Covid-19 numbers: Why India can ease lockdown between April 24 and May 6
We should be able to start gradual easing of the lockdown somewhere between April 24 and May 6, 2020.
Doom and gloom
Dr Eric Feigl-Ding, Epidemiologist at Harvard University tweeted (now deleted), "Holy mother of God! The new coronavirus is a 3.8! How bad is that reproductive R0 value? It is thermonuclear pandemic level bad."
Most mathematical models of the spread of Covid-19 epidemic point to a disaster of enormous proportions. With a reproductive rate of 3.8 per cent for the Covid-19 virus, some of these models predict that 50 per cent to 70 per cent of the world population will get infected with the disease. With a fatality rate of three per cent in India, this means more than 20 million people could die from the disease in India alone.
Most of the mathematical models are based on the probability of individuals moving from susceptible to infected, and then to a recovered state or death (Susceptible Infected Recovered or SIR models). However, a government-mandated lockdown can dramatically change the way the epidemic will progress.
In China, a strict lockdown resulted in a significant reduction in the infected population. Hence SIR models, which are not able to completely account for social distancing, might be overestimating the number of infections from the virus.
In this study, we have modelled the spread of the virus through the empirically observed total infection case curves. The pattern of growth of these curves will accurately reflect the transmission of the virus. The estimate of total infected cases can provide an estimate of the total fatalities based on the empirically determined fatality rate (about three per cent in India).
The Burning Questions
We attempt to answer the following questions in this study:
1. What is the predicted number of Covid-19 cases and deaths in India?
2. What will be the pattern of increase in the number of cases?
3. What is the expected date when the lockdown can be eased?
Data and Methodology
The data was collected from the European Center for Disease Control (ECDC) website, which provides data on Covid- 19 cases from December 31, 2019, and is updated daily. The data is grouped into 11 variables. We have used the data for the daily number of virus cases from China, India, Italy and Malaysia in our model.
China was chosen because it has the most comprehensive data. Italy was included because it represented the fastest-growing infections in the world. Malaysia was chosen because of its proximity to India in terms of geography, climate and ethnicity of population, and also because the growth pattern of cases is similar to India.
After collecting and processing the data, we construct a statistical model for estimating the total infected cases as a function of time. The model is used to predict the growth of infected cases in the future.
Statistical Model
We have used a nonlinear mixed-effects model to model the growth of total infected cases as a function of time. We tried a number of nonlinear functions including the Gaussian error function, Richards’ growth curve and the logistic function. The optimal and most parsimonious fit was provided by the following generalised logistic curve:
Results
Figure 1 (below) shows the curves for the total number of cases in each country, plotted against the number of days. Day 0 for each country represents the date when the total number of cases exceeded 20 in that country. This date will be different for different countries. For India, this date was March 5, 2020, when the total reported cases were 22. For every country, we have plotted the data until April 8, 2020.
We ran the model with two different data sets:
Scenario 1: In this model, only data from India and China were considered. India and China imposed the lockdowns at similar stages of the epidemic. Since India’s growth rate is clearly lower than China’s, it is expected that if India’s curve follows a similar pattern as China with a lower growth rate (lower value of parameter b), India will be able to control the epidemic better than China. This is the optimistic scenario and represented by the blue curve, marked Scenario 1 in Figure 2 (below).
Scenario 2: In this model, data from all the four countries were aggregated. This allowed the possibility of India’s growth curve not being similar to China’s. This is the pessimistic scenario and is shown as the red curve in Figure 2 (below).
Figure 3 (below) shows the same curves but for clarity, we have removed the data for the other three countries. The data for India starts from March 5, 2020, which is represented by Day 0, till April 8, 2020, which is the 34th day on the axis (dotted black line).
Scenario 1: The total number of infected cases are predicted to be 51,323. This means with a mortality rate of 3 per cent, we can expect 1,540 fatalities. The inflection point, when the curve flattens, will be on Day 50 (date will be April 24, 2020).
Scenario 2: The total number of infected cases are predicted to be 69,674. The total fatalities are expected to be 2,090. The inflection point, when the curve flattens, will be on Day 62 (the date will be May 6, 2020).
The actual infected case curve for India should lie between Scenario 1 and Scenario 2, though the actual data appears to be closer to Scenario 2. The total infected cases would lie between 50,000 and 70,000, and total fatalities between 1,500 and 2,100. We should be able to start gradual easing of the lockdown somewhere between April 24 and May 6, 2020.