Computational Modelling of Infectious Diseases using Global Stochastic Cellular Automata.

1. Epidemic and Endemic Outbreak Simulator:
A Global Stochastic Cellular Automata Approach
Presented by: Hector Cuesta-Arvizu
Advisor: Armin R. Mikler
Center for Computational Epidemiology and Response Analysis
University of North Texas
October 24, 2011
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2. Outline
Introduction (why this is important?).
Infectious Disease Model SEIR.
Infectious Disease Model SEIRS.
Cellular Automata (...the computational part).
Global Stochastic Contact Model.
Outbreak Simulator.
Vaccination Strategies.
Conclusions.
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3. Introduction
Why is this important?
The epidemiologist use Models to study the spread of an Infectious
disease outbreak.
These Models include, Mathematical, Statistical and Computational
approaches.
Simulating these models is the way that epidemiologist can observe
different outbreak outcomes.
With the simulation we can try different interventions strategies that
affects the prevalence of an Epidemic or Endemic outbreak.
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4. Infectious Disease Models
Infectious Disease Models
SEIR Susceptible-Exposed-Infected-Recovered
The SEIR models the shift of individuals’ status between four states:
susceptible (S), exposed (E), infected (I), and recovered (R). Each of
those variables represents the number of people in those groups.
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5. Infectious Disease Models
Infectious Disease Models
SEIRS Susceptible-Exposed-Infected-Recovered-Susceptible
The SEIRS differs from the SEIR model by letting recovered
individuals lose their resistance over time.
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6. Cellular Automata
Cellular Automata
What is a Cellular Automata?
Discrete model studied in computability theory and mathematics for a
non-linear problems.
Facts:
It consist of an infinite, regular grid of cells, each in one of a finite
number of states.
The grid can be any finite number of dimensions.
Each cell is a particular individual o group.
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7. Cellular Automata
Cellular Automata
Neighbourhood
The Neighbourhood is a selection of cells relative to some specified
cell and does not change.
Each cell has the same rules for updating based on the values in this
neighbourhood.
Each time the rules are applied to the whole grid a new generation is
produced.
Local an Global Neighborhoods, Von Newmnan and Moore Neighborhood
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8. Model
Model
The Global Stochastic Contact Model
The goal of this model is to describe the dynamics of an infectious
disease in a close population.
The model is a human-human Global Interaction model.
Its main purpose is the realization of contacts among individuals,
facilitating analysis of the spread of diseases
The cayley graph represent the global interaction between cells
(individuals).
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9. Model
Model
The global contact interaction
Contacts per Time Step:
CR∗N
C= 2
Total of Contacts in the Event:
Ctot = Σtπ CR∗N where te = (1, 2, 3, ..., n)
t=1 2
C = Number of interactions per each Time Step.
CR = Contact Rate.
N = Number of individual in the population.
tπ = Number of Time Steps.
Ctot = Total Number of interactions in the event
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10. Outbreak Simulator
Outbreak Simulator
Technological choices for the Simulator
The main contribution of this work is to present a software system
that incorporates a global stochastic cellular automata model.
Technological Choice:
C# .NET (as a programming language)
WindowsForms and MonoDesktop (to create graphic interface and grid
animations during simulations)
Modules:
The specification module.
The simulation module.
The visualization module.
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11. Outbreak Simulator
Outbreak Simulator
Specification and simulation modules
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12. Outbreak Simulator
Outbreak Simulator
Visualization module
In figure A we can observe the SEIR Epidemic Curve and in figure B
we can observe the SEIRS Endemic Curve.
(A)
(B)
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13. Intervention Strategies
Vaccination Strategies
Vaccination Strategies
Figure A.- Vaccination in SEIR Model
Figure B.- Vaccination in SEIRS Model
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14. Intervention Strategies
Vaccination Strategies
Vaccination Strategies
Scheduling Vaccination
Infected Population-Trigger Vaccination
Figure C.- Plot of Vaccination Strategies
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15. Conclusions
Conclusions and Future Work
Conclusions and Future Work
Simulation help to understand spread of diseases.
Also we can observe different outcomes from intervention strategies.
Future Work:
Try different kinds of contact models.
Integrate Seasonality.
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16. Conclusions
Questions??
Questions ???
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