = 2.5 D a = 3 mos monthly incidence

40. IDU Simulations N = 100,000 ß a = 0.1 ß b = 0.002 c = 2.5 » 4.5 D a = 3 mos N = 100,000 ß a = 0.1 ß b = 0.002 c = 2.5 » 4.5 D a = 3 mos

41. IDU Simulations N = 100,000 ß a = 0.1 ß b = 0.002 c = 2.5 » 4.5 D a = 3 mos N = 100,000 ß a = 0.1 ß b = 0.002 c = 2.5 » 4.5 D a = 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) 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 Epidemic Deadly 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 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) 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 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 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 de-institutionalization of mentally ill –without community services

51. Psychiatric Beds in Vancouver as well, places for treatment have fallen from 5000+ to < 800

52. MENTAL HEALTH 25% of VIDUS participants report a diagnosis of mental illness 31% of seroconverters report a diagnosis of mental illness 25% of VIDUS participants report a diagnosis of mental illness 31% of seroconverters report a diagnosis of mental illness

53. Blueprint for an Epidemic - 2 de-institutionalization of mentally ill –without community services synchronous welfare cheques –late in month, money scarce –promotes group purchase and sharing de-institutionalization of mentally ill –without community services synchronous welfare cheques –late in month, money scarce –promotes group purchase and sharing

54. Blueprint for an Epidemic - 2 de-institutionalization of mentally ill –without community services synchronous welfare cheques –late in month, money scarce –promotes group purchase and sharing inadequate detox facilities de-institutionalization of mentally ill –without community services synchronous welfare cheques –late in month, money scarce –promotes group purchase and sharing inadequate detox facilities

55. Blueprint for an Epidemic - 2 de-institutionalization of mentally ill –without community services synchronous welfare cheques –late in month, money scarce –promotes group purchase and sharing inadequate detox facilities inadequate addiction treatment de-institutionalization of mentally ill –without community services synchronous welfare cheques –late in month, money scarce –promotes group purchase and sharing inadequate detox facilities inadequate addiction treatment

56. Blueprint for an Epidemic - 3 prisons –no harm reduction –inmates learn to use dirty injection equipment prisons –no harm reduction –inmates learn to use dirty injection equipment

57. Blueprint for an Epidemic - 3 prisons –no harm reduction –inmates learn to use dirty injection equipment funding of needle exchange on “soft” money –syringe limits, lack of secondary exchange –additional services not targeted to NEP users prisons –no harm reduction –inmates learn to use dirty injection equipment funding of needle exchange on “soft” money –syringe limits, lack of secondary exchange –additional services not targeted to NEP users

58. Blueprint for an Epidemic - 3 prisons –no harm reduction –inmates learn to use dirty injection equipment funding of needle exchange on “soft” money –additional services not targeted to NEP users split responsibility - not shared –federal/provincial/regional –different ministries, different silos –aboriginals prisons –no harm reduction –inmates learn to use dirty injection equipment funding of needle exchange on “soft” money –additional services not targeted to NEP users split responsibility - not shared –federal/provincial/regional –different ministries, different silos –aboriginals

59. Deadly Public Policy