1. Vaccinations Strategies on the Transmission of the Hepatitis
B virus in Norway: Dynamic Modeling Approach
Ioana Bradeanu
University of Oslo, Norway

2. 12. June 2012 14th Biennial European Meeting of the Society for Medical Decision Making Oslo, Norway 3
NO CONFLICT OF INTERESTS

3. Hepatitis B in Norway
• Should universal vaccination against
hepatitis B be included in Norway?
• Health Council advice: vaccinate risk groups,
children with parent from high endemic
country
• Screening of all pregnant women was
recommended in 2007 by a Working Group
but is still not implemented.
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4. Geographic Distribution of Hepatitis B
Prevalence, 2007
12. June 2012 14th Biennial European Meeting of the Society for Medical Decision Making Oslo, Norway 5
Source: CDC

5. Incidence of notified cases of acute
HBV infection (1977-2011)
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Source: MSIS.no, Norwegian Institute for Public Health
Rimseliene et al. 2011

6. Age of infection in relation to probability of
becoming a persistent carrier of HBV
Age (years) Patients
becoming
carriers (%)
< 1 70 - 90
2-3 40 - 70
4-6 10 - 40
> 7 6 - 10
Shapiro CN. ’Epidemiology of hepatitis B ’ Pediatr Infect Dis J, 1993:12:443-447
Underreporting?
75% of symptomatic
cases reported
In England
(Ramsay et al. Vaccine 1998)
Age
Numbers
infected
Frac3on
clinical
infec3ons
0-­‐4
21
9.5
5-­‐9
61
9.8
10-­‐19
58
10.3
20-­‐29
22
13.6
>30
27
33.3
McMahon et al, JID 1985
Fraction of clinical infections

7. Seroprevalence study- HUBRO data,
Oslo cohort 2000
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0.00 % 20.00 % 40.00 % 60.00 %
Western Europe
Nord Africa
Middle East
East Asia
Central America
Australia Pacific
South-East Asia
Immune
Carrier
Immigrants from HUBRO :
Carriers 1.9%
95% CI (1.3% - 2.5%)
Immunes 19.8%
95% CI (18.0% - 21.6%)

8. Research objective for modeling HBV
infection
• What is the effectiveness of universal and
risk-based vaccination policies?
• It is effective to add universal vaccination to
the current risk-based vaccination strategies?
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9. Types of heterogeneity
• Transmission routes:
-Sexual, vertical, and horizontal transmission
• Age:
Age dependent immune response (clinical symptoms)
and development of chronic carrier state
• Disease states:
Latent (1-2 months), acute (3-4 months), and chronic
stages
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10. Insights from mathematical modeling – PDE - HBV
model
– Development of dynamic transmission model with stratified by age
and sexual activity
– Sexual, horizontal and vertical transmission
– hetero- and MSM populations
– Age dependent probability of becoming chronic carrier
– Includes immigration of carriers
Model used to assess effects of vaccination
∂Xgs
∂t
+
∂Xgs
∂a
= ΨVgs t,a( )− λgs t,a( )+ 1− umυe( )γcβ3 a( )+Φ a( )+Φm a( )+ ςgs a( )+θd a( )[ ]Xgs t,a( )
∂Hgs
∂t
+
∂Hgs
∂a
= λgs t,a( )+ 1− umυe( )γcβ3 a( )[ ]Xgs t,a( )− σ1 −θd a( )( )Hgs t,a( )
∂Ygs
∂t
+
∂Ygs
∂a
= σ1Hgs t,a( )− σ2 −θd a( )( )Ygs t,a( )
∂Zgs
∂t
+
∂Zgs
∂a
= 1− p a( )( )σ2Ygs t,a( )+ σ3 −θd a( )( )Cgs t,a( )+ ρθγz d a( )ωgsN
∂Cgs
∂t
+
∂Cgs
∂a
= p a( )σ2Ygs t,a( )− σ3 +θd a( )( )Cgs t,a( )+ ρθγcd a( )ωgsN
∂Vgs
∂t
+
∂Vgs
∂a
= Φ a( )+Φm a( )+ ςgs a( )[ ]Xgs t,a( )− Ψ+θd a( )( )Vgs t,a( )
Kretzschmar et al. Vaccine 2009
Kretzschmar et al. Epidemiol Infect 2002
Escalator Boxcar Train (EBT)
Phyton, C++

11. Susceptible
Latent
infection
Acute
infection
Vaccinated
Chronic
carrier
Immune
birth
birth
birth
HBV Model
Age as continous variable
6 exual activity classes
Kretzschmar et al. Vaccine 2009
Kretzschmar et al. Epidemiol Infect 2002
Williams et al. Epidemiol Infect 1996

12. Parameter assigments
• Length of simulation run 50 years
• Total population size (N) 4.9 mil
• Transmission coefficients (/year/partner)
• Heterosexuals Homosexuals
• Acute infections 0.33 0.46
• Carriers 0.25 0.30
• Rates of leaving defined compartments (per year)
• Latent class : 8,66
• Acute infection class: 3.76
• Carrier state: 0.015
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13. 6 sexual activity classes: Sexual behaviour
data, Norway 2002
11. april 2011 14
Heterosexual population
MSM population
The rates of partner change (per annum), by age class

14. Endemic equilibrium Norway
20% immigrants
• low ---------------Hetero------MSM-----------------------
• carrier % 0.42 0.87
• Immune% 5.20 12.5
• Incidence 48.9 392
• medium --------------------------------------
• carrier % 0.60 1.14
• Immune% 6.06 14.5
• Incidence 66.6 462
• high -------------------------------------------
• carrier % 0.79 1.38
• Immune% 6.86 16.3
• Incidence 82.4 516
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Estimates from HUBRO data
Scenarios: Carrier & Immune
low: 1.3% 18.0%
medium: 1.9% 19.8%
high: 2.5% 21.6%
annual immigration/capita/year: 0.008
Only screening, no mass vaccine,
no horizontal transmission

15. Total population, age distribution, initial state, no
screening, no vaccination
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16. Incidence of acute and chronic carriers by age
within the total population
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17. 18
Prevalence Incidence

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20. Conclusions
• In our model the estimates of infections were based
on seroprevalence study of the prevalence of
hepatitis B carrier state in the general population and
estimates of the carrier prevalence in immigrant
groups.
• The incidence in the model is higher than the
incidence of notified acute infections in Norway, 80%
of symptomatic infection.
Reasons: higher immigration rate, highly active
heterosexual population.
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21. Acknowledgment
• Mirjam Kretzschmar, University medical
Centre Utrecht, RIVM, The Netherlands
• Olav Dalgård, AHUS, Norway
• Synne Sandbu, Norwegian Institute for Public
Health, Norway
Thank you !
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