In this effort we consider the timeline of COVID-19 in Indian states by using the data released by Ministry of Health and Family Welfare for States and Union territories. Our primary aim is to provide a quick high-level intuitive understanding for anyone interested in studying the data and understanding infection spread across the states in India. Using the detailed media briefs provided by the Karnataka State's Ministry of Health and Family Welfare we study in depth the spread of COVID-19 in Karnataka.

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.

The two plots above are India timeline of Infected, Recovered and Deceased on a daily basis and the number of infections on log-scale. We track the data in the following aspects:

### States and Union Territories timeline of infections:

We track: Timeline, Cases, Active Cases, $R_t$, Doubling time , Falling off Exponential. These pages contain interactive plots of timeline of infected-recovered-deceased, the timeline of infections in log-scale, the active cases, time varying estimate of the reproduction number, the doubling times and one that tracks if the infection growth is in the exponential phase respectively.

### Trace history of patients for Karnataka state

The tree-like graph tracks every infection in the state providing a detailed log of its parent or the cluster of origin. This effort was entirely inspired by Channel News Asia-interactive graph for the trace history of Singapore cases and we have borrowed the javascript code in its entirety from their website. We had initially followed the trace history of Telangana till March 26th, 2020.

The Trace History Graph for Karnataka has not been updated since June 26th, 2020 as there was a pause in Contact tracing data in the media bulletins.

### Karnataka in Focus

In this page we track the various data provided in the Media Bulletins from Karnataka State to give a more comprehensive view of the COVID-19 infection in the state of Karnataka. In particular we track the cluster timelines, recovery and decea sed information, ICU timelines and information, the basic reproduction number, the infections in Karnataka across the cities, age distributions and testing data.

### Understanding Infection Growth

1. Doubling Times

Mathematical models used to characterize early epidemic growth feature an exponential curve. This phase of exponential growth can be characterised by the doubling time. Doubling time is the time it takes for the number of infections to double from a given day. In this page we analyse doubling times for all of India and for each state. For worldwide study of doubling times, we refer the reader to Deepayan Sarkar's website on github.

A detailed explanation of the method and inferences with respect to the lockdown can be found here.

2. Determining when a state/country falls off Exponential Growth.

We use a notion similar to moving average of net increase over a symmetric 7-day window. On log-scale, we plot on each day the net increase from three days before that day to three days after that day versus the total number of infections up to that day. This graph can be used to understand if the infection growth has deviated from the exponential phase. In this page we plot various states and observe that when the exponential growth is arrested then the respective plots will veer off the straight line. This effort has been inspired in part by Aatish Bhatia and Minute Physics's website where they study COVID-19 trends worldwide.

A detailed explanation of the method and inferences with respect to the lockdown can be found here.

### Notes

1. Effective Reproduction Number and Dispersion under Contact Tracing and Lockdown on COVID-19 Karnataka
We analyze the data provided in the Novel Coronavirus [COVID-19] media bulletins of the Government of Karnataka. We classify the patients of COVID-19 into clusters and study the Reproduction number and Dispersion for eight specific clusters. We find that it is uniformly less than one, indicating the benefits of contact tracing, lockdown and quarantine measures. However, the Dispersion is low indicating individual variation in secondary infections and the occurrence of Super-spreading events. Finally, we analyze the surge in infections after $27^{\mbox{th}}$ June and find it unlikely that it was caused solely by the large Migration in May and June 2020.
2. Doubling Time For Infection Growth
In this note we use doubling times to understand the trajectories of COVID-19 infection timeline for the States and Union Territories of India. We state a precise definition of Doubling time for continous non-decreasing functions. Using linear interpolation we present a procedure for calculating Doubling times for the discrete data. The procedure applies to discrete data that are specified at uniform intervals of time or otherwise.
3. Discrete Derivative as a Tool to Understand Deviations from Exponential Growth:
In this note, we consider the COVID$-19$ data of positive test cases in India and use the discrete derivative to detect if the number of positive test cases has stopped growing exponentially. We use a notion similar to moving average of net increase over a symmetric 7-day window. On log-scale, we plot on each day the net increase from three days before that day to three days after that day versus the total number of infections up to that day. This graph can be used to understand if the infection growth has deviated from the exponential phase.

### Data

Our data is sourced from the Ministry of Health and Family Welfare website and the Media Bulletins published regularly by the Karnataka government. The data available on these websites are in the form of PDF files which are difficult to extract automatically. We have collected this data and created a data repository. We have placed these as CSV files in our data respository page so that it can used easily by anyone.