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SEIR compartmental model
• Deterministic model with 4 compartments (susceptible, exposed, infectious, recovery)
• Time step = 1 day. Model period is from 2/14 to 12/14.• Model population is homogenous (no distinction of sex, age,
location, etc.), of entire country (10 mil). • Model parameters are chosen by inspection to fit data
through 6/18/14.
Disease model
• New cases go into Exposed compartment• Can come from transmission or imported; initially set to 25• Length of incubation follow log-normal distribution (max 25
days)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250.0000.0200.0400.0600.0800.1000.1200.1400.1600.180
Days
Incu
batio
ni D
istrib
ution
Disease model
• After incubation period, case moves to Infectious compartment
• Remain infectious for 6 days, including burial period. Has a large effect on epidemic.
• Then the case moves to Recovery compartment. This covers both recovery and death.
Incubation details
• : newly exposed at time t• Split into 25 days, based on the log-normal distribution for
length of incubation
• For each day in the duration of incubation, add to the new Infectious cases i days forward:
• From the perspective of new Infectious cases:
Transmission model
• Infectious cases are assigned to 3 categories: Hospitalized, Home isolation, or No isolation
• The proportion of cases in each category changes to reflect public health intervention to the epidemic
0-30
31-6
0
61-9
0
91-1
20
121-
150
151-
180
181-
210
211-
240
241-
270
271-
300
0.000.100.200.300.400.500.600.700.800.901.00 % Patients by category over time
Hospitalization Eff Home Isolation* No IsolationDays
% P
atien
ts
Transmission
• The daily transmission risk ρ is the probability of an infectious person to transmit, per day, in an infinite population. Transmission is deterministic, so if the risk is 0.3, then the number of new cases = 0.3 x number of infectious.
• ρ is different by category:– Hospitalized: 0.02– Home isolation: 0.03– Non isolated: 0.30
• Importance of public health response! Effective isolation will stop the epidemic.
Newly Infectious
Hospitalized Home isolation No isolation
Transmitt+1
t
Transmit Transmit
Transmitt+2 Transmit Transmit
Transmitt+3 Transmit Transmit
Transmitt+4 Transmit Transmit
Transmitt+5 Transmit Transmit
Transmitt+6 Transmit Transmit
Exposed
Recovered
Transmission details
• : newly infectious at time t• Split into three categories, based on the proportion of cases in
each category, at time t: • For each day in the duration of infectiousness, add the
number of new transmissions to the new Exposed cases:
• S/N adjusts for finite, declining population of Susceptibles
Assumptions and limits
• The model parameters are chosen to fit data from the first 135 days.
• Under-reporting: the corrected model assumes that the number of actual cases are 2.5 times the reported.
• CDC's deterministic model does not provide any measure of uncertainty. The WHO report and Rivers et al. uses simulations to provide uncertainty.
• "The mean time from the onset of symptoms to hospitalization, a measure of the period of infectiousness in the community, was 5.0±4.7 days ... The mean time to death after admission to the hospital was 4.2±6.4 days, and the mean time to discharge was 11.8±6.1 days." - WHO
Projection
0-30
31-6
0
61-9
0
91-1
20
121-
150
151-
180
181-
210
211-
240
241-
270
271-
300
0.000.100.200.300.400.500.600.700.800.901.00 % Patients by category over time
Days
% P
atien
ts
0
50
100
150
200
250
300
350Ebola cases per day: Estimates based on data from Generic, uncorrected and
corrected for potential under -reporting
Daily cases (corrected)
Daily cases (uncorrected)
Days
Dai
ly c
linic
al c
ases
of
Ebol
a
Total:—19,957 - -51,962
Projection - Delayed response
0200400600800
1,0001,2001,4001,6001,800
Ebola cases per day: Estimates based on data from Generic, uncorrected and corrected for potential under -reporting
Daily cases (corrected)
Daily cases (uncorrected)
Days
Dai
ly c
linic
al c
ases
of
Ebol
a
0-30
31-6
0
61-9
0
91-1
20
121-
150
151-
180
181-
210
211-
240
241-
270
271-
300
0.000.100.200.300.400.500.600.700.800.901.00 % Patients by category over time
Days
% P
atien
ts
Total:—72,754 - -190,717
Hospitalization
• CDC's model provides a deterministic model of patients transitioning to hospital
• Depends on the epidemic model, but does not affect it
Model improvements
• What more can be done with available data? (location of cases, size of communities)
• Model the delay between infectious status and hospitalization or isolation
• Simulate the transmission process to get a measure of uncertainty.
References• CDC article:
http://www.cdc.gov/mmwr/preview/mmwrhtml/su6303a1.htm• EbolaResponse model spreadsheet: http://dx.doi.org/10.15620/cdc.24900• WHO article: http://www.nejm.org/doi/full/10.1056/NEJMoa1411100?
query=featured_home&&#t=article• Rivers et al.:
https://statnet.csde.washington.edu/trac/attachment/wiki/Ebola/Modeling%20the%20Impact%20of%20Interventions%20on%20an%20Epidemic%20of%20Ebola%20in%20Sierra%20Leone%20and%20Liberia.pdf