1. Q1 (quarantined non-symptomatic)
Basic Diagram
B(t)
E (exposed)
S (susceptible)
QS(t)
QE(t)
C(t)
Q=Q1+Q2
Q1 (quarantined non-symptomatic)
I (infectious)
QQ(t)
QI(t)
RI(t)
DI(t)
Q2 (quarantined symptomatic)
DQ(t)
RQ1(t)
D (dead/disabled)
RQ2(t)
* Transitions are the # of people moving between states
(NOT the fraction of people who transition)
R (recovered)

2. States (sum up to the whole population)
S(t) = # of susceptible people at time t
E(t) = # of exposed people at time t (incubation state)
I(t) = # of infectious people at time t
Q1(t) = # of non-symptomatic people in quarantine at time t
Q2(t) = # of symptomatic (infectious) people in quarantine at time t
Q(t) = # of people in quarantine at time t
D(t) = # of people dead/disabled at time t
R(t) = # of people recovered at time t
Transitions (# of people transitioning between states during the time interval)
B(t) = # of susceptible people who become infected (exposed) during the time interval
C(t) = # of exposed people who develop symptoms during the time interval
QS(t) = # of susceptible people who are quarantined during the time interval
QE(t) = # of exposed people who are quarantined during the time interval
QI(t) = # of infectious people who are quarantined during the time interval
QQ(t) = # of quarantined exposed people who develop symptoms during the time interval
(currently do not include the QQ transition in the model)
DI(t) = # of infectious people who die or become disabled during the time interval
DQ(t) = # of quarantined people who die during the time interval
RI(t) = # of infectious people who recover during the time interval
RQ1(t) = # of quarantined non-symptomatic people who recover during the time interval
RQ2(t) = # of quarantined infectious people who recover during the time interval

3. Q1 (quarantined non-symptomatic)
β=transmission rate (# new people exposed per infectious person)
B(t)
β*I(t-1)
E (exposed)
S (susceptible)
α=close contacts of newly quarantined people
α*ΔQ*S(t-1)/(E(t-1)+S(t-1))
QS(t)
QE(t)
α*ΔQ*(E(t-1)/(E(t-1)+S(t-1))
C(t)
[E(t-1)-QE(t)]*(1/μ1)
ΔQ=QI(t-1)
Q1 (quarantined non-symptomatic)
q=quarantine rate
q*I(t-1)
QI(t)
φ=treatment rate
I (infectious)
Q2 (quarantined symptomatic)
RI(t)
(1-d)*[I(t-1)-QI(t)]*(1/μ2)
DI(t)
RQ2(t)
(1-d)*Q2(t-1)*(1/μ2)
d*[I(t-1)-QI(t)]*(1/μ2)
DQ(t)
d*Q2(t-1)*(1/μ2)
RQ1(t)
φ*Q1(t-1)
+ Q1(t-1)(1-φ)*(1/μ1)
d=mortality rate of the disease
D (dead/disabled)
R (recovered)
subtract off those who go to quarantine before determining how many people go to the other states
use 1/μ2 to account for time delay before a person dies or recovers (if they were infectious)
use 1/μ1 to account for time delay before a quarantined non-symptomatic person is considered recovered (unless they receive treatment … then they go immediately to recovered)

4. States (sum up to the whole population)
β=transmission rate (# new people exposed per infectious person)
States (sum up to the whole population)
S(t) = # of susceptible people at time t
E(t) = # of exposed people at time t (incubation state)
I(t) = # of infectious people at time t
Q(t) = # of people in quarantine at time t
D(t) = # of people dead/disabled at time t
R(t) = # of people recovered at time t
α=close contacts of newly quarantined people
q=quarantine rate
d=mortality rate of the disease
φ=treatment rate
Discretized model
subtract off those who go to quarantine first
use 1/μ2 to account for time delay before a person dies or recovers (if they were infectious)
use 1/μ1 to account for time delay before a quarantined non-symptomatic person is considered recovered (unless they receive treatment … then they go immediately to recovered)
S(t+h) = S(t) – QS(t) – B(t)
E(t+h) = E(t) + B(t) – C(t) – QE(t)
I(t+h) = I(t) + C(t) – QI(t) – RI(t) – DI(t)
Q1(t+h) = Q1(t) + QS(t) + QE(t) – RQ1(t)
Q2(t+h) = Q2(t) + QI(t) – DQ(t) – RQ2(t)
D(t+h) = D(t) + DI(t) + DQ(t)
R(t+h) = R(t) + RI(t) + RQ1(t) + RQ2(t)
ΔQ=QI(t-1)
B(t) = β*I(t-1)
C(t) = [E(t-1)-QE(t)]*(1/μ1)
QS(t) = α*ΔQ*S(t-1)/(S(t-1)+E(t-1))
QE(t) = α*ΔQ*E(t-1)/(S(t-1)+E(t-1))
QI(t) = q*I(t-1)
DI(t) = d*[I(t-1)-QI(t)]*(1/μ2)
DQ(t) = d*Q2(t-1)*(1/μ2)
RI(t) = (1-d)*[I(t-1)-QI(t)]*(1/μ2)
RQ1(t) = φ*Q1(t-1) + Q1(t-1)*(1-φ)*(1/μ1)
RQ2(t) = (1-d)*Q2(t-1)*(1/μ2)
constraints are included in the Excel implementation of this model
limits on the number of people being sent to quarantine (setting to a large number effectively removes the constraint)
limits on the B(t) transition (since it doesn’t depend on S(t) limits are needed to prevent more people from transitioning than are available)
State Transitions
(# of people moving between states)