Covid-19 Spread: Has the trend suddenly changed for India?

On 4th May, India has entered its third consecutive lockdown to slow down the spread of Coronavirus. Unlike the previous two lockdowns, the government has eased a lot of restrictions for business activities and allowed the movement of stranded people with a new set of guidelines. At the same time, we are reading headlines like ‘Coronavirus in India: 25% of all active cases detected in past 3 days’. This backdrop gives us an opportunity to indulge in interesting debates! Firstly, Covid-19 Spread: Is there any change of trend? If yes, then what has changed? Secondly, Are we testing enough? If not, then Will higher tests lead to higher recognition of positive cases? We will try to present a few arguments to participate in the first debate and arguments on second debate in next post. (Feel free to agree/disagree and present your side of arguments!)

Let’s say, two chess players, A & B won the right to choose their reward. A choose 100 coins for first square and additional 100 coins for every next square (so A will get 200 coins for second and 300 coins for third….). Now can you guess how many total coins will A receive? It would be 2,08,000 coins. On other hand, B chooses just 1 coin for the first square and asks to double coins for every next square. (So, B will get 2 coins for second and 4 coins for third …).  Now, can you guess how many total coins will B receive? I bet you can’t!  Just for the record, A series is arithmetic progression & B series is geometric progression. 🙂

Every infectious disease spread via human to human interaction, Covid-19 is no exception. Every infected person, is arguably a source of virus, can infect people around him. Human interactions (behavior) in public spaces, density of the population are factors, which decide the pace of the virus spread.

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In our chess player example, while the number of coins(cases) at next square(day) for A is increasing by 100, but the number of coins(cases) for B at next square(day) actually gets multiplied (r) by 2. Since each new COVID-19 infected person becomes a source of a new infection. Covid-19 spread behave more like series B (geometric progression) than series A. This brings us to a very important observation –

So, Is India’s daily Covid-19 cases have a similar trajectory to A or B? If your answer is B, then we are on same page. Above charts confirm that Daily Covid-19 cases are in geometric progression with like B. Once we have ascertained that Daily Covid-19 cases are in GP rather than in AP, we should be more concerned at the rate of spread rather than absolute change in new cases.

Daily New Case Nd+1 = Nd*r; Here Nd cases on prior day, r rate of infections!

Daily new cases should be dependent upon total number of sources(cases)(Nd) of virus and their social interactions(r). Value of (r) should be higher if social distancing norms are not followed and r should be lower if everyone follows strict social distancing norms.

Date Total Cases (Day -1)Rate of SpreadDaily New Cases

The data points given in the above table and equation can help us to understand the trend Covid-19 spread in India.

  1. Total infected cases (source of new infections) is a key factor in daily new cases. As number of new cases on 30th April is more than double of new cases on 10th April despite lower rate of infection on 30th April.  
  2. Total number of cases and rate of spread are two independent terms. Higher total cases do not necessarily mean lower/higher interaction.
  3. Since total number cases are unidirectional, it can’t be the measure of rate of spread of virus. Thus, rate of spread is true representation of growth of spread of coronavirus
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There is no doubt that the new cases released last week have been alarming. But as the above chart shows the rate of Covid-19 infection has actually reduced substantially during 1st and 2nd lockdown from nearly 23% to close to 7%. A closer look at last week’s rate infection shows that there has been a spike in the rate of infection for 5.82% to 7.03% but absolute numbers tend to exaggerate the situation.

(For the record B will get 9 Quintillion or 9*10^18, what was your guess??)

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