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
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
(%)
Explosive HIV spread among IDUsprevalence quickly rising to 40% or more
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
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?
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
• first 3 months = 100 x infectious
• can infect as many people in first 3 months as in 25 later years
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
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.
What fuels these HIV epidemics?
What fuels these HIV epidemics?
• 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
Blueprint for an Epidemic - 1Blueprint 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)
Blueprint for an Epidemic - 1Blueprint 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
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
Blueprint for an Epidemic - 2Blueprint for an Epidemic - 2
• de-institutionalization of mentally ill– without community services
• 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
Blueprint for an Epidemic - 2Blueprint 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
Blueprint for an Epidemic - 2Blueprint 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
Blueprint for an Epidemic - 2Blueprint 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
Blueprint for an Epidemic - 3Blueprint 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
Blueprint for an Epidemic - 3Blueprint 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
Blueprint for an Epidemic - 3Blueprint 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
Deadly Public PolicyDeadly Public Policy