million or 38 crore people already infected.
The detailed study published in the Indian Journal of Medical Research (IJMR) claims to have used susceptible-asymptomatic-infected-recovered (SAIR) model to assess the impact of the lockdown and make predictions on its future course.
“The SAIR model has helped understand the disease better. If the model is correct, we may have reached herd immunity with about 38 crore people already infected. However, personal protective measures remain crucial,” the authors Manindra Agrawal, Madhuri Kanitkar and M Vidyasagar were quoted in the study as saying.
The study strongly advocates the fact that a timely lockdown may have reduced the fatality of coronavirus cases in India. It also claims that without a lockdown intervention led by the Indian government in the month of March, Covid-19 infections would have peaked by June 2020.
“If there was no lockdown, the number of active infections would have peaked at close to 14.7 million (1.4 crore), resulted in more than 2.6 million (26 lakh) deaths, and the peak would have arrived by June 2020. The number of deaths with the current trends may be less than 0.2 million (2 lakhs),” notes the study.
Method and modelling
The standard mathematical models could not explain the role of asymptomatic cases in unfolding of the pandemic, the study noted. A new model was used which was developed on lines of SAIR.
“There is a paucity of data on the behaviour of the virus among Indian population. Limited testing capability in India at the time of onset of the pandemic, non-availability of standardized tests for serosurveillance and non-availability of data on asymptomatic cases were other limitations. In the current Covid-19 pandemic, a large fraction of population showed little or no symptoms,” said the study.
Four parameters were used, namely , , and .
measures the likelihood of the susceptible people getting infected, and denotes recovery rate of patients. The ratio / is denoted by R0 (basic reproduction number).
Pandemic progression in India
The actual data suggested a peak in coronavirus cases in India on September 17, 2020. The model overestimates the actual growth by around 1.5 per cent and the peak arrives four days later. Cumulative deaths are predicted to be around 0.2 million.
The and values for the last phase imply R0 value around 1.39, and the herd immunity for this value of R0 at around 28 per cent of population in A, I and R categories.
According to the study, around 3.9 million (39 lakh) population was infected or with antibodies at the peak. On September 17, the numbers in I and RI categories were around 5.2 million (52 lakh). Using the 1/ value (=67) of phase 6, the model predicts total population with infection or antibodies to be around 3.5 million (35 lakh).
Progression of disease in Delhi
In the case of Delhi, the second wave starts about a week early, first peak is about 20 per cent higher, and second is about 10 per cent higher. Cumulative deaths are to be around 6500. July sero-survey showed antibodies in 23.5 per cent of population and RI at the start of survey was around 55,000.
“If there was no lockdown, the number of active infections would have peaked at 14+ million and the peak would have arrived by mid-May. This would have resulted in overwhelming our hospitals and widespread panic. There was little qualitative difference between two lockdown timings of April 1 and May 1, 2020. These would have resulted in a peak between 0 and 5 million active infections by mid-June,” the study highlights.
“If there was no lockdown, it would have resulted in more than 2 million deaths. The lack of two lockdowns (April 1 and May 1, 2020) would have resulted in between 0.5-1 million deaths. The number of deaths with current trends is projected to be less than 0.2 million,” said the study.
Unavailability of accurate data a challenge
The major limitation of the model, scientist believe was the nonavailability of accurate data.
“While our modelling efforts have tried to match the available data, the utility of our projections is limited by the accuracy and reliability of the available data. Hence, more accurate and reliable input data to the model would result in more reliable projections,” said the study.
According to the study, this new model is useful to calculate the possible disease burden in a realistic manner and may help plan for the resources. The impact of lockdown and interventions undertaken in a timely manner has been highlighted. The continuing importance of interventions such as use of mask, hand hygiene and physical distance is reinforced.
A consultative committee was constituted by the Department of Science and Technology under the Ministry of Science and Technology, Government of India, to develop a supermodel consisting of mathematical predictions as related to the coronavirus pandemic in India.