$$\newcommand{\sub}{_} \newcommand{\confirmed}{x(#1)} \newcommand{\active}{a(#1)} \newcommand{\dactive}{a^{\prime}(#1)} \newcommand{\dconfirmed}{x^{\prime}(#1)} \newcommand{\ractive}{\lambda(#1)} \newcommand{\ractivehat}{\hat{\lambda}(#1)} \newcommand{\rconfirmed}{\gamma(#1)} \newcommand{\rincrement}{\rho(#1)} \newcommand{\rincrementhat}{\hat{\rho}(#1)} \newcommand{\rinactive}{\mu(#1)}$$

### Early Warning System for Indian States

(Based on Early Prediction of COVID Surge by Siva Athreya, Deepayan Sarkar, and Rajesh Sundaresan)

Goal: From the daily reported cases, create a stable early warning system based on each state's health care infrastructure capacity that provides:

• prediction of number of active cases in the next two weeks,
• days to critical (i.e. the number of days in which active cases will test health care infrastructure at current rate of growth), and
• warnings when the cases are low.

Suppose $\active{t}$ is the total number of active cases at time $t$ and $\ractive{t}$ is the number of new infections per active infection per unit time at time $t$. Assuming constant recovery : $\rinactive{t} \equiv 1/10$ we can estimate $$\ractivehat{t} = 0.1 + \frac{ \active{t + 7} - \active{t} }{ 7 \cdot \active{t} }$$ Note that at time $t$, $\ractivehat{t} > 0.1$ implies active cases will increase over time and $\ractivehat{t} < 0.1$ implies active cases will decrease over time. For prediction, we use average of last 4 calculated values of $\ractivehat{t}$ on date of last data point as the growth rate for the future.