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The COVID SUTRA

Manindra Agrawal

IIT Kanpur

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Existing Models for Pandemics

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Modelling of Pandemics

  • Pandemics such as plague, flu, cholera exhibit sharp rise and fall:

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Spanish flu deaths in UK (Source: https://doi.org/10.3201/eid1201.050979, CC)

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Modelling of Pandemics

  • To explain this phenomenon, Kermack-McKendrik (1927) proposed a mathematical model called SIR model.

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  • Susceptible: population not yet infected
  • Infected: population with infection
  • Removed: population no longer infected (includes fatalities)

Susceptible

Infected

Removed

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SIR Model

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SIR Model: Spread of Infection

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SIR Model: Removal of Infected

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SIR Model: Change in Infected

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SIR Model: Fatalities

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Herd Immunity

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Estimating Parameter Values

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Parameter Values from Data

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The problem is that reported values of infections may differ greatly from actual values.

That is why epidemiologists estimate parameter values using other methods like studying virus properties, population dynamics, and status of healthcare infrastructure.

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COVID-19 Pandemic

  • Different than earlier pandemics:

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  • Most of these asymptomatic cases are not detected, and continue passing infection to others.
  • Nearly all cases with severe symptoms get detected.

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Has a large number of asymptomatic cases

Without detecting, how does one estimate asymptomatic cases?

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COVID-19 Pandemic

  • On the positive side, extensive data is available for the first time about pandemic progression in different regions.

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Can one create a model that allows using reported data to estimate parameter values?

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The SUTRA Model

Authors: M Agrawal (IITK), M Kanitkar (MUHS), M Vidyasagar (IITH)

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SUTRA Model

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Susceptible

Undetected

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Tested +ve

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A at the end stands for Approach

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SUTRA Model

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SUTRA Model: Transition from U to T

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SUTRA Model: Analysis

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SUTRA Model: Analysis

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SUTRA Model: Analysis

  • We have:

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SUTRA Model: Analysis

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SUTRA Model: Analysis

  • This gives:

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Fundamental sutra of the model

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SUTRA Model: Parameters

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Estimation of Parameters

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Standard least square error method is used in estimation

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Estimation of Parameters

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Connection with Reality?

  • Does the model capture actual trajectory of Covid-19?
  • Fortunately, it can be tested easily.
  • Equation

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implies linear relationship over time between three known quantities.

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India Data

b = 3.86

e = 39164

R2 = 0.998

India data is taken from www.covid19india.org

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India Data

b = 6.38

e = 917

R2 = 0.999

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India Data

b = 6.29

e = 165

R2 = 0.999

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India Data

b = 6.68

e = 82

R2 = 0.999

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India Data

b = 4.93

e = 83.6

R2 = 0.999

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India Data

b = 4.29

e = 83.1

R2 = 0.999

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India Data

b = 2.64

e = 68.3

R2 = 0.999

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India Data

b = 3.52

e = 38.6

R2 = 0.999

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Observations

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  • There are eleven different phases with different values of b and e

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The equation holds for ~62% days in the entire timeline

Simulations of 26 countries, 35 states and UTs, and 500+ districts of India show same phenomenon!

e

Phase 1

Phase 2

Phase 3

Phase 4

Phase 5

Phase 6

Phase 7

Phase 8

Phase 9

Phase 10

Phase 11

India

5759253

39164

917

165

81.9

83.6

83.1

68.3

38.7

37.8

33.1

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Questions

 

Why does the relationship not hold for some days?

 

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Phase Changes

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This explains why does the relationship not hold for some days

 

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Spread of Pandemic: A Relook

  • Suppose the pandemic is spreading in China, but not in other countries of Asia
  • The population used for computing fractions would be of China, not of Asia
  • Then why should one use population of whole India when the pandemic just started?
    • At the time, it was confined to pockets of metro cities
  • Therefore, even the population changes with time!

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Spread of Pandemic: A Relook

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Spread of Pandemic: A Relook

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Estimating All parameters

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India: Pandemic Spread

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India: Pandemic Spread Captured by Model

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India: Parameter Values

 

Start Date

Drift Period

β

1/ϵ

ρ (in %)

Phase 1

03-03-2020

4

0.3 ±0.04

32

0 ±0

Phase 2

19-03-2020

5

0.32 ±0.01

32 ±0

0 ±0

Phase 3

16-04-2020

5

0.16 ±0

32 ±0

3.6 ±0.3

Phase 4

21-06-2020

25

0.16 ±0

32 ±0

20.8 ±1.9

Phase 5

22-08-2020

12

0.16 ±0

32 ±0

37.8 ±1.6

Phase 6

29-10-2020

10

0.19 ±0

32 ±0

42.3 ±0.8

Phase 7

18-12-2020

20

0.19 ±0

32 ±0

44.8 ±0.5

Phase 8

11-02-2021

35

0.4 ±0.01

32 ±0

46.2 ±0.8

Phase 9

30-03-2021

25

0.29 ±0

32 ±0

82.8 ±0.9

Phase 10

25-05-2021

0

0.28 ±0

32 ±0

85.9 ±2.6

Phase 11

20-06-2021

38

0.52 ±0

32 ±0

92 ±0.1

Phase 12

20-08-2021

2

0.6 ±0.01

32 ±0

92 ±0.4

Phase 13

01-11-2021

31

0.73 ±0.01

32 ±0

92.7 ±0.1

Phase 14

25-12-2021

11

1.54 ±0.17

32 ±0

104.5 ±2.9

Phase 15

10-01-2022

7

1.22 ±0.01

32.1 ±0

103.5 ±1

 

Calibrated with latest ICMR serosurvey

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Loss and Gain of Immunity

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Handling Loss of Immunity and Vaccination

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Impact of Omicron

 

 

 

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Remarks

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Strengths and Weaknesses of the Model

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Asking simple questions, and perusal of their answers often leads to interesting discoveries!

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Thank You