Math 464, Worksheet 26
In this worksheet will will add vaccination to the SIR model. As before, population of size
N
is
divided into three groups:
S
(susceptible),
R
(recovered/resistant), and
I
(infectious). Assumptions
are that
•
Total population is constant.
•
Infection rate is
βI/N
per person per time step.
•
Recovery rate is
γ
per person per time step.
•
Birth and death rates are
b
per person per time step.
•
All newborns are susceptible.
•
Everyone is in exactly one group.
•
From the susceptible group, there are
v
vaccinations per person per time step.
Schematically, it looks like this:
b
S
b
βI/N
b
b
v
I
b
γ
R
b
Part I
1. Develop a model. Write your model as a system of difference equations. Eliminate
R
using
that fact that total population is a constant.
NOTE: If you prefer numerical constants over symbolic parameters, you can use the numbers
from prior SIR models:
b
= 0
.
02
,
β
= 0
.
24
,
γ
= 0
.
1
,
and
N
= 100
However you have to keep
v
as a symbolic parameter.
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 Fall '08
 DougBullock
 Math, Epidemiology, Infectious Disease, γ, β, Economic equilibrium, total population

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