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1.
Examples (inc. measles)
1.
SIR models
1.
Epidemics
1.
Vaccinations
1.
Persistence (endemics)
Outline:
Disease Dynamics
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View Full Document Weekly deaths in Bombay (1906): plague
Examples:
Measles dynamics (prevaccination): 19441966
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View Full Document Epidemics – outbreaks
Epidemic dies out before all hosts are infected (or die)
Epidemic recurs
What determines if there will be an epidemic?
Why does it die out?
Why does it recur?
Let’s start by building a model…
Issues:
SIR model:
S
I
R
Three states of host:
1)
Susceptible (S)
2)
Infected (I)
3)
Removed (R): dead or immune
[N = S+I+R]
No host demography (no births or deaths)
All hosts start as “S”
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View Full Document SIR model:
S
I
R
Need to specify:
1)
Conversion of S to I
2)
Removal (I to R):
β
is “transmission rate”: set by contact rate and infection probability (“random encounter”)
γ
is removal rate
1/
γ
is mean time an individual remains infective
γ
I
β
SI
SIR model:
S
I
R
γ
I
β
SI
I
dt
dR
I
SI
dt
dI
SI
dt
dS
γ
β
=

=

=
/
/
/
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This note was uploaded on 07/13/2011 for the course PCB 4034C taught by Professor Osenberg during the Spring '11 term at University of Florida.
 Spring '11
 Osenberg

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