Julia Gog, University of Cambridge

1
Julia Gog, University of Cambridge
2
How do epidemics start?
3
Normal Flu
4
microbes
Person to person spread
5
Want to understand so make a model!
6
The Standing Disease!
7
The Standing Disease!

• Everyone starts sitting down
• One person stands and is the first case
• They pick two others to infect
• Those two stand up and each pick two others
• The next generation stands up and each pick two
  more and so on

• How many steps did the disease take to infect
  whole class?
• If time try with THREE instead of TWO
• What if your class was bigger?

8
1
9
2048
4096
8192
16384
32768
65536
131072
262144
524288
1048576
2097152
1 2 4 8 16 32 64 128 256 512 1024
33 steps!
10
Number of people standing
Number of steps
11
Bombay plague epidemic, 1906
12
Challenge the models!
Are they realistic enough?
Do they capture everything important?
Probably not important
13
Counter Plague!
1
6
6
1
3
1
14
Does epidemic take off or die out? How many
infecteds? How many steps?
0
0
0
1
1
1
0
0
1
2
2
2
1
1
1
3
3
3
1
1
1
4
4
4
1
2
2
5
5
5
2
2
2
6
6
6
1
6
6
1
3
1
15
0
0
0
1
1
1
0
0
1
2
2
2
1
1
1
3
3
3
1
1
1
4
4
4
1
2
2
5
5
5
2
2
2
6
6
6
Mean 5/6
Mean 1
Mean 7/6
gt1
1
lt1
16
Reproductive Ratio
R0
R0
Mean number of secondary cases at the start of
an epidemic
??
5/6, 1, 7/6
2
17
Reproductive Ratio
R0
R0
Measure of how quickly an epidemic will take off
R0 lt 1 Cases decrease each step
R0 gt 1 Cases increase each step
18
Reproductive Ratio
R0
R0
Measure of how quickly an epidemic will take off
so also measures how hard to control
19
R0 5
Vaccinate 4/5
Is like R0 1
20
Challenge the model!
Is it realistic enough? What else might be
important?
R0
21
SEIR Model
S
Susceptible to disease
E
Exposed but not infecting others yet
I
Infected and contagious
R
Recovered and immune to disease
22
Before
S
Susceptible
E
Exposed
I
Infected
Now whole epidemic
R
Recovered
23
Important numbers!
S
Susceptible
Incubation for how long?
E
Exposed
Contagious for how long?
I
Infected
How many contacts in that time?
R
Recovered
24
Incubation Contagious No. contacts Probability Proportion Initial Total time
(days) (days)   of dying immune population (days)
2 1 3 0 0 1,000 50
25
Incubation Contagious No. contacts Probability Proportion Initial Total time
(days) (days)   of dying immune population (days)
2 1 2 0 0 1,000 50