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

Concepts in Infectious Disease Epidemiology: Models &

Prediction

David Vlahov, Ph. D.

Log Normal - Epidemic Curve

Exposure Median

- Organism

- Time of Exposure

- Distribution of Cases

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.

Normal Curve and the Mean

Normal Curve: Corresponding Z Scores

-3 -2 -1 0 1 2 3

Normal Curve: Area Under the Curve

-3 -2 -1 0

Normal Curve: Area Under the Curve

-3 -2 -1 0

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

...

Normal Curve: Z score, probabilities and Area Under the Curve

1915191514989194401664913

-3 -2.5 -2.0 -1.5 -1.0 -0.5 0Z:

Histogram with Corresponding Area Under the Curve Identified

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

Ro = cD

R o = 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

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

Deadly Public PolicyDeadly Public Policy

Martin T. SchechterMichaelMichael V. O’Shaughnessy

University of British ColumbiaBC Centre for Excellence in HIV/AIDS

CHÉOSSt. Paul’s Hospital

Martin T. SchechterMichaelMichael V. O’Shaughnessy

University of British ColumbiaBC Centre for Excellence in HIV/AIDS

CHÉOSSt. Paul’s Hospital

59 years Japan 77Sweden 77Australia 77Canada 76Netherlands 75….….….Libya 63Egypt 60DTES 59Mongolia 59Bosnia 58Liberia 57….

• Life expectancy of men in the DTES (1992)

• Canada 1930

• Life expectancy of men in the DTES (1992)

• Canada 1930

Proportion of all new HIV infections inProportion of all new HIV infections ininjecting drug users: injecting drug users:

1998-19991998-1999

Proportion of all new HIV infections inProportion of all new HIV infections ininjecting drug users: injecting drug users:

1998-19991998-1999

0

10

20

30

40

50

60

70

80

90

100

CanadaCanada ChinaChina LatviaLatvia MalaysiaMalaysia MoldovaMoldova RussianRussianFederationFederation

UkraineUkraine Viet NamViet Nam

Source: National AIDS ProgrammesSource: National AIDS Programmes

Per

cen

tag

e

2020

4040

6060

808019

8319

83

1985

1985

1987

1987

1989

1989

1991

1991

1993

1993

1995

1995

HIV

pre

vale

nce

(%)

Explosive HIV spread among IDUsprevalence quickly rising to 40% or more


EdinburghEdinburgh

BangkokBangkok

MyanmarMyanmar

Manipur & YunnanManipur & Yunnan

OdessaOdessa

Ho Chi Minh CityHo Chi Minh City

1983

1983

1985

1985

1987

1987

1989

1989

1991

1991

1993

1993

1995

1995

1983

1983

1985

1985

1987

1987

1989

1989

1991

1991

1993

1993

1995

1995

2020

4040

6060

808019

8319

83

1985

1985

1987

1987

1989

1989

1991

1991

1993

1993

1995

1995

HIV

pre

vale

nce

(%)



EdinburghEdinburgh

BangkokBangkok

MyanmarMyanmar

Manipur & YunnanManipur & Yunnan

OdessaOdessa

Ho Chi Minh CityHo Chi Minh City

1983

1983

1985

1985

1987

1987

1989

1989

1991

1991

1993

1993

1995

1995

1983

1983

1985

1985

1987

1987

1989

1989

1991

1991

1993

1993

1995

1997

1995

1997

VancouverVancouver

Injection Drug Users (Vancouver)

Injection Drug Users (Vancouver)

0

5

10

15

20

1981 1983 1985 1987 1989 1991 1993 1995

0

5

10

15

20

1981 1983 1985 1987 1989 1991 1993 1995

Long standing patternLong standing pattern- low incidence- low incidence- stable prevalence- stable prevalence

IDUs in VancouverIDUs in Vancouver

0

5

10

15

20

1981

.08

1983

.08

1985

.08

1987

.08

1989

.08

1991

.08

1993

.08

1995

.08

1997

.08

0

5

10

15

20

1981

.08

1983

.08

1985

.08

1987

.08

1989

.08

1991

.08

1993

.08

1995

.08

1997

.08

- explosive outbreak- explosive outbreak- annual rates as high as 19%- annual rates as high as 19%

What fuels these HIV epidemics?


Viral Load (primary vs. latent)Vancouver Data

Viral Load (primary vs. latent)Vancouver Data

1

10

100

1000

10000

100000

1000000

10000000

100000000

1

10

100

1000

10000

100000

1000000

10000000

100000000

4.934.93

5.735.73

3.833.83

seroprevalentseroprevalentVIDUSVIDUS

seroincidentseroincidentVIDUSVIDUS

seroconverterseroconverterstudystudy

Implications

• first 3 months = 100 x infectious• first 3 months = 100 x infectious

Implications

• first 3 months = 100 x infectious

• can infect as many people in first 3 months as in 25 later years



Implications



• explosive epidemic behaves like an acute infectious outbreak



• explosive epidemic behaves like an acute infectious outbreak

Concurrency (sterile syringes)

Concurrency (sterile syringes)

Concurrency (monogamy)Concurrency (monogamy)

Concurrency (2-core)Concurrency (2-core)

Concurrency SimulationsConcurrency Simulations

0

200

400

600

800

1000

1200

1400

1600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

200

400

600

800

1000

1200

1400

1600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7increasing increasing concurrencyconcurrency

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



• primary infection (first 3 months)

• concurrent networks

• their interaction

• primary infection (first 3 months)

• concurrent networks

• their interaction

IDU Simulations - VancouverIDU Simulations - Vancouver

050

100150200250300350400450500

1981 1983 1985 1987 1989 1991 1993 1995

050

100150200250300350400450500

1981 1983 1985 1987 1989 1991 1993 1995

N = 100,000N = 100,000ßßaa = 0.1 = 0.1

ßßbb = 0.002 = 0.002

c = 2.5c = 2.5DDaa = 3 mos = 3 mos

N = 100,000N = 100,000ßßaa = 0.1 = 0.1

ßßbb = 0.002 = 0.002

c = 2.5c = 2.5DDaa = 3 mos = 3 mos

monthly incidencemonthly incidence

IDU SimulationsIDU Simulations

N = 100,000N = 100,000ßßaa = 0.1 = 0.1

ßßbb = 0.002 = 0.002

c = 2.5 » 4.5c = 2.5 » 4.5DDaa = 3 mos = 3 mos

N = 100,000N = 100,000ßßaa = 0.1 = 0.1

ßßbb = 0.002 = 0.002

c = 2.5 » 4.5c = 2.5 » 4.5DDaa = 3 mos = 3 mos

IDU SimulationsIDU Simulations

0

500

1000

1500

2000

2500

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999

0

500

1000

1500

2000

2500

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999

N = 100,000N = 100,000ßßaa = 0.1 = 0.1

ßßbb = 0.002 = 0.002

c = 2.5 » 4.5c = 2.5 » 4.5DDaa = 3 mos = 3 mos

N = 100,000N = 100,000ßßaa = 0.1 = 0.1

ßßbb = 0.002 = 0.002

c = 2.5 » 4.5c = 2.5 » 4.5DDaa = 3 mos = 3 mos

incidenceincidence

How to create an explosive HIV epidemic

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)

Blueprint for an Epidemic

Deadly Public Policy

Blueprint for an Epidemic

Deadly Public Policy

Blueprint for an Epidemic - 1Blueprint for an Epidemic - 1

• concentration of IDUs in small geographical area

• concentration of IDUs in small geographical area

Blueprint for an Epidemic - 1Blueprint 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

Social Housing Starts per Year (Vancouver)

Social Housing Starts per Year (Vancouver)

0

100

200

300

400

500

600

700

800

1990 1991 1992 1993 1994 1995 1996

0

100

200

300

400

500

600

700

800

1990 1991 1992 1993 1994 1995 1996


area

• inadequate housing– use of SROs– nightly exit fees (still in effect)


• inadequate housing– use of SROs– nightly exit fees (still in effect)


area

• inadequate housing– use of SROs– nightly exit fees (still in effect)– de facto shooting galleries


• inadequate housing– use of SROs– nightly exit fees (still in effect)– de facto shooting galleries

Blueprint for an Epidemic - 1Blueprint 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


• de-institutionalization of mentally ill– without community services


Psychiatric Beds in VancouverPsychiatric Beds in Vancouver

175

200

225

250

1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

175

200

225

250

1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

• as well, places for treatment have fallen from 5000+ to < 800• as well, places for treatment have fallen from 5000+ to < 800

MENTAL HEALTHMENTAL 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



• synchronous welfare cheques– late in month, money scarce– promotes group purchase and sharing






• inadequate detox facilities



• inadequate detox facilities




• inadequate detox facilities• inadequate addiction treatment



• inadequate detox facilities• inadequate addiction treatment


• prisons

– no harm reduction – inmates learn to use dirty injection equipment

• prisons



• prisons


• funding of needle exchange on “soft” money– syringe limits, lack of secondary exchange– additional services not targeted to NEP users

• prisons


• funding of needle exchange on “soft” money– syringe limits, lack of secondary exchange– additional services not targeted to NEP users

Blueprint for an Epidemic - 3Blueprint for an Epidemic - 3• prisons


• 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

Deadly Public PolicyDeadly Public Policy

Documents

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