Calibrating large-scale ABM models with Bayesian Emulation and History Matching

Arnau Quera-Bofarull

 April 2022 - ABM Workshop, Oxford

JUNE Collaboration: Ian Vernon, Jonathan Owen, Joseph Aylett-Bullock, Carolina Cuesta-Lazaro, Jonathan Frawley, Aidan
Sedgewick, Difu Shi, Henry Truong, Mark Turner, Joseph Walker,
Tristan Caulfield, Kevin Fong, and Frank Krauss

A case study: the JUNE epidemiological model

June Dalziel Almeida

Modelling an epidemic

Two common approaches:

1. SIR models

\frac{dS}{dt} = -\frac{\beta S I}{N}
\frac{dI}{dt} = \frac{\beta SI}{N} - \gamma I
\frac{dR}{dt} = \gamma I

Pros:

"cheap",

simple,

...

Cons:

only models "averages",

...

Two common approaches:

2. ABM models

Pros:

individual agents,

individual interactions,

...

Cons:

computational cost,

calibration,

...

Modelling an epidemic

The JUNE

agent-based model

github.com/IDAS-Durham/JUNE

Many other epi ABMs exist:

  1. Covid-sim
  2. Covasim
  3. OpenABM
  4. etc.

What makes JUNE special?

England digital twin

England Digital twin

Geography

England Digital twin

Demography

  • age  (27)
  • sex (f)
  • ethnic group (Caribbean)
  • deprivation index 2 (1-10)
  • work sector / subsector (healthcare/doctor)
  • mode of transport (public)
  • area of residence
  • super area of work

Main data source: census data (NOMIS)

~56 million agents

male

female

Demographic granularity

male

female

Some things are homogeneous, though...

Pubs in the UK

England Digital twin

Dynamics (where can people go?)

  • Residence
    • Care Home
    • Household
  • Primary activity
    • Company
    • Hospital
    • School
    • Care Home
    • University
  • Travel
    • Commute
    • National travel
  • Leisure
    • Shopping
    • Pubs / restaurants
    • Cinema
    • Gyms
    • Residence visits

City of London workers' usual residence

Matching workplace and residence

Commute

  • Census -> method of transportation.

  • Two kinds: Inner city commute, outer city commute

Hub

Hub

Venues geolocalisation

Durham student population

43 yo

38 yo

10 yo

Infection transmission

j

j

i

Intensity of contacts (per group)

Infectiousness profile

Contact

Matrix

p_i = 1- \exp\left({-\lambda_{ij}\;\Delta t}\right)

Disease Trajectory

Odds calibrated to data

import scipy

Policies

The challenge of calibration

Very detailed model, but

is it useful?

is it realistic?

can we 'fit' it?

The challenge of calibration

Unknown parameters:

  1. Location contact intensity (13)

  2. Effectiveness of policies (5)

  3. Seed cases (1)

19 parameters to fit

JUNE's computational cost

typical England run ~ 600 CPU hours / 100 GB RAM

Parallelisation by domains of equal population

JUNE's computational cost

Still too expensive

Build an emulator of the model

solution

Bayesian emulation

\text{Model: }\;\;(x_1, \dots, x_d) \to (f_1(x), \dots, f_q(x))

contact intensity in pubs

hospitalisations

f_i(x) = \text{Gaussian process}(x_A) + \text{Noise}(x)

Emulation:

Bayesian emulation

The emulator returns

\mathrm{E}[f_i(x)]
\mathrm{Var}(f_i(x))

on new unexplored points, but several orders of magnitude faster than the original model

Training the emulator

  1. Run the simulator on n points
D_i = (f_i(x^{(1)}), \dots, f_i(x^{(n)}))

and obtain:

2. Update the emulator's paramaters using Bayes linear methods

Linking the model to reality

  1. Observational

  2. Model discrepancy

z = y + e
y = f(x^*) + \epsilon

History matching

Goal: Find all sets of input parameters that lead to acceptable matches.

Method: Iteratively rule out implausible parameter sets.

Reject when

I > 3

The full picture

Train Bayesian emulator

Run emulator

O(500k) times

Run full simulation O(100) times

Discard implausible regions

Sample O(100) parameter sets from latin hypercube

Sample O(100) parameter sets from non-implausible region

Visualising the non-implausible regions

History matching in JUNE

Why we needed the complexity

JUNE reproduces infection disparities among various demographic groups thanks to its granularity.

Outlook

  1. High resolution ABM models are a powerful tool to understand social dynamics.
  2. ABM model calibration is often computationally prohibitive.
  3. Emulation + history matching enables global exploration of parameters and uncertainty quantification.

Slides: slides.com/arnauqb/abm_workshop

Paper: https://www.medrxiv.org/content/10.1101/2022.02.21.22271249v1

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