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

**Goals**- 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**

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

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.

- 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

Days to | Days to | |||
---|---|---|---|---|

State | Active Cases | GrowthRate | 50 Active Cases | 1500 Active Cases |

p.m.p | p.m.p | |||

Dharwad | 2 | 0.243 | 30 | 56 |

Tumakuru | 9 | 0.17 | 41 | 91 |

Days to | Days to | |||
---|---|---|---|---|

State | Active Cases | GrowthRate | 50 Active Cases | 1500 Active Cases |

p.m.p | p.m.p | |||

Bengaluru Urban | 1 | 0.148 | 141 | |

Bidar | 114 | 0.133 | 0 | |

Chamarajanagar | 5 | 0.138 | 65 | 155 |

Chitradurga | 0 | 0.243 | ||

Davanagere | 10 | 0.113 | ||

Gadag | 8 | 0.109 | ||

Mandya | 0 | 0.1 | ||

Ramanagar | 0 | 0.1 | ||

Uttara Kannada | 0 | 0.243 | ||

Yadgir | 0 | 0.243 |

State | Active Cases | GrowthRate | ||
---|---|---|---|---|

Chikkaballapur | 11 | 0.087 |

| ||||
---|---|---|---|---|

State | Active Cases | GrowthRate | ||

Bagalkot | 0 | -0.007 | ||

Ballari | 0 | 0.001 | ||

Belgaum | 2 | 0.076 | ||

Bengaluru Rural | 2 | 0.029 | ||

Chikmagalur | 1 | -0.055 | ||

Dakshina Kannada | 0 | 0.001 | ||

Hassan | 0 | 0.001 | ||

Haveri | 2 | 0.029 | ||

Kalaburagi | 0 | 0.001 | ||

Kodagu | 0 | 0.001 | ||

Kolar | 3 | -0.025 | ||

Koppal | 6 | 0.062 | ||

Mysuru | 1 | 0.025 | ||

Raichur | 3 | 0.064 | ||

Shivamogga | 0 | 0.043 | ||

Udupi | 1 | 0.05 | ||

Vijayapura | 0 | 0.001 |

- 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

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

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

- 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

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

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

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

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

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

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

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

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

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

Days to 50 Active Cases per million population:

Days to Critical to previous peak

- 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

Days to 50 Active Cases per million population:

Days to Critical to previous peak

- 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.*

Active Cases: 0, Growth Rate: -0.007

Days to 50 Active Cases per million population:

Days to Critical to previous peak

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

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

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

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

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

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

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

Days to 50 Active Cases per million population:

Days to Critical to previous peak

Days to 50 Active Cases per million population:

Days to Critical to previous peak

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

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

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

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

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

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

Days to 50 Active Cases per million population:

Days to Critical to previous peak

Days to 50 Active Cases per million population:

Days to Critical to previous peak