Dr Sandip Ratna, Asst. Prof.
State College of Teacher Education, Kohima
One of the most circulated WhatsApp massages go like this:
“Our mental state right now, is such, that CARNIVOROUS is also being read as CORONAVIRUS… (Now read it again…!).”
Hope you read it correct…!! If not, no worries, its due to hangover of the pandemic. Likewise, same hangover, forces me to analysis the role of Mathematics behind the Lockdown.
We all know that, the mode of transmission of the COVID-19 virus is through droplet transmission at close contact of the infected person or in contact with contaminated materials around us. Therefore, transmission of the virus can occur by direct contact ie with infected people or by indirect contact ie with contaminated surfaces in the immediate environment like wood, iron, plastic, paper surfaces etc. Hence, any person moving freely in an affected environment is at the high risk of getting infected and thus emerging the concept of Lockdown in order to be safe for one and for others.
It is also a common understanding that, Lockdown is not a cure to the virus but a pose to the process of spreading further. The way we can hold our breath momentary, likewise the Lockdown is also a process of slowing down the spread of corona virus.
If we don’t take precaution and take necessary action on our part, this is going to affect all of us very severely in every aspect of our life. As per the world report published by WHO as on 3rd July 2020, the top most affected countries in the world are: USA, 0.857%, Brazil, 0.706%, Russia, 0.453%, and India, 0.045% [1].
To understand the scientific impact of Lockdown the reference of the following articles may prove very insightful. The SIR model (Susceptible, Infective, and Removed groups, 1927) [2] the SEIR (Susceptible, Exposed, Infected, Recovered) Model [3]nor Probabilistic models [4].
In the context of Lockdown, the above mentioned articles can be illustrated and explained better with the help of mathematical reasoning that is the probability curve (Chance of occurrence of an expected event). Here probability means chance of getting infected of COVID-19 when we are exposed to the affected area.
This write-up is divided into two parts:
The 1st part explains our contact points in a normal day to day’s activities (before pandemic).
The 2nd part explains chance of getting infection from the affected environment and how Lockdown can help in it.
The 1st part: Susan, working as a Clark in an office travels 3 km each day, walks out of home at 9.10am opening her house entrance gate (1), waits for a taxi near a roadside pan shop buying chewing gums (2), collects changes(1), as taxi arrives sits in the taxi (1) opening the taxi door (1), on reaching office collects changes (2) from taxi, puts her attendance in the bio-matrix(1), wishing and shaking hands with at least 15 collogues on the way to her chamber(15). She wipes her table and chair (3), starts her work with cup of tea (2) where 20 files (20) are waiting pass through her. After 4 pm she walks out of the office along with her collogues car (2) and gets down on the way home for vegetables (5) and window shopping(5), then catches a taxi to reach home(3). (Numerical inside the brackets indicate contact count to a person/material by Susan, counting to 63). Hence, Susan comes across minimum 63 contact points in 7 hours out of home.
The 2nd part: Suppose in a population where 1% (i.e. 1 out of 100 person affected by COVID-19) is affected with COVID-19 and Susan is exposed to such environment for her daily work. Table 1, indicates Probability chat of getting COVID 19 infection.
Table 1: Probability chat for getting COVID 19 infection
Note: As probability lies between ‘1’ and ‘0’, scores above ‘1’ reflects as ‘EXCEEDS’ indicating high risk of getting infected.
Calculation: For, 1st visit to office, consider a minimum 50 contacts (Infected or uninfected person or materials).
Similarly, for 2nd visit to office, consider double of the first that is 2x 50 =100 contacts.
For 1% affected population, P(chance of getting infection ) = Com(1,1)/Com(100,1)=0.01
For 2% affected population, P(chance of getting infection) = Com(2,1)/Com(100,1) =0.02 ; etc
Analysis: In the case of Susan, by the probability chat (Table 1) of getting infected per day is 0.50, that is 50% chance per day or there is every chance that she may get affected on the second day.
If we look into 3% and above concentration of infected person in a population, there is every chance that the first visit to outside may infect the person which is evident from the above table. As this calculation is made on ideal situation of an office working person, individual cases may be more or less vulnerable along with other preventative measures against the pandemic.
If we look into WHO report as on 3rd July 2020, Indian infected population is 0.045% (i.e Infected Persons Number x 100/Total Population) which is much lower than that of top three countries USA, Brazil and Russia and the above table appears to be exaggerated.
Whereas, if we look into any quarantine centers where doubtful individuals are kept under observation without protection measures (as reported by many) [5], the percentages of the concentration may go much higher than the above tabulated categories leading to high risk.
Hence, implementing and abiding by Lockdown, reduces the risk factor of getting infected that is restricting Susan of going out, and the probability of infection will be ‘0’.
The recent serological survey of the Indian Council of Medical Research (ICMR) which suggests that 0.73% of the population has been exposed to the virus corroborates this analysis. Laxminarayan says he believes India could have 200 million people infected with COVID in September [6]. Even though Lockdown is not a permanent solution of the problem and implantation of it arrases to other related problems. Therefore, Lockdown is a preemptive step taken so that the number of infection will not increase exponentially and that the Indian Health System remain strong and active (Graph 1). We need work systematically in order to face the pandemic. That is to get enough time to prepare in terms of infrastructure, human resources, equipments, medication etc.
So, go out only in needs using protection measures, else stay home stay safe….
Because, Everything worthy around us till we are alive only.
Reference:
[1] Coronavirus disease (COVID-2019) situation reports. WHO. 3rd July 2020.
https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports
[2]https://towardsdatascience.com/the-mathematics-behind-the-lock-down-of-a-country-af5e31a8fdf
[3https://towardsdatascience.com/the-mathematics-of-lockdown-social-distancing-1257bc685022
[4]https://www.statisticshowto.com/probabilistic/#:~:text=What%20is%20a%20Probabilistic%20Model,probability%20distribution%20as%20a%20solution.
[5] the coronavirus crisis. npr. 25th March 2020.
https://www.npr.org/sections/goatsandsoda/2020/03/25/821431916/quarantined-in-india-no-soap-dirty-toilets-not-enough-coronavirus-tests
[6] 'India Probably Has Tens of Millions of COVID-19 Infections Already'. Karan Thapar 16th June 2020. https://thewire.in/health/india-probably-has-tens-of-millions-of-covid-19-infections-already
Disclaimer: This article is purely an opinion. The following piece of writing is not intended to cause panic, or hurt feelings. No political ideology is expressed in this article. This is not based on mathematical modeling or epidemiology but the conclusions of this study are supported by simple mathematical logic and reasoning.
