Swedish Institute for Infectious Disease Control,Karolinska Institutet,Stockholm University

Martin CamitzMacro versus micro in epidemic simulations and other

stories

Assault strategy

MacroMacrovs.vs.

MicroMicro

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

IS L R

3 events

•Number of infectious

•Infectiousness

•Incubation time •Recovery time

etc…

×289

SLIR-model

IS L R

3 events

•Incubation time •Recovery time

in Solna

•Infectious in other municipalities

•Travel intensity

•Number of infectious

•Infectiousness

in Solna

Dispersion equations

1. Pick an event

QL QR

QL QI QR

QL QI

2. Pick a time step t

3. Update intensities

QIStockholm

4. Repeat from 1.

Kalmar

Solna

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

08.00

23.00

09.00

Working At home [unemployed, retired or ill]

Traveling Visiting the emergency room

Home for the night

08.00

DaytimeInfection all places

Day nEarly morning

NighttimeInfection at home

Day n+1Early 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), 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

• Don’t need to vaccinate the whole family.

Workplace

Family

BackgroundZhenhua Wu, Lidia Braunstein, Shlomo Havlin, Eugene Stanley,

Transport in Weighted Networks: Partition into Superhighways and Roads, Physical Review Letters 96, 148702 (2006)

Random (ER) and scale free nets. Random weights.

Superhighways

Roads

Method/Result

• Remove links, lowest weight first until percolation threshold (pc) by 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.