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

2. Some Simple Disease Models

3. 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)

4. Irreversible 2-Threshold Process 4 t=0

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

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

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

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

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

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

11. A Simple Model 11

12. A Simple Model 12

13. A Simple Model 13

14. A Simple Model 14

15. A Simple Model 15

16. A Simple Model 16

17. 17

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

20. 20

21. Saving Vertices in 21