Simulation for India: Practical Reproduction Rate Hypothesis
Dr Himanshu Shekhar
Introduction: Reproduction rate is analyzed and discussed in one of the previous posts and it was stated that though it is not a mathematical parameter, but it can be correlated with the spread of Pandemic. The URL is as follows:
https://himanshushekharscience.blogspot.com/2020/06/the-concept-of-r-naught-r0-for.html?m=1
https://himanshushekharscience.blogspot.com/2020/06/the-concept-of-r-naught-r0-for.html
A formulation is developed for infection rate, which can be considered as equivalent to reproduction rate, using incubation period and doubling period. In this post, an attempt is made to simulate the available data of India, using the developed mathematical formulation of reproduction rate.
Mathematical Formulation: The infection rate or reproduction rate is defined as R0 = 2(IP/DP), where IP = Incubation period, which is taken 14 days and DP is doubling period, which can be used for the simulation of data for India. For different assumed reproduction rate, doubling period is calculated and starting with 90 confirmed cases on 15.03.2020, the cases are multiplied, so as to get the cumulative confirmed cases, matching to the practical data for India till 12.06.2020. The effect of lockdown and unlocking on reproduction rate is hypothetically assumed and the hypothetical predictions are made for India.
Simulation for India: The cumulative confirmed cases of India are simulated by various combination of reproduction rates. The simulation is shown below.
The reproduction rate by 15.03.2020 was 8, which has a doubling period of around 4.67 days. The effect of imposing lockdown was seen. As lockdown was implemented on 22.03.2020, 14 days later, or on 06.04.2020, the reproduction rate dropped to 5. The rate of rise of confirmed cases in India, would have been slower, had the reproduction rate been reduced further to a level below 1. However, around 01.05.2020, the reproduction rate dropped to 2 and this continued to remain so. The reproduction rate in India, never touched less than 1 and expecting a total control is slightly an impossible goal. With unlocking, even if the current reproduction rate of 2 is maintained, cases are going to rise at a faster pace. Some people movement to bring down this reproduction rate to less than 1 is required in the unlocked India.
Simulation: Ideally, it was expected to have a less than 1 reproduction rate in May 2020, which could not be achieved. A hypothetical situation is considered, when on 06.04.2020, reproduction rate is reduced to 5, followed by reduction to 0.7 on 01.05.2020, and then the confirmed cases could have come down. However, this could not be achieved in practice. Under such circumstances, maximum number of cases could be around 36000 on 01.05.2020, as peak confirmed cases. But this becomes a highly hypothetical and impractical situation. This was practically not achieved.
The
curve generated for the practical and actual situation is reproduced
below, extending the time domain to 15 August 2020. It is clear that
with reproduction rate of 2.0, it is not possible to get a
turnaround. With this speed, 3.0 Lakh cases are simulated on
12.06.2020, 4.0 lakh on 18.06.2020 and 5.0 lakh on 23.06.2020. The
rise seems to be very scary and with unlocked condition, onus is on
people to understand the gravity and exhibit self-imposed lockdown
and restrictions.
Somehow, if reproduction rate is brought down to 1 by 15.06.2020, the rising curve will continue, then level off. The cases with reach a maximum of around 350000 by 15.06.2020 and then stagnate. But it is looking not very likely. If this control is possible by 30.06.2020, then by that time 7.0 Lakh cases are possible.
Conclusion: Using reproduction rate, the situation in India is simulated and cumulative confirmed cases till 12.06.2020 is correctly reproduced. The reproduction rate of 8 on 15.03.2020 has become 2 by 01.05.2020 and it remained so even after lockdown is unlocked on 01.06.2020. the confirmed cases are rising at same rate as it was during lockdown. So, it was immaterial, whether lockdown is retained or not after 01.06.2020. The major concern is high value of reproduction rate and if it remained at 2, the 4.0 lakh cases will be counted by 18.06.2020 and 5.0 lakh cases by 23.06.2020. However, any attempt to bring this reproduction rate 1 at any time can stagnate the rise. If it is implemented on 30.06.2020, the total confirmed cases by that time will be 7.0 lakh.
Dr Himanshu Shekhar
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