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<!doctype html>
<html>
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
<title>Ebola Transmissibility in the 2018–19 Kivu Ebola Epidemic</title>
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<div class="slides">
<section class="title-slide" data-background-image="img/jhuapl-background.png" data-background-size="contain" data-markdown>
<textarea data-template>
# Ebola Transmissibility in the 2018–19 Kivu Ebola Epidemic
James P. Howard, II <<[email protected]>><br/>
2020 Joint Statistical Meetings—Coronavirus Edition
</textarea>
</section>
<section class="" data-background-image="img/jhuapl-background-blank.png" data-background-size="contain" data-markdown>
<textarea data-template>
<figure class="featured right">
<img src="img/ebola-virus.jpg" />
<figcaption>Transmission electron microscope of the Ebolavirus particle (Cynthia Goldsmith/CDC)</figcaption>
</figure>
## 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
</textarea>
</section>
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<textarea data-template>
<figure class="featured left">
<img src="img/kivu-epidemic-map.jpg" />
<figcaption>Congolese provinces affected by the epidemic (NordNordWest, DaB./Wikimedia Commons)</figcaption>
</figure>
## 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
</textarea>
</section>
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#### 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
`$$ R_0 = \frac{\beta}{\gamma} $$`
</div>
## The SIR Model
<div>
* 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
</div>
<figure>
<img src="img/sir-model.svg" />
</figure>
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<figure class="featured right">
<img src="img/pyomo-cover.png" />
</figure>
## 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
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<figure class="featured right">
<img src="img/ebola-i-cases-byweek.png" />
</figure>
## 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
</textarea>
</section>
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<textarea data-template>
<figure class="featured right">
<img src="img/ebola-deaths-byweek.png" />
</figure>
## 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
</textarea>
</section>
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<figure class="featured right">
<img src="img/ebola-file.jpg" />
<figcaption>Ebola treatment in the Democratic Republic of the Congo (WHO)</figcaption>
</figure>
<div style="width: 50%; font-size: 1rem;">
## 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.
</div>
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