The objective of this to present the Epidemic Volatility Index (EVI) and demonstrate its use as an early warning indicator for upcoming surge in the number of cases of ongoing epidemics. Its application in the case of (i) the COVID-19 pandemic, (ii) the yearly influenza epidemics and (iii) the Dengue epidemic in Brazil revealed the universal applicability and efficiency of EVI.
Methods
The Epidemiologic Volatility Index
The epidemiologic volatility index is calculated for a rolling window of time series epidemic data (i.e. the number of new cases per day or per week depending on the surveillance setting). The rolling window size - that is the number of consecutive observations per rolling window - is fixed and at each step the observations within the window that are analyzed are obtained by shifting the window forward over the time series data one observation at a time. Let \(y_i=\left\{y_1,\ y_2,...,y_n\right\}\) be a time series of length \(\left(N\right)\). For a fixed window size \(\left(m\right)\), with \(0<m\le m_{\max}\) and \(0\le m_{\max}\le N\), there are \(t=N-m+1\) consecutive rolling windows.
At each of the \(t\) steps, EVI uses the standard deviation \(\left(\sigma_t\right)\) of the newly reported cases \(\left(y_{j_t}=\left\{y_{1_t},\ y_{2_t},...\ ,y_{m_t}\right\}\right)\) within the specified rolling window:\[\sigma_t=\sqrt{\frac{1}{m}\sum_{i_t=1}^m\left(x_{i_t}-\overline{\mu}_t\right)}\]
with \(\overline{\mu_t}\) the mean of the \(t^{th}\) window. Subsequently, EVI is calculated as the relative change of \(\left(\sigma_t\right)\) between two consecutive rolling windows:
\[EVI_{t-1,t}=\frac{\sigma_t-\sigma_{t-1}}{\sigma_t}\]
We expect an increase in the future number of cases if \(EVI_{t-1,t}\) exceeds a threshold \(c\) \(\left(c\in\left[0,1\right]\right)\) and the observed cases at time point \(t,\left(y_t\right)\) are higher than the average of the reported cases in the previous week:
\[Ind_{EVI_{t-1,t}} = \begin{cases}
1 \;\;\; if \;\;\; EVI_{t-1,t}>=c \;\; \wedge \;\; y_t>=\overline{\mu}_{t:t-7} \\
0 \;\;\; \text{otherwise}
\end{cases} \]