The R0 Effect
The Covid19 pandemic is a full fledged global threat today. At the time of writing, we now have more than 472,907 cases across the planet with 21,315 deaths. For now, India has 681 confirmed infections with 12 deaths. Although it seems that while India is on the cusp of an exponential breakout, the Prime Minister has announced a “21 day Lockdown” to take the virus head-on.
This is a great move, albeit a little too late. That’s because
a) India hasn’t tested enough — granted that only ~2.5% of all tests have come back positive, compared to a much higher number for other countries. But I would much rather feel safer with the knowledge that there are ~3100 Indians that have tested positive and have been isolated (with additional tests completed for say 100,000 people) than with the knowledge that there are only 681 infections and an unidentified number of carriers more.
b) 17.9% of people testing positive for the virus are asymptomatic (95% credible interval for this number of 15.5% to 20.2%). This could possibly mean that there are far more carriers of the infection that haven’t been close to a testing centre yet. With an R0 (this is important — this is the Reproductive factor of a typical infection) of 2.4, each asymptomatic person is now infecting an average of 2.4 more people.
(Source: https://www.forbes.com/sites/brucelee/2020/03/18/what-percentage-have-covid-19-coronavirus-but-do-not-know-it/#5a9acb5a7e90)
c) A lockdown for 3 weeks is frankly not enough. This will be apparent shortly.
The Epidemic Model
This brings us to the epidemic model. The model that’ll be the difference between life and death.
A typical infectious disease typically follows the following model:
Susceptible → Exposed → Infected → Removed
The dynamics of this model are characterized by the following set of four ordinary differential equations that correspond to the stages of the disease’s progression
dS/dt=−(Rt/Tinf)⋅IS
dE/dt=(Rt/Tinf)⋅IS−(E/Tinc)
dI/dt=(E/Tinc)−(I/Tinf)
dR/dt=(I/Tinf)
In these equations:
Rt= R0 factor (the multiplicative factor for the infection) at a certain period of time
Tinc= Length of incubation period
Tinf =Duration the patient is infectious
(Source: https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)30260-9/fulltext)
This now brings us to a couple of simulations of how this would progress in India.
Simulation 1: If we never had a lockdown
The Indian Government announced a massive lockdown starting 25th of March 2020 for a period of 21 days. Had this not been announced and people continued their lives, we would be facing a pandemic of epic proportions.
(Hat-tip to Gabriel Goh for the Epidemic Calculator — the graph above has been based on this calculator)
Assumptions: a) A person who recovers once will not contract the virus again b) Other assumptions are the standard medical/clinical values plugged in for realism — eg morbidity ~2%, average recovery time ~11 days, Tinc ~5.2 days, Tinf ~2.9 etc
Summary: This scenario predicts that within the Indian population of ~1.33B, the virus runs amok unchecked with an R0 of 2.4, putting an enormous stress on the hospital system, leading to more than 22 million fatalities with a peak hospitalization of ~62 million on day 166. Another estimate — of the 62M hospitalizations, at its peak, an approximate 15 million people would need ventilator support (20–25%). At present, India has only 30,000–40,000 ventilators available.
This is obviously a) Just unimaginable and untenable and b)Hypothetical, since we have already announced a lockdown.
That brings us to the next scenario.
Simulation 2: Lockdown for 21 days
This is where things get interesting.
The single biggest factor in helping reduce the impact of this virus is the R0. The larger the R0, the faster the infection spreads. If R0>1, the virus will continue to spread until everyone is infected at least once. If R0<1, people would continue to infect a much smaller group, thereby leading to the end of the spread of the infection.
The biggest purpose of this lockdown is reducing the R0 so that it reaches <1. If the R0 does not fall <1, the lockdown would have failed.
Here’s an example of some of the types of lockdowns:
Status 0 Green: Business as Usual
Status 1 Blue : Case Isolation, Medium Social Distancing, Closure of group activities >50, Limited mass-transit stoppages, Personal sanitation
Status 2 Yellow: Blue + Household quarantine, Closures of Schools/Universities, Work-From-Home, Restrictions on travel
Status 3 Orange: Yellow+Stoppage of deliveries, maids/cooks in societies, Strong Social Distancing, Groups activities >5, Complete Travel lockdown
Status 4 Red: Orange+Complete isolation, Complete distancing (especially for people aged>70), No Personal travel, Large-scale Govt intervention
It is quite evident that the R0 factor would be inversely proportional to the Emergency status — the higher the alert, the lower the reproductive factor R0. The R0 for an Orange lockdown would << R0 for a Yellow lockdown. Additionally, there would exist multiple versions of an R0 even within a single Stage.
For example, if India with its current format of a lockdown were at a Status 4 Red, but given its dense population and general inability to implement a complete lockdown, we could assume the new R0 (lets call it Rt) to be close to 0.79 post implementation.
With this, here’s how the new infection curve would look like (assuming a complete indefinite lockdown)
In an attempt to simulate the conditions for India, this scenario assumes that we have implemented a lockdown after 7 deaths (much like what happened here)
Summary: The results are quite surprising — By Day 218, the total number of fatalities would be close to 266 and a total number of infected individuals would not cross ~13500. This also assumes that the peak number of hospitalizations would be close to 473, with a peak of ~118 requiring ventilator support. Quite manageable?
Again, this assumes that we have an indefinite lockdown — unlike what has been announced by PM Modi. Lets simulate what would happen if the lockdown was indeed lifted in 21 days.
In this simulation, after 21 days of a lockdown (on Day 75), the R0 changes back from 0.79 to say, 1.8 (possibly because people are still quite careful, washing their hands etc but just not good enough?). On this day, India still has 505 infectious citizens actively circulating the disease with a total of 59 fatalities.
Summary: Here we are back again — the virus infecting ~75% of the entire population, leading to 18m fatalities, peak hospitalization of 39.7m on Day 220 (54+166) and a peak of ~9.9m ventilators required on the same day.
If you thought that just a 21 day lockdown would end Covid19’s run in India, I hope this chart helps you understand the situation a little better.
So what do we do?
Simulation 3: Indefinite and Complete Lockdown
There is no other way. The virus will have a resurgence, primarily since its hosts (at least most of them) show symptoms much later — thereby infecting many others in this duration. What we need to do is make that R0 as small as possible. Here’s what India could do to make this a short affair and reduce R0 immediately:
a) Test, test, test. No better way to identify infections, isolate them and treat them. This is one of the BEST ways to reduce R0.
b) A complete and a total lockdown. Extend the current one until the number of active infectious citizens drops to 0. This might take at least ~160 days (fewer days if the R0 is even lower than 0.79). So its in our best interests to make this lockdown a successful one (at least until a treatment is found)
c) Build/Acquire ventilators. This is again something that goes without saying. People with pre-existing unrelated conditions need ventilator support as well. Its impossible to turn away these patients.
d) Find Treatments. While a number of drugs have shown promise, even with expedited approvals, human trials to evaluate long-term effects would take at least 12–18 months. We need to buy time.
e) Stimulate the economy. Its great that business leaders are talking about supporting their employees during these tough times. But if this goes on for more than 2 months, we could expect many, many more people to lose their jobs. This is where the Government would need to step in and support payments, rent/other liabilities, direct cash transfers to stimulate demand.
f) Educate. Educate your neighbors, family, friends and other citizens on proper social-distancing and quarantining themselves — to help lower R0.
Lives are at stake. Time to act.
