Simple Disease Models

The Model: Moving From State to State
t=0
Simplified Model: Two states:
= susceptible, = infected (SI Model)
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Some Simple Disease Models
The Model: Moving From State to State
More complex models: SI, SEI,
SEIR, etc.
S = susceptible, E = exposed,
I = infected, R = recovered
(or removed)
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Irreversible 2-Threshold Process
t=0
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Irreversible 2-Threshold Process
t=0
t=1
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Irreversible 2-Threshold Process
t=1
t=2
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Irreversible 3-Threshold Process
g
f
a
e
b
c
d
t=0
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Irreversible 3-Threshold Process
g
g
f
a
f
a
e
b
e
d
b
c
t=0
c
d
t=1
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Irreversible 3-Threshold Process
g
g
f
a
f
a
e
b
e
d
b
c
t=1
c
d
t=2
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A Simple Model (k = 1) (v = 3)
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A Simple Model
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A Simple Model
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A Simple Model
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A Simple Model
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A Simple Model
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A Simple Model
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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)
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Saving Vertices in
Pl  Pm  Pn
MVS ( P3  P3  P6 , (1,1,1))  21
MVS ( P3  P3  Pn , (1,1,1))  9n  33, n  6
21

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