2018 Ebola outbreak in the DRC

What you see below are the results of fitting a stochastic SEIR model to the 2018 Ebola outbreak in the Democratic Republic of Congo. This interactive visualisation attempts to replicate the results by Cristian Althaus.

The model is defined by

$\frac{\rm{d}\mathbf{x}}{\rm{d}t} = \mathbf{A}(\mathbf{x}) + \boldsymbol{\eta}(t)$ $\left\langle \boldsymbol{\eta}(t)\boldsymbol{\eta}(t')^\top\right\rangle = \mathbf{B}(\mathbf{x}) \delta(t-t')$

where $\mathbf{x}=(S,E,I)$, and

$\mathbf{A}(\mathbf{x}) = \left(\begin{array}{c}-\beta(t) S I/N \\ \beta(t) S I/N - \sigma E \\ \sigma E - \gamma I\end{array}\right)$ $\mathbf{B}(\mathbf{x}) = \left(\begin{array}{ccc} \beta(t) S I/N & -\beta(t) S I/N & 0 \\ -\beta(t) S I/N & \beta(t) S I/N + \sigma E & -\sigma E \\ 0 & -\sigma E & \sigma E + \gamma I\end{array}\right)$

Here, $\beta(t)=\beta e^{-k(t-\tau)}$ for $t>\tau$ and $\beta(t)=\beta$ otherwise. The parameters to estimate are the base transmission rate $\beta$ and its rate of decay $k$. The remaining parameters are given by $1/\sigma=9.31\,\text{days}$, $1/\gamma=7.41\,\text{days}$, and $\tau=28\,\text{days}$.

The estimation is done from the data for cumulative incidence corresponding to $N-S(t)$, where the population size is fixed at $N=10^6$, using the linear noise approximation as described in Zimmer and Sahle (2014) and Zimmer (2015). The likelihood function is handled by sdeparams.

Forecast (shaded region) is shown for the mean plus/minus std of 50 stochastic simulations run for 30 days starting from the latest data-point for any given pair of parameters.

The code for the app is available in this Github repository.