cdc's model for west africa ebola outbreak summarized by li wang, 11/14

CDC's Model for West Africa Ebola Outbreak

Summarized by Li Wang, 11/14

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.

Exposed

Susceptible

Transmit

Imported

Recovered

Infectious

Hospitalized Home isolation

No isolation

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





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


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


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.

Compared to Rivers et al.

Compared to Rivers et al.

CDC equivalent0.30.020.36.3?NA6NANA66VaryNANA

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




cdc's model for west africa ebola outbreak summarized by li wang, 11/14

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