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A data-driven approach to dynamic face-to-face contacts in structured populations Gnter Schneckenreither Information and Sofware Engineering Vienna University of Technology Gnter Schneckenreither F2F contacts in structured populations

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A data-driven approach to dynamic face-to-face contacts in structured populations

Günter Schneckenreither

Information and Sofware Engineering Vienna University of Technology

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 1 / 24

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Spread of infectious diseases

Aim

Increase the fidelity of simulations by implementing new data-driven models.

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 2 / 24

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Spread of infectious diseases

Aim

Increase the fidelity of simulations by implementing new data-driven models. = ⇒ Structured Population = ⇒ Interaction patterns = ⇒ Disease characteristics

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 2 / 24

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Spread of infectious diseases

Aim

Increase the fidelity of simulations by implementing new data-driven models. = ⇒ Structured Population ≈ Topology = ⇒ Interaction patterns ≈ Transport = ⇒ Disease characteristics ≈ Reaction

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 2 / 24

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Spread of infectious diseases

Evolution of epidemiologic models Topology Transport Reaction homogeneous population abstracted interaction simplified disease compartments along social dimensions aggregated interaction multiple disease stages individual-based models extrapolated interaction

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 3 / 24

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Spread of infectious diseases

Evolution of epidemiologic models Topology Transport Reaction homogeneous population abstracted interaction simplified disease compartments along social dimensions aggregated interaction multiple disease stages individual-based models extrapolated interaction additional heterogeneous structures pairwise interaction

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 3 / 24

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Spread of infectious diseases

Evolution of epidemiologic models Topology Transport Reaction homogeneous population abstracted interaction simplified disease compartments along social dimensions aggregated interaction multiple disease stages individual-based models extrapolated interaction additional heterogeneous structures pairwise interaction

= ⇒ Race availability of data vs. model capabilities!

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 3 / 24

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A new data-driven approach

  • 1. Demographic data

= ⇒ statistical population

  • 2. Socioeconomic data

= ⇒ structured population model

  • 3. Dataset on self-reported close proximity contacts

= ⇒ equip individuals with interaction patterns according to their attributes

  • 4. Pairwise matching

= ⇒ connect pairs of ego-centric contact information into interaction links

  • 5. Time dependent instantiations

= ⇒ to simulate dynamic interaction

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 4 / 24

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Demographic and socioeconomic data

district 1 district 2

Austria

1 2

municipalities

work place 1 work place 2 work place 3 school class 2 school class 3 school class 1 house- hold 1 house- hold 2 house- hold 3

age sex

f m

individuals

work places number and size per district, age distribution of employed population school classes number and size per district, age distribution depending on size households number and size per district, age distribution depending on size administrative structure geographic information individuals number per municipality, count, age, sex per district allocation to households same municipality, age distribution within households depending on size allocation to work places geographic proximity, size of work place, age distribution allocation to school classes geographic proximity, size of school classes, age distribution of students

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 5 / 24

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Demographic and socioeconomic data

Dataset: Statistics Austria

Sampling of individuals and blocks = ⇒ intersection of multiple statistical data sets

Person Household Schoolclass Workplace age size size size gender age distribution age distribution age distribution income school-type municipality district district district

Allocation of individuals into blocks = ⇒ first optimization problem

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 6 / 24

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Self-reported contact patterns

Dataset: [POLYMOD, FP6, SSP22-CT-2004-502084] Mossong, J., Hens, N., Jit, M., Beutels, P., Auranen, K., Mikolajczyk, R., Massari, M., Salmaso, S., Tomba, G.S., Wallinga, J., Heijne, J., Sadkowska-Todys, M., Rosinska, M., Edmunds, W.J.: Polymod Social Contact Data. Zenodo (2017).

ego (paticipant) age, gender household size, employment, school type, ... alter age, gender characterization periodicity, duration, physical contact, ... regime during work, at home, in school, ...

data errors, missing values, inconsistencies, only sub-population covered, ...

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 7 / 24

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Self-reported contact patterns

  • 1. Interpolate and extrapolate reported

contact patterns

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 8 / 24

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Self-reported contact patterns

  • 1. Interpolate and extrapolate reported

contact patterns

  • 2. Assign contact patterns to persons

= ⇒ second optimization problem

school work home leisure

  • ther

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 8 / 24

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Self-reported contact patterns

  • 1. Interpolate and extrapolate reported

contact patterns

  • 2. Assign contact patterns to persons

= ⇒ second optimization problem

  • 3. Match contact patterns into pairs

= ⇒ third optimization problem

school work home leisure

  • ther

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 8 / 24

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Summary

Theoretical model

H S H H W 6 2 3 7 8 5 4 9 1

Data-driven implementation

H S H H W 6 2 3 7 8 5 4 9 1 Günter Schneckenreither F2F contacts in structured populations 2019-10-08 9 / 24

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Summary

Theoretical model

H S H H W 6 2 3 7 8 5 4 9 1

Data-driven implementation

H S H H W 6 2 3 7 8 5 4 9 1 Günter Schneckenreither F2F contacts in structured populations 2019-10-08 9 / 24

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Summary

Theoretical model

6 2 3 7 8 5 4 9 1

Data-driven implementation

6 2 3 7 8 5 4 9 1 Günter Schneckenreither F2F contacts in structured populations 2019-10-08 9 / 24

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Summary

Theoretical model

6 2 3 7 8 5 4 9 1

Data-driven implementation

6 2 3 7 8 5 4 9 1 Günter Schneckenreither F2F contacts in structured populations 2019-10-08 9 / 24

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Summary

Theoretical model

6 2 3 7 8 5 4 9 1

Data-driven implementation

6 2 3 7 8 5 4 9 1 Günter Schneckenreither F2F contacts in structured populations 2019-10-08 9 / 24

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Discussion

Structural observations

Contact network = Social network

  • Face-to-face contacts can be instantiations of social ties.
  • Random contacts are not induced by social relations.
  • Social relations can persist without physical contact.

Block structure plays an important role

  • Organizational blocks vs. emerging communities.
  • Individual contact behavior is mainly driven by social

communities.

  • Random contacts are “weak ties”.

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 10 / 24

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Discussion

Dynamics on multiple time-scales Time-scale Network layer and data Mechanisms / simulation life-time nodes node creation and deletion (births, deaths, migration) decades social structure creation and allocation of new blocks (household, workplace) years social structure creation of new blocks, block swapping (workplaces and schoolclasses) months, weeks social ties, contact patterns new links, alteration, deletion days contact patterns sampling of random contact patterns hours contacts temporary instantiation of face-to-face contacts

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 11 / 24

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Static analysis

Topological characteristics of instantiated contacts

  • 1e+01

1e+03 1e+05 25 50 75 100

degree count (logarithmic) frequency

  • ALL

DAILY WEEKLY RANDOM

degree distribution

0.0 0.5 1.0 1.5 0.01 1.00

clustering coefficient (logarithmic) density frequency

DAILY WEEKLY RANDOM

clustering coefficient distribution

  • Aggregated degree distribution is exponential.
  • Clustering predominantly in high frequency contacts.

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 12 / 24

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Static analysis

Block size and intra-block degree distribution (School-classes)

5 10 15 20 25 30 35 size 0.00 0.05 0.10 0.15 0.20 frequency distribution of school class size by type 5 10 15 20 25 30 35 size 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 frequency distribution of school class size by region Österreich Wien Vorarlberg SO-Steiermark Linz (Stadt)

  • Block size is superposition of normal

distributions with mean n0 ≈ 20 and limited variance.

  • Degree follows power laws with exponential

cutoff in high frequency contacts at k ≈ 20.

5 10 15 20 25 30 number of contacts 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 frequency

distribution of number of contacts (school) ... non-periodic contacts monthly contacts weekly contacts daily contacts all periodic contacts

10 20 30 40 50 60 number of contacts 10-4 10-3 10-2 10-1 100 frequency

... in logarithmic scale and ...

100 101 102 number of contacts 10-4 10-3 10-2 10-1 100 frequency

... in double logarithmic scale

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 13 / 24

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Static analysis

Random intra-block contacts

Optimal matching (R-tree search)

... from contact data

Random intra-block contact allocation (ER model)

... from demographic and socioeconomic data

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 14 / 24

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Dynamic simulation

A prototypic disease

Define a SIR-type disease scenario similar to Measles:

  • average latent period of 12 days
  • average infectious period of 16 days
  • average effective infection probability of 0.6
  • 95% immunization assumed

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 15 / 24

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Dynamic simulation

The strength of weak ties

  • “Weak ties can have strong effects.” (Granovetter 1973)
  • Also in epidemic spread?
  • Different concepts of weakness:

social low frequency or random contacts algorithmic neither instantiated by triadic closure nor as intra-block contact epidemiologic low infection probability topological inter-block contacts (bridges)

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 16 / 24

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Dynamic simulation

The strength of weak ties

800 1200 1600 2000 500 1000 1500 2000 2500

time [hours] infected penalty

none frequency (strong) regime (strong) algorithmic (strong) epidemiologic (strong) topologic (strong) random freqency (weak) regime (weak) algorithmic (weak) epidemiologic (weak) topologic (weak)

prevalence

12.5 15.0 17.5 20.0 22.5 500 1000 1500 2000 2500

time [hours] new infections

incidence

  • Penalty on weak ties slows spread.
  • Penalty on strong ties increases speed of spread.

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 17 / 24

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Dynamic simulation

Basic reproduction threshold – herd immunity

Basic Reproduction Threshold:

  • “Average number of secondary infectious persons resulting from
  • ne infectious person following their introduction into a totally

susceptible population (S).”

  • Measles: R0 ≈ 12 − 18
  • Effective reproduction number Rn = R0 · S
  • Measles: Threshold for Rn < 1 is about 95%.

Effect of inhomogeneous immunization?

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 18 / 24

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Dynamic simulation

Basic reproduction threshold – herd immunity

5000 10000 15000 200 400 600

time [hours] infected placement

block regime cluster random

prevalence

  • ●
  • ●
  • 1e+01

1e+03 1e+05 20 40 60

secondary infections count (logarithmic) placement

  • block

regime cluster random

secondary infections

2 4 6 25 50 75 100

degree secondary infections placement

block regime cluster random

secondary infections by degree

block All members of selected blocks in the school-class layer are susceptible. regime Arbitrary individuals who are members of any school-class are susceptible. cluster Random nodes and their neighbors are susceptible. random Random nodes are susceptible.

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 19 / 24

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Epidemiological results

General findings:

  • Incidence of infections is not (only) due to personal attributes,

but to exposed positions in the interaction network.

  • Heterogeneity of immunization is a crucial factor.
  • Strength of weak ties.

Model capabilities:

  • Simulation of transmission trajectories and vectors.
  • Simulation immunization scenarios.

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 20 / 24

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A data-driven approach to dynamic face-to-face contacts in structured populations

Information and Sofware Engineering Vienna University of Technology

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 21 / 24

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Index-based search strategies

Exact matching of target attributes. The regime, day of week and periodicity of joined contact patterns should match exactly. Asymmetric allocation. The ego-age and alter-age of two contact patterns must be matched asymmetrically. Disallow multiple links. A matched pair of contact requests is immediately stored as a link in a graph data structure. Before a pair of contact requests is joined, the graph is queried for already existing links. Intra-block allocation. Contact request matching can be restricted to individuals within the same

  • block. This is wanted for generating contacts within households, school classes or

workplaces (the block model). Bounding boxes. In order to restrict deviation of certain attributes from their target value it is possible to define bounding boxes in arbitrary dimensions. This strategy can be extended with iterative relaxation of bounding criteria. Assortative matching. Bounding boxes can be used for assortative matching of attributes like income and geographic position. Triadic closure. Based on already established links in the graph new links which close open triangles can be preferred. This technique is required for reproducing clustering effects which are not covered by the block model. Nearest neighbor. In certain circumstances nearest neighbor search can be used if other strategies fail to deliver enough matched pairs. Random contact allocation. Can be an alternative model for matching contacts within blocks.

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 22 / 24

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Implementation and algorithms

  • Aim: 8 million individuals

Currently: 400,000 individuals on a PC in a couple of hours

  • Large scale optimization problems
  • Heuristic search strategies based on R-trees:

Subpopulations can be matched in parallel.

  • Simulated annealing:

Subpopulations in parallel, additional parallel strategies?

  • Implementation: Python, C++ Boost, R
  • High memory usage, exponential runtime

Günter Schneckenreither F2F contacts in structured populations 2019-10-08 23 / 24

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Visualization

  • Very large number of edges.
  • Fixed geographic positions.
  • Use GIS sofware for static images.

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