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)

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

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

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 Transmit t+1 t Transmit t+2 Transmit t+3 Transmit t+4 Transmit t+5 Transmit t+6 Transmit Exposed Recovered

Transmission details

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 Total: —19, ,962

Projection - Delayed response Total: —72, ,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.

CDC equivalent ? NA 6 NA 6 Vary NA

References CDC article: EbolaResponse model spreadsheet: WHO article: home&&#t=article Rivers et al.: g%20the%20Impact%20of%20Interventions%20on%20an%20Epidemic%2 0of%20Ebola%20in%20Sierra%20Leone%20and%20Liberia.pdf g%20the%20Impact%20of%20Interventions%20on%20an%20Epidemic%2 0of%20Ebola%20in%20Sierra%20Leone%20and%20Liberia.pdf