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Towards Computational Epidemiology
Using Stochastic Cellular Automata in Modeling Spread of
Diseases
Sangeeta Venkatachalam, Armin R. Mikler
Computational Epidemiology Research Laboratory
University of North Texas
Email: {venkatac, mikler}@cs.unt.edu
This research is in part supported by the National Science Foundation award: NSF-0350200
Showcase 2005 05/06/2005
Overview
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Mathematical Epidemiology
Cellular Automata and
Epidemiology
Stochastic Cellular Automata
- A Global Model
Composition Model
Experiments
Summary
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Mathematical Epidemiology
Susceptibles Infectives Removals (SIR) model
SIR state diagram
◦ A SIR model simulation of a
disease spread
◦ The graph shows the transient
curves for the susceptibles ,
infectives and removals during
the course of a disease epidemic
in a given population.
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Susceptibles Infectives Removals (SIR)
model
oHomogeneous
mixing of people
oEvery
individual makes same
contacts
oNo
demographics considered
oGeographical
considered
distances not
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The Model
Population
Disease
Parameters
Vaccination
Demographics
Interaction
factors
Distances
Data
Sets
Visualization
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Parameters considered
o Latent period
o Infectious period
o Contact
o Infectivity
o Population
o Index case
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Illustrates time-line for infection (influenza)
Multiple index cases
Location of index case
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Stochastic Cellular Automata
A Global Model
ΥC i ,j, C k ,l represents an interaction
coefficient that controls all possible
interactions between a cell Ci,j and its global
neighborhood Gi,j.
A function of inter-cell distance and cell
population density.
Definition of a Fuzzy Set
Neighborhood of cell Ci,j is global SCA
Gi,j := {(Ck,l, ΥC i ,j, C k ,l) |for all Ck,l Є C, 0 ≤ Υ Ci,j, Ck,l ≤
1}
C is a set of all cells in the CA.
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Interaction Metrics
Interaction Coefficient defined as
1/Euclidean distance between the
cells
Interaction coefficient based on
distance
Interaction coefficient based on
distance and population
Global Interaction Coefficient
Infection factor is calculated as the
ratio of interaction coefficients
between the cells and the global
interaction coefficient
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Experiments
o Spread of a disease for different
contact rates.
o Disease parameters
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Contact rates of 8, 15, 25
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Infectivity of 0.005
o As the contact rate decrease spread
of disease is slower and prolonged.
Spread of a disease for different contact rates.
o Spread of different diseases on a
specific population with fixed contact
rate.
o Disease parameters such as latency,
infectious period, infectivity and recovery
different with respect to a disease.
o The graph illustrates different diseases
spread differently in a given population
set.
Spread of different diseases in a given population
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Experiments – Behavior change
◦ Assumption : Sick or infected individuals are less
likely to make contacts during the infectious period.
◦Model adjusts the contact rate of individuals based
on the number of days infected.
◦The graph compares the infection
spread for the model with the behavior
change and without behavior changes.
◦Infection spread is slower if behavioral
change is considered.
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Distance dependence of disease spread
◦ Assumption : Individual is more
likely to make contact with some
one closer than some one farther.
◦Spread of disease is slower
when the assumption is
considered.
◦Spread of disease is distance
dependent
Comparison of spread of disease considering
and not considering distance dependence for
contacts
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Composition Model
Assumption : Sub-regions (or cells) with a
larger proportion of a certain demographic
may display increased or decrease prevalence
of a certain disease as compared to a subregion with a larger proportion of a different
demographic
Composition model reflects the
spread of the infection in each subregion.
Cell interaction is controlled by age
proportions and population
densities.
Observed Cumulative Epidemic caused by Temporally and
Spatially Distributed Local Outbreaks
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Composition Model -Experiment
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The population distribution over the region is non-uniform.
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Contacts made between cells depends on the population of the cell.
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Assumption : Regions with high population make more contacts than
regions with low population.
Simulation parameters:
Disease Simulated : Influenza like disease
Incubation period : 3 days
Infectious period: 3 days
Recovery period: 5 days
Infectivity : 0.020
Contact rate/person : 11
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Composition Model -Experiment
Population distribution over the
north Denton region.
Total Population of 110000 distributed
over a grid size of 50 * 100.
Infected Population distribution over
the north Denton region.
Total Population infected at
the end of simulation: 48000
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Contact Rate
Contact rate defines the number of contacts an
individual is involved in a day.
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May vary depending on the age or occupation of the
individual.
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Contact is considered as any situation which may lead to
a successful disease transmission.
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The graph illustrates the
epidemic curves for the same
disease parameters with varying
dcontact rates.
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be thought of as for different
demographics such as age groups
and occupation.
oEvidently
incidence is lower for
lower rates of contact.
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Experiment-- Infectivity
The probability of a contact
resulting in a successful disease
transmission depends on the
infectivity/virulence parameter
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Experiment was conducted to
analyze the prevalence of influenza
for varied levels of infectivity.
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Incidence is lower for lower
levels of infectivity.
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Epidemic curves for varied levels of infectivity
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Experiment-- Immunity
The probability of a contact with an infectious person resulting in a
successful disease transmission depends on the immunity of the individual.
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Experiment was conducted considering that people residing in a particular
region were immune to the particular virus as means of either vaccination or
previous infection.
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oThe
results show lower level of prevalence of disease in that region compared
to other regions.
Region Immunized
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Composition Model – Modeling Distance Dependence
Dichotomy introduced between local and global
interactions.
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Global interactions are between any two cells in the grid
Local interactions are within a Manhattan block distance
of given distance k.
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Incidence of disease prevalence
decreases with higher proportions
of local mixing.
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Disease prevails over a longer
period of time with higher
proportions of local mixing.
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Epidemic curves for the different rates of global and local mixing.
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Spatial Spread of Influenza simulated over
Northern Denton County with local contacts
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Index case
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Spatial Spread of Influenza simulated over Northern
Denton County with local and global contacts
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Summary
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Designing tools for investigating local disease clusters
through simulation.
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What’s New?
 Utilizing GIS and EPI information for modeling
 Combining different simulation paradigms
 Designing of a Global Stochastic CA
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The goal: Contribute to establish computational epidemiology
as a new research domain.
Showcase 2005 05/06/2005