Ebola Transmissibility in the 2018–19 Kivu Ebola Epidemic
James P. Howard, II <james.howard@jhu.edu>
2020 Joint Statistical Meetings—Coronavirus Edition
Ebola Background
- Viral hemorrhagic fever
- Transmission via bodily fluids
- Mortality rate of approx. 50%
- Limited to primates, including humans
- Five known strains of the virus
- First case believed from wild animal
- First identified in 1976 in Sudan
- Periodic outbreaks in Africa since
- 2014 spread to U.S. and Europe
2018–19 Kivu Ebola Epidemic
- Started August 1, 2018
- Currently active
- Spread across eastern DRC
- Ituri (green, top)
- North Kivu (orange, middle)
- South Kivu (dark red, bottom)
- As of November 30, 2019:
- 3195 confirmed cases
- 2205 dead
- Another 4 cases in Uganda
Model equations
$$\begin{aligned} \frac{dS}{dt} & = -\frac{\beta IS}{N} \\ \frac{dI}{dt} & = \frac{\beta IS}{N} - \gamma I \\ \frac{dR}{dt} & = \gamma I \end{aligned} $$
After Estimation
$$ R_0 = \frac{\beta}{\gamma} $$
The SIR Model
- Standard epidemiological model
- Multicompartment mode
- Catenary model of progression
- Cell descriptions
- S: susceptible, base pool of persons
- I: infective, those who can transmit
- R: removed, through recovery or death
Model Estimation
- Software used
- Pyomo 5.6.6—optimization
- Ipopt 3.13.0—solver
- R 3.6.1—data preprocessing
- Modified SI model provided by Hart, et al.
- Adds R compartment
- Pyomo available upon request
- Assumptions
- 10,000,000 initial susceptible pool
- Expected infectious period of 21 days
- Not infectious until symptomatic
Data Acquisition and Preparation
- Data from Humanitarian Data Exchange
- Daily case count from August 3, 2018
- Data through November 28, 2019
- Aggregated from DRC MOH reports
- Data Preparation
- Aggregated to weekly case counts
- Established running sums weekly cases
- 3-week run period
- Weekly counts for the I compartment
- Plot of I compartment by week at right
Discussion and Conclusions
- Estimated
$$ 𝑅_0=2.017148$$- Prior estimates range from 1.5 to 2.5
- Landed right in the middle
- Future Directions
- Expanding to SEIR model (exposed)
- Re-estimates based on new data
- Meta-analysis of all estimates
References
- Althaus, C. L. (2014). Estimating the reproduction number of Ebola virus (EBOV) during the 2014 outbreak in West Africa. PLoS Currents, 6.
- Godfrey, K. (1983). Compartmental models and their application. New York: Academic Press.
- Hart, W. E., Laird, C. D., Watson, J. P., Woodruff, D. L., Hackebeil, G. A., Nicholson, B. L., & Siirola, J. D. (2017). Pyomo-optimization modeling in Python (2nd ed.) (Vol. 67). Berlin: Springer.
- Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character, 115(772), 700-721.
- Wächter, A., & Biegler, L. T. (2006). On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming, 106(1), 25-57.
Ebola Transmissibility in the 2018–19 Kivu Ebola Epidemic James P. Howard, II < james.howard@jhu.edu > 2020 Joint Statistical Meetings—Coronavirus Edition