India’s COVID-19 fight — The Storm
The second wave of Covid19 has hit India like a tsunami. The dire news of the number of cases is overwhelming the healthcare system and straining every supporting system. This wave of Covid19 also has brought many cases within the 1st degree of separation. Hearing personal stories who have lost their loved ones are excruciating. It is almost unbearable to see the widespread suffering and tribulations.
For the last few days, the case counts seem to be over 300K and fatalities hovering around 3K. A few people have asked me what we can expect the numbers to look like for the next week if the trend sustains. Although it seems scary to run the simulation models, the data would help us psychologically prepare ourselves for the very worst.
This Data is sourced from covid19india.org. In this Blog, The main focus will be on 2 things: Volume of the cases and fatalities. I tried to understand if there are any fundamental changes to the dynamics of these two. If there is a big difference in the behavior of this virus, it could potentially help all the actors in the system — The Government, the front line workers, hospitals, and patients — a means of approaching this menace that is threatening to wreak havoc in the country. Preventing the spread, triaging the cases, treating the patients right, and saving lives should be the primary objectives to reduce the strain on various systems.
Case Fatality Rate (CFR)
One of the main metrics to check the virulence of the virus is to measure the Case Fatality Rate. It is the ratio of reported Deaths to the number of Reported Positive Cases on a particular Day. It can be calculated by:
CFR = (Daily Deceased/Daily Confirmed)*100
I have done Statistical Analysis on the Day-wise ‘CFR’ values by dividing the timeline into three phases: ‘Dawn’(phase 1), ‘Calm’(phase 2), and ‘Storm’(phase 3), where I’ll be comparing each of them. Please check my GitHub repository for the code and data I have used (the link is given in the references section of this blog).
The Phases
To understand the virus's behavior, I have split the history of this pandemic into three phases. In the graph below, you can see the blue portion is “The dawn,” Pink is the “Calm,” and the green phase is the “Storm” ( the phase we are currently in):
Dawn: Phase 1 (April — September)
The First Case of Covid19 in India is reported in Kerala on Jan 27th, 2020 and the rest is history. To mitigate the spread of the virus, Social Distancing has been imposed, followed by the closing of Universities, Schools, Movie Theatres. A nationwide Lockdown has been announced from 24th March 2020 to 19th April 2020, yet the cases of Covid19 continued to proliferate in April and gradually plummeted in September after peaking in August.
- A downward trend in the CFR can be observed in the ‘Dawn’ (left), which means that the number of deaths per the number of positive cases has decreased, resulting from improved triage and behavioral alteration therapeutics much more prepared medical care.
- The CFR at the end of this phase-stabilized at around 1%.
- The distribution of the variable CFR is skewed on the left side from the Histogram above(right) with a mean of 2.21 and a Standard deviation of 0.943.
Calm: Phase 2 (October — Feb)
Just like the calmness of the eye of a Cyclone, there seems to be a steady decrease in the Daily cases between October 2020 to February 2021; As the Outbreak appeared to be in control, few states have decided to reopen Universities, Offices, Malls, etc. Parallelly, countries like The United States, United Kingdom, etc., are already hit by a much severe Second Wave.
- The CFR seems to be hovering around 1.0% in the graph above(left), which means approximately 99% of the patients recover.
- 1.2% is the median with a mean of 1.16 and a Standard deviation of 0.238 for the ‘Calm’ phase.
It is quite heartening to see this steady decline, and India has declared the end game in the fight against Covid19. The data suggested as such. Any model we ever run would also not foresee the 2nd wave, although epidemiologists can! The precedence from the other countries that have gone through the 2nd wave could have pre-empted India to be a little more on guard. We have a great distribution system of vaccines and must have taken this window to vaccinate aggressively. In hindsight, these seem to have been a rational response. Perhaps, we took the eyes off the ball.
Storm: Phase 3 (March — till Date)
The Virus story isn’t over, as the cases started rising as we became more complacent, and we were hit by the second storm, following the same pattern as the other countries, just with a lag. There has been a steep increase in the day-wise reported cases and deaths since March 2021 after loosening the ‘Calm’ phase restrictions. Hospitals are being flooded with covid19 patients, and there’s a shortage of oxygen tanks exacerbating the severity.
- As observed above (right), The Case Fatality Rate for the last few days has been below 1%, which can give us hope for surviving this phase. Most of the ‘CFR’ values are between 0.5% to 0.6%, as shown in the histogram. The mean and Standard deviation are 0.606 and 0.145 respectively.
- The implications of this performance indicator may be a rare silver lining in the otherwise morose story. It indicates the fatalities can still be maintained at low levels if we evolve necessary triage procedures, create adequate treatment plans for mild to moderate cases to be treated at home with the help of telemedicine, increasing lockdowns to contain the explosion of the cases till the strain of the health-care infrastructure is brought to manageable levels.
Understanding behavior of fatalities across the phases.
I have mapped the distributions of CFR across the phases and one for the overall CFR. The intent is to compare if each phase has a significantly different distribution; if so, identify what strategies and underlying conditions made it possible.
By Looking at ‘Dawn,’ ‘Calm’ and ‘Storm,’ the ranges and the medians appear to be shifting downwards. I have performed statistical hypothesis testing to infer the significance. There are 2 ways I adopted to conclude the significance: the mean and the variation.
Comparison of the Means of Each Phase
I have compared each phase along with the entire population by using z-test, t-test (only for April data which has a sample size less than 30), and ANOVA to see if their means are equal.
Z-test Statistical test determines if two populations' means are different when the sample size is more than 30.
ANOVA is to compare more than two means of independent samples by using F-distribution.
The T-test is commonly used to test the Statistical difference between a mean and a known or hypothesized value of the mean population. For the T-test, I have considered only the last 4 week’s data and tested it against the population.
The table below is a summary of the results. The “reject” in the null Hypothesis should be interpreted as “the behavior” is different. If a Null Hypothesis is rejected, it is unlikely to occur at 95% confidence, and the means differ significantly, So we can infer that there is a disruption between the phases.
As we can observe, while ‘Dawn’ showed a Significant Difference with The Population Mean, ‘Calm’ and ‘Storm’ didn’t. Therefore only the last two phases follow a similar pattern of the Population. I have also ensured that the results are consistent by comparing all the samples with ANOVA — which has proved that the CFR behavior is different across all the phases. Since we should be concerned about the previous month, After doing a T-test with the Population, which surprisingly rejected the Null Hypothesis. I decided to further look into the data of the last 4 weeks because this analysis would be of greatest significance in formulating appropriate mitigation strategies to tackle this dire situation.
CFR looks like it has been elevating for the last few days; it looks like a warning! To help plan for the capacity planning and increasing the triage efficiency, I tried to forecast how the cases may perform for the next week. Using only this data, I’ll try using the SIR model to forecast how the trend might look like next week.
SIR Model
A SIR model is an epidemiological model that estimates the number of people infected with a contagious illness in an area over time. This model involves three equations relating to the number of susceptible people, the number of people infected, and the number of people who have recovered, denoted by S(t), R(t), and I(t), respectively.
Since we don’t have the number of Susceptible people, we will be predicting the Daily Cases and Deaths for the next week by fitting with the bell curve equation.
Fitting with Polynomial and Quadratic Equations
I tried to fit different models to predict the Cases and Fatalities in the “Dawn” phase. Please read Part-I for details.
Predictions for the Next Week with different Models
If the numbers hold this trajectory, India will have to brace for a challenging course ahead. India will have to find ways to increase the production of Oxygen, increase hospital beds, increase ICU bandwidth, Ventilators, availability of drugs that could potentially treat severe symptoms. Besides this, the vaccination will have to get into hyperdrive. These are extraordinary things to do but, India has to find a way to do these on a war footing.
This is the time, all of humanity shall have to come together to beat this menace of the world. It is testing time for India, and its spiritual strength and faith will be tested.
The code and a complete analysis are in my Github repository. https://github.com/5re5htaRushya/covid_19_projections/tree/master/updated
Kaggle Notebook: https://www.kaggle.com/sreshta140/analysis-of-the-second-wave-in-india