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

### Early Warning System for Districts

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

• Goals
• From the daily reported cases, create a stable early warning system based on each district'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
• early warning before the active cases increase substantially.
• Summary of Method
• For details and limitations of the method we refer to Early Prediction of COVID Surge-Slides.

Summary:

Suppose $\active{t}$ is the total number of active cases at time $t$ and the relative growth rate $\ractive{t}$ 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. To predict active cases at any given time, we average the last 4 calculated values of $\ractivehat{t}$ on that date and then use this average as the growth rate for the prediction.

Days: For the plots below, we have assumed that health infrastructure capacity in a district is proportional to its population. Hence we have used Days to 50 active cases per million Population and Days to 1500 active cases per million Population as markers for health care infrastructure capacity.
Days to Critical to previous peak: In the slides at: Estimated Growth Rate of Active Infections for districts in Karnataka are plotted along with days to critical, we assume the health-care infrastructure capacity to have been exceeded when it reaches the previously attained peak. For predicting the days to previous peak we do a smoothening of the data and use $1$ day lag instead of the $7$ day lag used otherwise.

We have divided the states into four categories:
• Category 1: Predicted Days to 1500 Active cases per million population is less than 100 days
• Category 2: Growing and Alert Raised
• Category 3: Stable but Need to be watched
• Category 4: Stable
• Data in CSV

• Data in HTML
• Predicted Days to 1500 Active cases per million population is less than 100 days
Days to Days to
StateActive CasesGrowthRate 50 Active Cases1500 Active Cases
p.m.pp.m.p
Tumakuru 90.1741 91
Days to Days to
StateActive CasesGrowthRate 50 Active Cases1500 Active Cases
p.m.pp.m.p
Bengaluru Urban 10.148141
Bidar 1140.1330
Chamarajanagar 50.13865 155
Davanagere 100.113
Mandya 00.1
Ramanagar 00.1
Stable but Need to be watched
StateActive CasesGrowthRate
Chikkaballapur 110.087
Stable
StateActive CasesGrowthRate
Bagalkot 0-0.007
Ballari 00.001
Belgaum 20.076
Bengaluru Rural 20.029
Chikmagalur 1-0.055
Hassan 00.001
Haveri 20.029
Kalaburagi 00.001
Kodagu 00.001
Kolar 3-0.025
Koppal 60.062
Mysuru 10.025
Raichur 30.064
Shivamogga 00.043
Udupi 10.05
Vijayapura 00.001
For all the graphs on this page, if you click on the image then it will display an interactive graph, where as you hover your mouse pointer over the graph annotations with details will be displayed.

#### Predicted Days to 1500 Active cases per million population is less than 100 days

• Below we plot the active cases as reported in blue.
• For the past data we have picked a few critical instances where Growth rate:= the number of new infections per active infection per unit time at time $exceeds recovery rate plot in red the surge in active cases predicted by the warning system (Note: false alarms do happen). • Finally at the current date we use the model to predict the active cases for the next 14 days. If the green curve is shooting upward then this is an early warning to the respective district. • For predicting the days to previous peak we do a smoothening of the data and use$1$day lag instead of the$7$day lag used otherwise. • For the plots below, we have assumed that health infrastructure capacity in a district is proportional to its population. Hence we have used Days to 50 Active cases per million Population and Days to 1500 Active cases per million Population as markers for health care infrastructure capacity. Based on these we have divided the districts into four categories Active Active cases: 2, Growth Rate: 0.243 Days to 50 Active cases per million population: 30 Days to 1500 Active cases per million population is 56 Days to Critical to previous peak Active Active cases: 9, Growth Rate: 0.17 Days to 50 Active cases per million population: 41 Days to 1500 Active cases per million population is 91 Days to Critical to previous peak #### Growing and Alert Raised • About the plots • Below we plot the active cases as reported in blue. • For the past data we have picked a few critical instances where Growth rate:= the number of new infections per active infection per unit time at time$ exceeds recovery rate plot in red the surge in active cases predicted by the warning system (Note: false alarms do happen).
• Finally at the current date we use the model to predict the active cases for the next 14 days. If the green curve is shooting upward then this is an early warning to the respective district.
• For predicting the days to previous peak we do a smoothening of the data and use $1$ day lag instead of the $7$ day lag used otherwise.
• For the plots below, we have assumed that health infrastructure capacity in a district is proportional to its population. Hence we have used Days to 50 Active cases per million Population and Days to 1500 Active cases per million Population as markers for health care infrastructure capacity. Based on these we have divided the districts into four categories

Active Cases: 1, Growth Rate: 0.148
Days to 50 Active Cases per million population: 141
Days to Critical to previous peak
Active Cases: 114, Growth Rate: 0.133
Days to 50 Active Cases per million population: 0
Days to 1500 Active Cases per million population is 99
Days to Critical to previous peak

Active Cases: 5, Growth Rate: 0.138
Days to 50 Active Cases per million population: 65
Days to 1500 Active Cases per million population is 155
Days to Critical to previous peak
Active Cases: 0, Growth Rate: 0.243
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 10, Growth Rate: 0.113
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 8, Growth Rate: 0.109
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 0, Growth Rate: 0.1
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 0, Growth Rate: 0.1
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 0, Growth Rate: 0.243
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 0, Growth Rate: 0.243
Days to 50 Active Cases per million population:
Days to Critical to previous peak

[Top], [Category 1], [Category 2], [Category 4]

#### Stable but Need to be watched

• Below we plot the active cases as reported in blue.
• For the past data we have picked a few critical instances where Growth rate:= the number of new infections per active infection per unit time at time $exceeds recovery rate plot in red the surge in active cases predicted by the warning system (Note: false alarms do happen). • Finally at the current date we use the model to predict the active cases for the next 14 days. If the green curve is shooting upward then this is an early warning to the respective district. • For predicting the days to previous peak we do a smoothening of the data and use$1$day lag instead of the$7$day lag used otherwise. • For the plots below, we have assumed that health infrastructure capacity in a district is proportional to its population. Hence we have used Days to 50 Active cases per million Population and Days to 1500 Active cases per million Population as markers for health care infrastructure capacity. Based on these we have divided the districts into four categories Active Cases: 11, Growth Rate: 0.087 Days to 50 Active Cases per million population: Days to Critical to previous peak [Top], [Category 1], [Category 2],[Category 3] #### Stable • About the plots • Below we plot the active cases as reported in blue. • For the past data we have picked a few critical instances where Growth rate:= the number of new infections per active infection per unit time at time$ exceeds recovery rate plot in red the surge in active cases predicted by the warning system (Note: false alarms do happen).
• Finally at the current date we use the model to predict the active cases for the next 14 days. If the green curve is shooting upward then this is an early warning to the respective district.
• For predicting the days to previous peak we do a smoothening of the data and use $1$ day lag instead of the $7$ day lag used otherwise.
• For the plots below, we have assumed that health infrastructure capacity in a district is proportional to its population. Hence we have used Days to 50 Active cases per million Population and Days to 1500 Active cases per million Population as markers for health care infrastructure capacity. Based on these we have divided the districts into four categories

Active Cases: 0, Growth Rate: -0.007
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 0, Growth Rate: 0.001
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 2, Growth Rate: 0.076
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 2, Growth Rate: 0.029
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 1, Growth Rate: -0.055
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 0, Growth Rate: 0.001
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 0, Growth Rate: 0.001
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 2, Growth Rate: 0.029
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 0, Growth Rate: 0.001
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 0, Growth Rate: 0.001
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 3, Growth Rate: -0.025
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 6, Growth Rate: 0.062
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 1, Growth Rate: 0.025
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 3, Growth Rate: 0.064
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 0, Growth Rate: 0.043
Days to 50 Active Cases per million population:
Days to Critical to previous peak
Active Cases: 1, Growth Rate: 0.05
Days to 50 Active Cases per million population:
Days to Critical to previous peak

Active Cases: 0, Growth Rate: 0.001
Days to 50 Active Cases per million population:
Days to Critical to previous peak