Measure If You Can, Measure If You Can, Simulate If You MustSimulate If You Must

Joseph S. Y. LEE

Pierce K. H. CHOW

Jorgen SELDRUP

T. K. TAN

Joseph S. Y. LEE

Pierce K. H. CHOW

Jorgen SELDRUP

T. K. TAN

The QuestionsThe Questions

• How long do patients remain infectious?

• How infectious is SARS?

• How many people will get infected during the epidemic?

• Are there better public health measures to contain the spread of the virus?

Common ApproachesCommon Approaches

• Traditional methods involving complex analytic/computational ODE and/or PDE models are inadequate.

• Cellular automata–Uniform

–Non-uniform

The ModelThe Model

• Each individual is modeled as a node in a simple, undirected graph.

• An arc linking 2 nodes represents a connection between the two persons.

Simple Undirected GraphSimple Undirected Graph

An ExampleAn Example

Node 1

Node 2 Node 3 Node 4

Node 5 Node 6 Node 7 Node 8 Node 9 Node 10

Graph AbstractionGraph Abstraction

Node 1

Node 2 Node 3 Node 4

Node 5 Node 6 Node 7 Node 8 Node 9 Node 10

Modeling Social CliquesModeling Social Cliques

Node 1

Node 4

Node 5 Node 7 Node 8 Node 9 Node 10

ParametersParameters

Per-Edge ParametersConnectivity

• Family Clique is strong.• Work Clique is moderate.• Casual Clique is very weak.

Global Parameters1. Basic Infectivity2. Basic Incubation Period3. Basic Infection Period4. Clinical Probability5. …

Node 1 Node 2

Per-Node Parameters1. Immunity Level2. Recovery Rate

State Transition DiagramState Transition Diagram

Normal InfectedClinical

Dead

Subclinical

Recovered FullyRecovered

The SituationThe Situation

• 6 April 2003, 70 patients in 2 surgical wards in SGH were believed to have been exposed to the SARS virus.

• They were quarantined in 3 isolated wards in TTSH.

The SituationThe Situation

• Temperature readings were taken 4-hourly.

• Patients with temperature above a certain threshold were isolated.

• They were observed over a period of three weeks.

ObjectiveObjective

1. To see whether it is likely that there is no sub-clinical case for SARS.

2. If sub-clinical cases are likely, what is the sub-clinical rate.

Edge Setting for the Edge Setting for the graphgraph

• Patients in the same room have strong edges.

• Patients in the same ward have weak edges.

• Patients in different ward have no edge at all.

AssumptionsAssumptions

• The incubation period is set to follow a Gamma distribution (with = 6.4 days).

• Infection is independent of previous encounters.

• There is no vehicular transmission.

• Detection rate: 0.9

AssumptionsAssumptions

• Medical staff are not carriers/vectors.

• Existing medical condition does not alter the basic parameters significantly.

• Infectious period (normal = 5 days, = 1 day).

Experiment SetupExperiment Setup

1. We implement our model using Python running on FreeBSD.

2. Each simulation is run 1,000 times for a set of parameters.

3. The epidemic curve generated from the simulation is compared with the observed data.

A Sample RunA Sample Run

Result (1)Result (1)

If there is no sub-clinical case, and the virus does not survive for more than one day, then the clinical-infection rate for the patients in the ward is lower than 10%.

If the clinical probability is set to 1.0, many more people would have been

infected.

Second ObjectiveSecond Objective

We run 9000 sets of different parameter sets to find reasonable range of clinical-infection rate and clinical probability.

Our Result (2)Our Result (2)Possible range of parameters

are in the blue region:

Our Result (3)Our Result (3)

• Result consistent with observed data– If Clinical prob < 0.3

–Else• Inter-room connectivity = 0.1, clinical

infectivity < 0.2• Inter-room connectivity = 0.3, clinical

infectivity < 0.1

Future RefinementFuture Refinement

More refined individual modeling:

Just as the community acquired pneumonia, mortality rate of SARS varies across different age group. For example,

death rate from SARS in Hong Kong is– 43% (35-52%) for those over 60 years old.– 13% (10-17%) for those under 60s.

Future RefinementFuture Refinement

– Confidence level estimation of each parameter set.

– Time-series analysis.

– Application of the model on larger populations.

Thank YouThank You