Covid cases started increasing rapidly in UP from middle of March.
The rise was very sharp: from around 150 new cases on March 15 to almost 30,000 cases on April 20 – an increase by a factor of nearly 200.
To control this unabated rise, measures such as night and weekend curfews were put in place from April 21, culminating imposing of partial curfew in which markets, malls, restaurants, etc were closed and large gatherings were prohibited.
The number of cases peaked at around 38,000 on April 24, and started reducing thereafter going below 4,000 new cases on May 25.
What was the impact of containment strategy adapted by the state? Could earlier imposition of curfew have been better? We address and answer these questions below.Sutra ModelWe use SUTRA model to analyze and study the pandemic progression in the state and simulate different strategies.
The model has two parameters that govern how fast infection is spreading and its duration.
These are called reach and contact rate.
Parameter reach measures the fraction of population over which the pandemic is currently active.
It increases when the pandemic reaches new regions.
It also increases when someone in a previously protected group, living inside a “bubble”, gets infected.
Parameter contact rate measures how fast pandemic is spreading in the population.
It increases when people stop taking precautions, or a faster spreading mutant arrives.
It decreases due to interventions like lockdown.
The model can estimate the value of contact rate at any point in time from the reported daily new infections data.
While it cannot calculate the value of reach at a given time, it can estimate changes in the value of reach between two given dates.
This allows one to estimate value of reach at any time relative to its value at a fixed time.
By suitably changing the values of these two parameters, one can compute alternative trajectories of the pandemic.
Parameter values during March-MayParameter values started increasing in the state from March 15 and by the end of the month, reach doubled and contact rate rose by 35% to become 0.54.
This increase was due to the spread of delta-variant as well as people not following Covid-appropriate behaviour.
The resulting rise was very sharp as observed earlier.
Parameter values started changing again from April 21 – over the next two weeks, reach increased by another 60% but contact rate came down to 0.29, a decline of almost 50%.
While the former was due to pandemic spreading into villages, reduction in contact rate was due to containment measures taken.
AnalysisWhat would have happened had the contact rate not reduced in April-end? The following plot shows that 7-day average of daily new infections would have peaked around 70,000 cases in the first week of May, which is double of actual peak value.
By April-end the hospitals in the state were finding it difficult to accommodate patients and oxygen supply was running short, and a real catastrophe would have happened without the containment measures.
In the plot, the blue line indicates the trajectory of 7-day moving averages of daily infections, orange one denotes the trajectory predicted by the model after estimating the parameters, and dotted purple one denotes the projected trajectory in the scenario where no containment measures are taken.
Seven-day averages are used because there are weekly variations in reported number of cases.
Could an earlier imposition of measures have reduced the case load significantly? To analyze this, it is useful to understand the impact of change in contact rate.
When reach increases significantly, it makes a large number of susceptible persons available for pandemic to infect.
If at the time contact rate is high, the infection starts spreading rapidly.
On the other hand, if contact rate is low at the time, the spread of infection is slow and the numbers peak at significantly lower level.
The same is evident in the plot above, which shows a gradual reduction from April-end instead of continued rise due to significantly lower contact rate.
If reduction in contact rate happens well after the expansion of reach, the pandemic gets a chance to rapidly spread in the newly available susceptible population, and so the benefits of reduction in contact rate are not that significant.
The next plot brings it out clearly: even one week delay in imposing the measures in UP would have resulted in a peak of over 50,000 for 7-day average of daily infections by April-end.
Above suggests that earlier containment measures would have helped significantly only if they were taken in the middle of March – at the time, however, no one could anticipate what was to come! The plot below shows the trajectory if measures were taken a week earlier.
There is no significant gain achieved here: 7-day average of daily infections peak at around 30,000, which is only 5,000 less than the actual peak.
The peak is also delayed by about a week.
ConclusionsThe analysis done with the help of SUTRA model demonstrates the success of the containment measures taken in UP.
These helped avoid a major crisis since the pandemic was spreading in rural areas that do not have good access to healthcare facilities, and managed to control the speed of spread significantly.
The timing of the measures was also appropriate, even a slight delay could have resulted in significantly higher case load and earlier measures would have helped only a little more.
The best part of the strategy was that, unlike many other states, it did not confine everyone to their residences and permitted significant number of activities thereby not disrupting livelihood of a large section.
(The writer is a professor of computer science and engineering at IIT Kanpur)