Question

Question 1 PSE PEI PIR S E R Psv PEV V ??? M Above is a state diagram for a virus disease for which a vaccine has just been introduced. For this disease, if an individual is vaccinated after being exposed, but before their viral load is high enough to be infectious, disease development can be prevented. The states are: S: Susceptible E: Exposed I: Infectious R: Recovered M: Dead (mortality) V: Vaccinated a. Please write the difference equation for $V_{t+1}$ based off of the population distribution at time t. An example of the difference equation for $S_{t+1}$ is given. (5 pts). $S_{t+1} = S_t - p_{SE} S_t - p_{SV} S_t$ $V_{t+1} = $ b. Fill in the transition matrix below for the disease depicted in the state diagram above. (One cell has been filled in as an example). (18 pts) V P_{SE} R M V c. The following values are known for the weekly transition probabilities between states: $p_{SE} = 0.08$ $p_{EI} = 0.4$ $p_{IR} = 0.6$ $p_{IM} = 0.005$ $p_{SV} = 0.09$ $p_{EV} = 0.03$

          Question 1
PSE
PEI
PIR
S
E
R
Psv
PEV
V
???
M
Above is a state diagram for a virus disease for which a vaccine has just been introduced. For this
disease, if an individual is vaccinated after being exposed, but before their viral load is high enough
to be infectious, disease development can be prevented.
The states are:
S: Susceptible
E: Exposed
I: Infectious
R: Recovered
M: Dead (mortality)
V: Vaccinated
a. Please write the difference equation for $V_{t+1}$ based off of the population distribution at time t.
An example of the difference equation for $S_{t+1}$ is given. (5 pts).
$S_{t+1} = S_t - p_{SE} S_t - p_{SV} S_t$
$V_{t+1} = $
b. Fill in the transition matrix below for the disease depicted in the state diagram above. (One cell
has been filled in as an example). (18 pts)
V
P_{SE}
R
M
V
c. The following values are known for the weekly transition probabilities between states:
$p_{SE} = 0.08$
$p_{EI} = 0.4$
$p_{IR} = 0.6$
$p_{IM} = 0.005$
$p_{SV} = 0.09$
$p_{EV} = 0.03$

Question 1
PSE
PEI
PIR
S
E
R
Psv
PEV
V
???
M
Above is a state diagram for a virus disease for which a vaccine has just been introduced. For this
disease, if an individual is vaccinated after being exposed, but before their viral load is high enough
to be infectious, disease development can be prevented.
The states are:
S: Susceptible
E: Exposed
I: Infectious
R: Recovered
M: Dead (mortality)
V: Vaccinated
a. Please write the difference equation for Vt+1 based off of the population distribution at time t.
An example of the difference equation for St+1 is given. (5 pts).
St+1 = St - pSE St - pSV St
Vt+1 =
b. Fill in the transition matrix below for the disease depicted in the state diagram above. (One cell
has been filled in as an example). (18 pts)
V
PSE
R
M
V
c. The following values are known for the weekly transition probabilities between states:
pSE = 0.08
pEI = 0.4
pIR = 0.6
pIM = 0.005
pSV = 0.09
pEV = 0.03

Added by Kelsey W.

Question

Please give Ace some feedback