EVI uses the standard deviation \(\left(\sigma_t\right)\) of the observed number of newly reported cases for each of the time units \(i\) within a prespecified fixed time interval \(\left(t\right)\):
\[\sigma_t=\sqrt{\frac{1}{N_t}\sum_{i_t=1}^{N_t}\left(x_{i_t}-\mu_t\right)}\]
Susbsequently the relative change \(\left(RC_{t-1,t}\right)\) of \(\left(\sigma_t\right)\) between two subsequent time intervals \(\left(t-1,t\right)\) is calculated:
\[EVI_{t-1,t}=\frac{\sigma_t-\sigma_{t-1}}{\sigma_t}\]
At each time point of the time series of the recorded number of new cases, if \(EVI_{t-1,t}\) exceeds a prespecified threshold \(\left(c\right)\) it indicates an upcoming surge in the future number of new recorded cases:
\[EVI_{t-1,t} = \begin{cases} EVI_{t-1,t}>=c & \text{expected rise in cases}\\ EVI_{t-1,t}<c & \text{steady number of cases or decline} \end{cases} \]