Transcript Presentation - S-GEM

Swedish Institute for Infectious Disease Control,
Karolinska Institutet,
Stockholm University
Martin Camitz
Macro versus micro in epidemic simulations and other
stories
Assault strategy
Macro
vs.
Micro
Simple
Realistic
(Used without any permission whatsoever from A. Vespignani.)
Simple
Realistic
(Used without any permission whatsoever from A. Vespignani.)
Dispersion
•Person to person
–Residual viral mist
•Random mixing
•Travel
Our Travelrestrictions model
• Martin Camitz & Fredrik Liljeros, BMC
Medicine, 4:32
– Inspired by Hufnagel et al., PNAS, 2004
Swedish travel network
•
•
•
•
•
Survey data with 17000 respondents
3 year sampling duration
1 day sample
60 days for long distance
35000 intermunicipal trips
SLIR-model
etc…
3 events
L
S
•Number of
infectious
•Infectiousness
×289
•Incubation time
I
R
•Recovery time
SLIR-model in Solna
3 events
I
L
S
•Number of
infectious in Solna
•Infectiousness
•Infectious in other
municipalities
•Travel intensity
•Incubation time
R
•Recovery time
Dispersion equations
1. Pick an event
Stockholm Q L Q I
Kalmar Q L
Solna
QI
QL
QR
2. Pick a time step Dt
QR
QI
3. Update intensities
4. Repeat from 1.
Question
•
What happens if we restrict travel?
– Say longer journeys than 50 km or 20 km no
longer permitted.
Restricting travel
Restricting travel
Our agent based micromodel
• Micropox to be published
• Microsim under construction
• With Lisa Brouwers at SMI + crew
We have microdata on:
•
•
•
•
•
•
Age, sex, region…
Family
Workplace
Schools
Coordinates of all the above
Traveldata
– Improved aggregation for Microsim
– More variables
• Duration
• Traveling company
• Business trip, vacation etc
Day n
Early morning
08.00
Daytime
Infection all places
09.00
Working
23.00
At home
[unemployed,
retired or ill]
Traveling
Visiting the
emergency room
Home for the
night
Nighttime
Infection at home
08.00
Day n+1
Early morning
Calibration
• Reasonable attack rate
• A version of R0 calibrated on other
peoples version of R0
• Expected place distribution of prevalence
Place distribution of prevalence
Results for Micropox
• Targeted vaccination of ER-personel in
combination with ring vaccination (5.3)
superior to
• Mass vaccination (13.5)
• Ring vaccination only (28.0)
• ER-personell only (30.4)
Microsim disease model
• Infectivity profile and susceptibility from
Carat et al., 2006
• Certain other parameters from Ferguson,
2005
– Latency time
– Subsymptomatic infectiousness
– Death rate
Advantages
• We can model everything!
Disadvantages
• We can model everything!
Keep in mind that:
• ”All simulations are doomed to succeed.”
- Rodney Brooks
• Strive to minimize assumptions
• Comparative results only
– Possibly infer infectious disease parameters
• Sensitivity analyses
• Predictability
We still have no clue
• Disease dynamics
• Social behaviour
Reviewers dream
• Did you take inte account…
– the size of subway train compartments?
– in Macedonia child care closes at 4pm?
• It’s Sweden
– The general applicability is questionable.
– Suggest using a Watts/Strogatz network
instead.
Comparative results
• Is this a limitation?
– Vaccination policies
– Travel restrictions
– School/workplace closing
Output
•
•
•
•
Incidence
Hospital load
Place distribution
Workforce reduction
Still not convinced
• Steven Riley, Science, June 1
– ”Detailed microsimulation models have not yet
been implemented at scales larger than a
city.”
Company network
• Real data of the Swedish population,
workplaces and families
• Workplaces connected via the families of
employees
• 500 000 nodes
• 2 000 000 links
• Weighted according to probability to
transmit a disease
• Ex assign p=.5, the probability to
transmit to/from family/workplace
• Yeilds weights p(p), a probability to
transmitt workplace to workplace.
Company network
2.04
Company network
Breaking links vs nodes
• Don’t have to visit leaves.
Leaves
Breaking links vs nodes
Family
Workplace
• Don’t need to vaccinate the
whole family.
Background
Zhenhua Wu, Lidia Braunstein, Shlomo Havlin, Eugene Stanley,
Transport in Weighted Networks: Partition into
Superhighways and Roads, Physical Review Letters 96,
148702 (2006)
Superhighways
Roads
Random (ER) and
scale free nets.
Random weights.
Method/Result
• Remove links, lowest weight first until
percolation threshold (pc) by
k-method.
• The remaining largest cluster (IIC-cluster)
have a higher Betweeness Centrality than
those of the Minimum Spanning Tree.
Percolation threshold in
workplace network
• ~200 distinct weights
• Second largest cluster-method
• Remove all same-weight links, lowest first,
plotting size of the second largest cluster
• Maximum => pc
Community structure
Modularity
• M <= 0
• M = 0 for random graphs
Maximizing M
• Newman/Girvan
• Simulated annealing
• Greedy method
– New one by Aaron Clauset for large networks
Hub clusters
• Fix number of modules to 2 (or ~10).
• Fix number of nodes in all but one module
to n=100.
• Minimize M
• Then increase n in increments of 100.