Download Measure If You Can, Simulate If You Must

Measure If You Can,
Simulate If You Must
Joseph
Joseph S.
S. Y.
Y. LEE
LEE
Pierce
Pierce K.
K. H.
H. CHOW
CHOW
Jorgen
Jorgen SELDRUP
SELDRUP
T.
T. K.
K. TAN
TAN
The 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 Approaches
• Traditional methods involving
complex analytic/computational
ODE and/or PDE models are
inadequate.
• Cellular automata
– Uniform
– Non-uniform
The 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 Graph
An Example
Node 1
Node 2
Node 5
Node 3
Node 6 Node 7
Node 4
Node 8
Node 9 Node 10
Graph Abstraction
Node 1
Node 2
Node 5
Node 3
Node 6 Node 7
Node 4
Node 8
Node 9 Node 10
Modeling Social Cliques
Node 1
Node 4
Node 5
Node 7
Node 8
Node 9 Node 10
Parameters
1.
2.
3.
4.
5.
Global Parameters
Basic Infectivity
Basic Incubation Period
Basic Infection Period
Clinical Probability
…
Node 1
Per-Node Parameters
1. Immunity Level
2. Recovery Rate
Node 2
Per-Edge Parameters
Connectivity
• Family Clique is strong.
• Work Clique is moderate.
• Casual Clique is very weak.
State Transition Diagram
Dead
Clinical
Normal
Infected
Recovered
Subclinical
Fully
Recovered
The 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 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.
Objective
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 graph
• 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.
Assumptions
• 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
Assumptions
• Medical staff are not
carriers/vectors.
• Existing medical condition does
not alter the basic parameters
significantly.
• Infectious period (normal  = 5
days,  = 1 day).
Experiment 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 Run
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 Objective
We run 9000 sets of different
parameter sets to find reasonable
range of clinical-infection rate and
clinical probability.
Our Result (2)
Possible range of parameters
are in the blue region:
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 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 Refinement
– Confidence level estimation of each
parameter set.
– Time-series analysis.
– Application of the model on larger
populations.
Thank You