In this article we estimate and quantify the number of corona affected cases and highlight it in the context of complete lock-down. We also show through data and analyses the consequence of inaction and we speculate the number of calamities with and without the Janata curfew. Finally, we do predictive modelling for future .
Prominent steps taken by the Indian Government
14th March: Number of Covid-19 cases was 102 in India. Media raised alarm and started a widespread literacy about essential steps that are to be taken, like regular hand-wash and social distancing. Less number of Covid-19 cases led to a denial of the threat in some sections of the society leading to exponential growth of the virus.
In Delhi, shutdown of schools, colleges, and cinema halls was declared and this shutdown was initially planned to be till 31st of March. Further, the government started disinfecting all the public places, including government, private offices and shopping malls.
22nd March: 396 cases were observed till this date and the announcement of ‘Junata Curfew was made’, which is a 14 hour voluntary public curfew at the instance of the Prime Minister Shri Narendra Modi. The government followed it up with lockdowns in 75 districts where Covid-19 cases had occurred. During this period, 103 additional cases were reported owing to the incubation period lag as will be discussed in the following section. Lock-down couldn’t contain the virus entirely, but significantly slowed down the growth of this virus.
24th March: 536 cases were tested positive till this date and the Prime Minister declared a nationwide lock-down for 21 days. This decision greatly reduced the social contact structures.
All existing visas, except diplomatic, official, UN/International Organisations, employment, project visas, were suspended till April 15, while Indian nationals were strongly advised to avoid all non-essential travel abroad. On their return, quarantine for a minimum of 14 days made mandatory. This reduced the social contact pattern, otherwise the situation would have been much worse as shown in the graph - ‘Comparison of cases with and without lockdown’. Based on these developments, for the mathematical analysis, the timeline in India is considered in the following steps:
I. Initial phase till mid-March, when the corona virus increased rapidly
II. Phase when self-isolation and social distancing were advised heavily until the complete lockdown, implemented from 25th of March.
III. Phase after the complete lockdown was announced
Death Rate: This is defined as the number of deaths / confirmed cases. This metric is of importance as the death rate is merely 2% for the virus, but more fatal for elderly people and those having other complications. But this increases as the number of infections goes up, this can go up to 10% and in a country having a population of 134 crore, 10% death rate phase has to be avoided at any cost.
Death Rate of Italy and what it means for India
1. This represent the death rate of Italy over the time, which shoots up as soon as Italy crosses a figure of 12,000 COVID 19 patients
2. The death rate reaches as high as 10% and is dependent on the percentage of the elderly people and number of beds per 1000 citizens.
3. Number of beds per 1000 people in Italy is 3.18 while it is around 0.55 in India. The total number of beds available in India is around 7 Lakhs, which is one seventh of Italy.
4. The percentage of people over 60 years is 23% in Italy unlike where as in India, it is around 8%.
5. It is safe to assume a death rate of 8% when the number of patients overwhelms as the mortality of COVID 19 is less about the disease and more about the health care system and mass of patients.
6. The white line represents the threshold for the spike in death rate which is 12,000 patients in Italy, this is estimated to be 84,000 patients in India for such spike in death rate, and this spike can very well be between 7% – 10% based on the data provided.
Confirmed cases vs. Total infected cases
There is a period between which a person gets infected, and he or she is confirmed positive. Hence the total number of infected people is greater than the total number of confirmed positives in an exponential growth phase. So, can the total number of infections be ever reported correctly? The answer is yes, but the only way of achieving this is to strictly follow social distancing and have near 100% reduction in new cases per day, so that all the cases gets recognized and treated. The graph below shows the analysis of the consequences of not having this parameters matched, which will help us to judge the situation in India better.
1. Increase in the reported confirmed cases as well as the actual cases in Hubei, after which the two curves came closer making the scenario controllable
2. Number of reported cases kept on rising after the halt of increase in actual cases after lock-down, this shows the influence of incubation period.
3. These are majorly the cases where people were infected before the lockdown and their incubation period continued after lockdown. As expected, the two parameter meets when there is no new cases and the pandemic is contained as seen in Huebei.
4. Failure of controlling the situation, and the number of unreported new cases kept on rising in Italy causing the pandemic to explode.
South Korea achieved the suppression of COVID 19 spreading, the trends are similar to the later trends in Hubei-China. They tested aggressively to identify cases, and quarantined high number of people susceptible to COVID 19.
Death Rate of South Korea was never more than 1.5 percent as they ensured early halt of COVID 19 spread before it crossed the threshold barrier of their health care system.
India is in the very critical situation right now, if we continue doing what we are doing, we’ll be hitting 0.66 Million cases very soon.
Mathematics behind the predictions
Since we are in exponential phase, a time series analysis was done based on regression model, which was implemented on the logarithm of the active cases. The logarithm curve better shows change in trends in different phases and was used for regression, which was tuned by performing it for several phases of COVID 19 spread.
Neural Networks, and deep learning models were implementation using pytorch were done in previous studies and seasonality was calculated using ARIMA (Autoregressive integrated moving average), but due to limited data, these model ends up overfitting the data. As for the seasonality, a monthly seasonality from ARIMA model doesn’t really makes sense and a high weekly seasonality was observed in the initial month, with highest surge in cases in Wednesdays, but it becomes redundant after lockdown imposed, hence a simple exponential smoothing or a regression will give best results
Trend in the data
The rough trend of the data goes through the three stages, but the number of patients and the stage at which the virus is halted strongly depends on the steps taken by the government and the community response
1. It takes 2-14 days for a person to develop the symptoms and to be tested positive. This causes the total number of COVID 19 cases to be much higher that the number of confirmed positives.
2. Number of unconfirmed infections is rising at a rapid rate as compared to the number of confirmed cases. This is on the contrary to the case of Hubei, and it shows that we have to take severe measures, otherwise the two curves are not meeting anytime soon
3. The mortality rate remains close to 2% but this will definitely increase with the surge in number of cases, as we can see from the above figure, it went up to 10% in case of Italy.
Predictive Modelling for Forecasting
1. The data assumes different trends at different levels; hence the data was converted to a logarithmic scale and then machine learning model for time series analysis was implemented
2. The logarithmic data was then converted back to original scale.
3. Death Rate was predicted at different levels as a function of total number of patients, and the capacity of health care system relative to Italy.
1. The orange curve represents the spread of COVID 19 if the recent measures after 22nd March were not taken, the total number of cases would be around 1.2 Million
2. The blue line takes into account the change in trends in recent days, and at least 0.66 Million total COVID 19 by mid of May cases is still estimated with total death count over 2400, many more severe changes are required to control this trend, this means we need to observe stricter lockdown.
3. This is the correct time to take actions, because if we continue doing what we are doing, we will end up in a similar situation as Italy with a death rate approaching 10%. At this death rate, medical system as well as the economy will take a drastic hit.
It is indeed quantitatively very clear that the timely, well planned and a comprehensive step of a nation-wide lock down has immensely helped in reducing both the infections and mortality. A 2% death rate doesn’t imply 98% probability of survival for an infected individual This is where the data misguides the seriousness of the scenario. Let’s break it down
1. In the rare case of deaths, it takes on an average 20 days, from getting infected by the virus to the day of death. Death rate becomes incredibly low due to high number of new patients after 20 days, which are also included in calculating the death rate
2. The doubling rate of corona virus is 5-6 days, according to the analysis. So if there are 1000 new cases on day 1, there will be 8000 new cases on day 20, new deaths around Day 20 with a standard deviation of 3 days will give an estimation of the outcomes of the 1000 people who were hospitalised on day 1.
3. Say 20% of the people from day one died in the course of 20 days, which makes 200 Deaths around Day 20. New deaths from the new cases will be observed further after few days.
4. The death rate still is 200/8000 = 2.5% but the actual probability for the death of a person contracting the virus is 20%
5. Currently total cases in India are coming close to 1000. It’s just a matter of days we will see 1000 new cases in a day!
6. A statistical comparison with Italy shows that out of 20,000 cases which were confirmed, just 10,950 recovered, making the death percentage among these cases close to 45% whereas this figure is 20% in India!
Insights for the number of mortalities
1. Total number of cases by Mid of May is estimated to be 0.66 Million.
2. The total death toll will be 2911 by mid-April and whooping a figure of 25,000 by mid of May
3. However due to recent measures of the country, including lockdown, this is likely to change if every citizen of India follows the guidelines provided by the government and mould the trend close to that of South Korea.
4. If the government had not implemented recent changes mentioned in the point number 3, which is after 22nd March, provided in this link, the figure would have been around 1 Million positive cases and 62,000 deaths
In conclusion, it is quite clear from the data and our analysis that we are sitting on a time bomb. If the lock-down is seriously implemented, we can expect to see lesser number of people dying in the days to come. So our appeal to common people is to strictly follow the guidelines laid by our government and self-quarantine even if they don’t have any symptom.
(The authors are faculty at Department of Chemistry, IT(BHU) Varanasi, U.P)