1. 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
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This research is in part supported by the National Science Foundation award: NSF

2. Overview Mathematical Epidemiology Cellular Automata and Epidemiology
Stochastic Cellular Automata - A Global Model
Composition Model
Experiments
Summary

3. 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.

4. Susceptibles Infectives Removals (SIR) model
Homogeneous mixing of people
Every individual makes same contacts
No demographics considered
Geographical distances not considered

5. The Model Disease Parameters Vaccination Population Demographics
Interaction factors
Distances
Data Sets
Visualization

6. Parameters considered
Latent period
Infectious period
Contact
Infectivity
Population
Index case
Multiple index cases
Location of index case
Illustrates time-line for infection (influenza)

7. 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.

8. 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

9. Experiments Spread of a disease for different contact rates.
Disease parameters
Contact rates of 8, 15, 25
Infectivity of 0.005
As the contact rate decrease spread of disease is slower and prolonged.
Spread of a disease for different contact rates.
Spread of different diseases on a specific population with fixed contact rate.
Disease parameters such as latency, infectious period, infectivity and recovery different with respect to a disease.
The graph illustrates different diseases spread differently in a given population set.
Spread of different diseases in a given population

10. 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.

11. 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

12. 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 sub- region with a larger proportion of a different demographic
Composition model reflects the spread of the infection in each sub- region.
Cell interaction is controlled by age proportions and population densities.
Observed Cumulative Epidemic caused by Temporally and Spatially Distributed Local Outbreaks

13. Composition Model -Experiment
The population distribution over the region is non-uniform.
Contacts made between cells depends on the population of the cell.
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

14. Composition Model -Experiment
Population distribution over the north Denton region.
Infected Population distribution over the north Denton region.
Total Population infected at the end of simulation: 48000
Total Population of distributed over a grid size of 50 * 100.

15. Contact Rate
Contact rate defines the number of contacts an individual is involved in a day.
May vary depending on the age or occupation of the individual.
Contact is considered as any situation which may lead to a successful disease transmission.
The graph illustrates the epidemic curves for the same disease parameters with varying contact rates.
Can be thought of as for different demographics such as age groups and occupation.
Evidently incidence is lower for lower rates of contact. d

16. Experiment-- Infectivity
The probability of a contact resulting in a successful disease transmission depends on the infectivity/virulence parameter
Experiment was conducted to analyze the prevalence of influenza for varied levels of infectivity.
Incidence is lower for lower levels of infectivity.
Epidemic curves for varied levels of infectivity

17. Experiment-- Immunity
The probability of a contact with an infectious person resulting in a successful disease transmission depends on the immunity of the individual.
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.
The results show lower level of prevalence of disease in that region compared to other regions.
Region Immunized

18. Composition Model – Modeling Distance Dependence
Dichotomy introduced between local and global interactions.
Global interactions are between any two cells in the grid
Local interactions are within a Manhattan block distance of given distance k.
Incidence of disease prevalence decreases with higher proportions of local mixing.
Disease prevails over a longer period of time with higher proportions of local mixing.
Epidemic curves for the different rates of global and local mixing.

19. Spatial Spread of Influenza simulated over Northern Denton County with local contacts

24. Index case

45. Spatial Spread of Influenza simulated over Northern Denton County with local and global contacts

68. Summary
Designing tools for investigating local disease clusters through simulation.
What’s New?
Utilizing GIS and EPI information for modeling
Combining different simulation paradigms
Designing of a Global Stochastic CA
The goal: Contribute to establish computational epidemiology as a new research domain.