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

Some Simple Disease Models

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)

Irreversible 2-Threshold Process 4 t=0

5 t=1t=0 Irreversible 2-Threshold Process

6 t=1t=2 Irreversible 2-Threshold Process

7 Irreversible 3-Threshold Process t = 0 a e d c b f g

8 Irreversible 3-Threshold Process t = 0 a e d c b f g a e d c b f g t = 1

9 Irreversible 3-Threshold Process t = 1 a e d c b f g a e d c b f g t = 2

A Simple Model (k = 1) (v = 3) 10

A Simple Model 11

A Simple Model 12

A Simple Model 13

A Simple Model 14

A Simple Model 15

A Simple Model 16

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Assumptions: 1.1 firefighter is deployed per time step 2.Fire starts at one vertex 3.Grid is finite (stops at the edges) 18

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Saving Vertices in 21