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The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI...

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The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0
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Page 1: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

The Model: Moving From State to State

1

Simplified Model: Two states: = susceptible, = infected (SI Model)

t=0

Page 2: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

Some Simple Disease Models

Page 3: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

The Model: Moving From State to State

3

More complex models: SI, SEI, SEIR, etc.

S = susceptible, E = exposed, I = infected, R = recovered (or removed)

Page 4: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

Irreversible 2-Threshold Process

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t=0

Page 5: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

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t=1t=0

Irreversible 2-Threshold Process

Page 6: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

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t=1 t=2

Irreversible 2-Threshold Process

Page 7: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

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Irreversible 3-Threshold Process

t = 0

a

e

d c

b

f

g

Page 8: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

8

Irreversible 3-Threshold Process

t = 0

a

e

d c

b

f

g

a

e

d c

b

f

g

t = 1

Page 9: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

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Irreversible 3-Threshold Process

t = 1

a

e

d c

b

f

g

a

e

d c

b

f

g

t = 2

Page 10: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

A Simple Model (k = 1) (v = 3)

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Page 11: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

A Simple Model

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Page 12: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

A Simple Model

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Page 13: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

A Simple Model

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Page 14: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

A Simple Model

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Page 15: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

A Simple Model

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Page 16: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

A Simple Model

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Page 17: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

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Page 18: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

Assumptions:1. 1 firefighter is deployed per time step2. Fire starts at one vertex3. Grid is finite (stops at the edges)

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Page 19: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.
Page 20: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

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Page 21: The Model: Moving From State to State 1 Simplified Model: Two states: = susceptible, = infected (SI Model) t=0.

Saving Vertices in

21

nml PPP

21111633 )),,(,( PPPMVS

,)),,(,( 33911133 nPPPMVS n 6n


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