Concepts in Infectious Disease Epidemiology: Models

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Concepts in Infectious Disease Epidemiology
Models Prediction

• David Vlahov, Ph. D.

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

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Normal Curve and the Mean
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Normal Curve Corresponding Z Scores
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Normal Curve Area Under the Curve
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Normal Curve Area Under the Curve
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• 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
• ...

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Normal Curve Z score, probabilities and Area
Under the Curve
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Histogram with Corresponding Area Under the Curve
Identified
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• Cases First Ratio Second Ratio
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• 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

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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

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To Sustain an Epidemic

• Ro gt 1 but also
• ? gt 0 (transmission must be possible)
• can block with barriers
• c gt 0 (new susceptibles) can reduce contacts
• D gt0 (maintain infectiousness)
• can treat infection

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Deadly Public Policy
Martin T. Schechter Michael V. OShaughnessy Univ
ersity of British Columbia BC Centre for
Excellence in HIV/AIDS CHÉOS St. Pauls Hospital
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59 years

• Life expectancy of men in the DTES (1992)
• Canada 1930

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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
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Explosive HIV spread among IDUsprevalence
quickly rising to 40 or more
80
Myanmar
HIV prevalence ()
60
Manipur Yunnan
Edinburgh
40
Ho Chi Minh City
Bangkok
20
Odessa
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Explosive HIV spread among IDUsprevalence
quickly rising to 40 or more
80
Myanmar
HIV prevalence ()
60
Manipur Yunnan
Edinburgh
Vancouver
40
Ho Chi Minh City
Bangkok
20
Odessa
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Injection Drug Users (Vancouver)
Long standing pattern - low incidence - stable
prevalence
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IDUs in Vancouver
- explosive outbreak - annual rates as high as 19
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What fuels these HIV epidemics?
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Viral Load (primary vs. latent)Vancouver Data
seroconverter study
seroincident VIDUS
seroprevalent VIDUS
5.73
4.93
3.83
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Implications

• first 3 months 100 x infectious

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Implications

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

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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

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Concurrency (sterile syringes)
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Concurrency (monogamy)
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Concurrency (2-core)
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Concurrency Simulations
increasing concurrency
Morris M, Kretzschmar M. Concurrent partnerships
and the spread of HIV. AIDS 1997 11641-8.
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What fuels these HIV epidemics?

• primary infection (first 3 months)
• concurrent networks
• their interaction

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IDU Simulations - Vancouver
N 100,000 ßa 0.1 ßb 0.002 c 2.5 Da 3
mos
monthly incidence
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IDU Simulations
N 100,000 ßa 0.1 ßb 0.002 c 2.5 4.5 Da
3 mos
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IDU Simulations
N 100,000 ßa 0.1 ßb 0.002 c 2.5 4.5 Da
3 mos
incidence
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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)

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Blueprint for an EpidemicDeadly Public Policy
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Blueprint for an Epidemic - 1

• concentration of IDUs in small geographical area

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Blueprint for an Epidemic - 1

• concentratation of IDUs in small geographical
  area
• inadequate housing
• use of SROs

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Social Housing Starts per Year (Vancouver)
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Blueprint for an Epidemic - 1

• concentratation of IDUs in small geographical
  area
• inadequate housing
• use of SROs
• nightly exit fees (still in effect)

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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

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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

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Blueprint for an Epidemic - 2

• de-institutionalization of mentally ill
• without community services

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Psychiatric Beds in Vancouver
as well, places for treatment have fallen from
5000 to lt 800
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MENTAL HEALTH

• 25 of VIDUS participants report a diagnosis of
  mental illness
• 31 of seroconverters report a diagnosis of
  mental illness

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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

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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

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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

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Blueprint for an Epidemic - 3

• prisons
• no harm reduction
• inmates learn to use dirty injection equipment

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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

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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

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Deadly Public Policy