Losing and Winning Strategies of the Covid War

The Epidemic Equation

Every epidemic, including Covid-19, turns around a single equation,

R = N x p x (1-f).

N is the average number of persons who come into contact with an infected person while she is infectious;

p is the probability of the virus being transmitted during a contact;

f is the fraction of the population immune to the infection.

When an infected person comes into contact with an uninfected person she spreads the virus to the contact with probability p; the contact may either be immune or susceptible. The probability of being immune is f while that of being susceptible is1-f. So p x (1-f) is the probability of the contact becoming infected.

R — the Reproduction Number — is the average number of persons an infected person infects in turn. The disease grows exponentially if R is greater than 1; decays exponentially and dies away if R is less than 1; and persists at a steady rate if R is exactly 1.

Tactics of the Covid War

The epidemic equation severely restricts the tactics that may be used against the Sars-CoV-2 or any other virus for which no cure or vaccine is available just as the rules of chess dictate how the game may be played.

p — the probability of transmission-depends mostly on the contagiousness of the virus, though it may still be lowered by wearing masks and practicing physical distancing & hand hygiene.

Consequently only a few tactics are available for fighting Covid-19 and they all involve reducing N; travel restrictions, testing, contact tracing, isolation and social distancing.

Yet countries have combined these tactics in a surprising variety of ways to devise and execute different strategies for combating the Coronavirus, just as chess players play an astonishing number of different games using just a few legal chess moves. And that’s not true of just countries. Different provinces or states, within larger countries such as India, Canada or the United States, have often dealt with the pandemic in significantly different ways.

The Island Fortress

Prince Edward Island (P.E.I), Canada’s smallest province, is mainly known for its stunning scenery and agricultural produce — potatoes above all. It seems to have hardly been in the news even in Canada during the Covid-19 crisis. Yet the story of P.E.I’s stunning success against Covid-19 deserves to be known much more widely than it is.

This is what Canada’s Covid-19 case graph looks like. As of today (May 17, 2020) it has a total of 75,864 cases.

Growth of Total Coronavirus Cases in Canada (From: https://www.worldometers.info/coronavirus/country/canada/)

This is what P.E.I’s Covid-19 case graph looks like. It had a total of 27 cases. All have recovered.

Growth of Total Coronavirus Cases in P.E.I. (From: https://bing.com/covid/local/princeedwardisland_canada)

To put it in perspective, about four out of every thousand Canadians live in P.E.I. Yet P.E.I. accounts for only four out of every ten thousand confirmed Covid-19 cases in Canada. And while 5,679 (i.e. about 7.5% of all confirmed cases) have died in Canada, in P.E.I. the death toll is zero.

What makes it even more amazing is that P.E.I. is the most densely populated province in Canada which, one would think, would make it more infection prone than other provinces.

Canadian Provinces and Territories by Population Density (From: https://www.worldatlas.com/articles/canadian-provinces-and-territories-by-population-density.html)

How did P.E.I. do it?

By turning itself into an island fortress, pulling up the drawbridge and barricading itself against all-comers.

The defense against Covid-19 starts at a country’s border. Since Covid-19 spreads by human-to-human transmission you will cut the infection off at the source if you restrict travel from affected areas.

This seems too obvious to require stating. Yet the simplest things often prove hard to do.

On January 24, Theresa Tam, the Chief Public Health Officer, was asked whether travelers from Wuhan should be asked to self-isolate for two weeks on entering Canada. She thought it inadvisable on the ground that it would “stigmatize” the affected community.

The Canadian government’s commitment to minorities and immigrants is commendable but this was surely taking political correctness to the point of insanity. However, Canada was far from alone in hesitating to restrict travel from China. When I was in Bangkok in mid February big banners proclaimed in Thai, Chinese & English “We stand with Wuhan”. The Thai government was at that point was actually thinking of making travel to Thailand visa-free for Chinese citizens to show their empathy, and of course also grab a greater share of Chinese tourist dollars.

Canada finally scrambled to close its borders in the third week of March. By that time plenty of Covid cases had reached Canada, mostly by the way of Europe. There were several hundred confirmed cases already, one being the Prime Minister’s wife.

Checkpoint for people traveling to P.E.I from Canadian Mainland (Photo Credit: https://www.cbc.ca/news/canada/prince-edward-island/pei-public-heath-checkpoints-screening-covid-19-1.5507473)

Unlike the Canadian federal government, P.E.I. acted swiftly after recording its first case on March 14. A state of public emergency was declared on March 16. From March 21 onward all arriving travelers were being screened at bridges, ferry terminals and airports. Out of state arrivals to P.E.I. —including even Canadians from other states — were banned altogether and returning residents were asked to self-isolate for 14 days. These measures were backed by stiff fines and neighbors were encourage to report violators.

P.E.I. did not rely on travel restrictions and isolation alone. It also banned gatherings, closed schools and tested islanders extensively. Its testing rate of ~23,000 per million is quite close to Canada’s national rate of 30,000 per million. It also dis-allowed all non-essential services though its definition of “essential services” seems to have been fairly relaxed. Canabis and liquor sales were initially dis-allowed but later re-classified as essential and allowed!

However, it was really the travel restrictions which kept Covid-19 out of the state; all 27 positive cases were travel related.

The P.E.I. economy obviously took a hit since it relies on tourism to a large extent. However agriculture, the backbone of the economy, does not seem to have been seriously affected. In the long run, P.E.I.’s actions might even have a positive impact on tourism as its brand image and reputation for safety have been enhanced. And P.E.I. is now cautiously relaxing restrictions (though not the ones on travel) while the rest of Canada still struggles.

Of course it is not necessary to literally be an island in order to adopt the island fortress strategy. The tiny Himalayan kingdom of Bhutan has used it successfully as has the neighboring Indian state of Sikkim. In order to use this strategy it is necessary to be able to control your borders tightly. Having just a few points of entry and exit helps. So does being small and loosely coupled to the global supply chain.

Covid Denial

What do you do if the virus has already breached your defenses?

The easiest strategy — or perhaps non-strategy-is to simply pretend that the problem doesn’t exist.

I had previously discussed Covid denial in a blog published on April 5.


How are the Covid deniers doing?

Covid-19 has caught up with Belarus and this is what the country’s case curve now looks like.

Growth of Total Coronavirus Cases in Belarus (From: https://www.worldometers.info/coronavirus/country/belarus/)

There have been 28,681 cases and 160 Covid-19 deaths in Belarus. President Lukashenko still continues to insist that nobody died from coronavirus alone and that all the deaths where due to underlying conditions such as heart disease and diabetes. The death rate at 0.6% is indeed very low — lower than South Korea’s or Germany’s. This could be due to good luck or good case management but some suspect that deaths are being deliberately under-reported.

Belarus holds a massive victory parade to commemorate the Soviet Union’s victory in the Second World War (Photo credit: https://www.aljazeera.com/news/2020/05/belarus-holds-massive-victory-day-parade-coronavirus-200509143227588.html)

The Belarus premier football league continues though the stadiums are much emptier and the President insisted on holding a massive victory parade to commemorate the Soviet Union’s victory in the Second World War.

Places of worship are still open in Tanzania and President John Magufuli wants people to go there to find true healing. Till May 8 Tanzania had reported 509 Covid-9 cases and 21 deaths. However, the President questioned the official data and had the head of National Laboratory suspended. Since May 8 Tanzania has stopped reporting Covid-19 figures.

In my previous blog I expressed the fear that “when the lockdowns begin to bite both Trump and Bolsonaro may flip-flop again.” Unfortunately this has proved true. President Jair Bolsonaro continues to minimize the Covid-19 crisis and has been described by the respected medical journal Lancet as “perhaps the biggest threat” to Brazil’s ability to successfully fight the coronavirus pandemic. And Brazil is quickly becoming an epidemic hotspot.

In the Hollywood movie “Independence Day” the US President led the world against alien invaders. It was reasonable to expect that in real as in reel life, any war waged by humanity against an aggressive non-human species, such as Sars-CoV-2, would be led by the President of the country with the largest economy, strongest military and best scientific resources. However, the story of President “Trump’s coronavirus meltdown” is now too well known to require re-telling.

Covid denial goes hand-in-hand with belief in magical cures. The President of Tanzania is relying on a Madagascar herbal remedy, that is being trialed in several African countries. President Trump has touted the benefits of hydroxychloroquine, promised a vaccine in just a few months and expressed the dubious hope that exposure to ultraviolet light and the injection of disinfectants could help Covid patients.

Herd Immunity

India imposed a stringent lockdown in the third week of March. Of course the point of a lockdown is to reduce N in the epidemic equation and thereby bring down R.

To an extent India succeeded. The R for India dipped from 1.83 in March to 1.27 in May according to researchers at the Institute of Mathematical Sciences in Chennai. This probably saved thousands or tens of thousand lives.

Growth of New Coronavirus Cases in India (From: https://www.worldometers.info/coronavirus/country/india/)

However the number of daily new cases in India still kept on rising. At the same time the lockdown froze India’s economy. The composite Purchasing Managers Index (PMI) is a measure of economic trends between successive months. Numbers above 50 indicate expansion while those below 50 indicate contraction. India’s in April was 7.2 — its lowest ever and the lowest in the world. According to Bloomberg this indicates economic contraction at an annual rate of 15% . Rajiv Bajaj, an eminent industrialist wondered whether India would have an economy left if the lockdown continued any longer.

The lockdown also caused India’s poor -who number in the tens of millions - enormous hardship and may have resulted in the loss of 122 million jobs. It is difficult to get hard data but there have been credible reports of up to 600 deaths — the majority from suicides due to financial distress-due to the lockdown.

Dr. Jayaprakash Muliyil, the former principal of Vellore Christian Medical College and a distinguished Indian epidemiologist, believes that herd immunity holds the key to a way out of India’s lockdown.

Graphic Illustration of Herd Immunity (Source: https://www.weforum.org/agenda/2020/03/coronavirus-can-herd-immunity-really-protect-us/)

To explain the concept of herd immunity let’s go back to the epidemic equation R = N x p x (1-f).

When an epidemic starts f is near zero. R at that point is N x p — which we call R0 the basic reproduction number of the disease. Most experts believe that R0 is a number between 2 and 3 for Covid-19 though some research indicates that it could higher.

As the epidemic progresses more and more people get infected. Infection is believed to confer a degree of immunity — though since Covid-19 is such a new disease we can’t be totally sure. So f increases and consequently R decreases. The number of infections climbs faster and faster as long as R remains greater than 1. However the epidemic peaks when R becomes 1. School algebra shows that this happens when the fraction infected becomes 1–1/R0. If R0 is, e.g. 2.5, this point is reached when the fraction is 60%. This is known as the herd immunity threshold (HIT).

The epidemic does not magically stop when threshold is reached. Cases and deaths continue. In epidemiology this is know as overshoot. However, from that point onward the virus finds it increasingly hard to find people to infect and the epidemic begins to die down. (See graphic).

This explanation is a bit too simplistic. It doesn’t take into account the fact that disease transmission may be different for different segments of a population. So different segments of the population could have different herd immunity thresholds.

Dr. Mulyil’s proposed way out of lockdown is based on the following.

  1. His estimate that the herd immunity threshold is only 40% in India’s villages — where the majority of its population lives -as against 60% in cities.
  2. The fatality rate for Covid-19 is much higher among older people than the young; and much higher among those with underlying conditions than the healthy.

Dr. Mulyil advocates letting most economic activities proceed normally, while the epidemic runs its course in India, till herd immunity is achieved. In a television interview he seems to suggest that this would take 3–4 months, after which life could go back to normal. Of course many would fall sick and die while the disease progresses. However, the numbers can be reduced by educating families and communities to care for the elderly and the vulnerable.

Dr. Mulyil estimates that this strategy could lead to two million deaths, mostly of people over 60. However, he considers the price worth paying to spare tens or hundreds of millions, further hardship.

The herd immunity strategy, in its pure form, seems too risky to be adopted by the Indian or any other government, though the Swedish, Dutch and British have all reportedly flirted with it. Given how little we still know about the disease, the outcome could be even worse than Dr. Mulyil’s projection. Even the current Covid-19 caseload is severely stressing the healthcare system in cities such as Ahmedabad and Mumbai, where hospitals are scrambling to “create” beds for critically ill Covid-19 patients. India in these circumstances, is very unlikely to relax the lockdown without keeping several controls in place.

The Turkish Way

Still, is it possible to find a way to keep major parts of the economy functioning normally, while protecting the vulnerable and not letting Covid-19 overwhelm the healthcare system?

Several countries tried. Many had to resort to a hurried lockdown when the number of cases threatened to spin out of control.

A few however seem to have succeeded.

While a lot has been written about the Swedish experiment, much less attention has been paid to Turkey whose performance on almost all metrics has been better than Sweden’s.

Growth of New Cases in Sweden and Turkey (From:https://www.worldometers.info/coronavirus/country)

The above graph suggests that the number of new cases is stable in Sweden while it is decreasing in Turkey.

Calculated/Compiled from https://www.worldometers.info/coronavirus/country

Turkey also seems to be doing much better than Sweden when it comes to per capita case & death rates. And it is way ahead in case fatality rate (total number of deaths divided by total number of confirmed cases).

Turkey, had a strong and universal healthcare system but that, by itself, was not enough protection against Covid-19 as Italy, Spain and France had learned. It was necessary to have an effective pandemic plan which could be put into practice fast.

Restrictions on travel to China, Iran, Italy, Iraq and South Korea were imposed in February even before there was a single confirmed case in Turkey. (However, there probably were unreported cases in Turkey by then.) Further travel bans were imposed after the first case was confirmed on March 11. By April 2 Turkey had banned not only all international travel but also travel between different states and in and out of 30 major cities. 25,000 international visitors and 10,000 pilgrims had been quarantined.

By early April the steep growth of cases was reminiscent of Italy and the Western media was predicting the collapse of Turkey’s healthcare system. Cases in fact grew tenfold in April but Turkey’s healthcare system did not collapse.

Turkey’s considerable indigenous manufacturing capabilities helped. And its investment in healthcare in the past 2 decades paid off. There was no shortage of intensive care units, medical equipment, health care staff or hospital beds. In fact a hospital with 2,862 beds was built during the pandemic and began functioning on April 21.

Source: https://www.trtworld.com/turkey/how-turkey-succeeded-in-producing-ventilators-within-a-month-35619

Unlike Sweden, but like most other countries, Turkey closed bars, restaurants, malls, universities and schools and mandated social distancing in public places and public transport. However in some respects its social distancing rules were unique. Curfew was imposed on the under 20’s, the over 65’s and the chronically ill. The remaining population was subject to a curfew — but only on weekends and festival days like the last 10 days of Ramadan. Free masks — five each week — were distributed to each household.

Most offices and factories remained open in Turkey though work from home was encouraged whenever possible. To keep factories open Turkey had to put in place a massive program of testing and contact tracing. Turkey’s contact tracing is mainly carried out by 6,000 teams, of 2–3 medics and claims a success rate of 99%. A digital app is also now available for this purpose. It has also ramped up its testing tremendously and now conducts 30,000–40,000 tests per day.

Turkey also introduced a number of clinical innovations which it claims contributed to its success. These include the use of the Japanese drug favipiravir, which Turkey stocked up one-and-a-half months before any cases were seen in the country, and the use of high oxygen flow rather than early intubation. The efficacy of these methods has however still needs to be established by rigorous research.

Turkey did commit several missteps. Its initial curfew announcement was abrupt and led to confusion and panic buying. Labor unions have claimed that keeping factories open puts workers at risk and that their probability of being infected is 3.2 times as high as the general population. The situation is expected to get worse; several factories are still working at reduced capacity because of the lack of demand and once capacity increases social distancing will become harder to maintain. The accuracy of Turkey’s data has also been questioned.

The economic impact of Turkish policies is not yet clear. Turkey’s manufacturing PMI hit a record low of 33.4 in April. However, some economic contraction was inevitable given the reduced demand from Europe and elsewhere. The economy, never having stopped, will not require restarting and will probably pick up speed quickly once demand returns.

The Turkish experiment seems promising and if successful may provide a model for India and other less developed countries trying to find their way out of lockdown. It is a much more relevant example than much touted Sweden for several reasons. One is that in India and similar countries usually many people — often from different generations-share a home. The average household size is 2.2 in Sweden, 3.35 in Turkey and 4.9 in India.


Disclosure: I am the Director of Smart Consulting Solutions Pte Ltd, incorporated in Singapore and its subsidiary Radix Analytics Pvt Ltd, incorporated in India. I am also a Visiting Faculty Member at the Indian Institute of Management, Udaipur. However, the opinions expressed in this post are solely mine and not necessarily shared by any company or institution with which I am affiliated.

I thank Dr. Alice Metzlar Horrocks for first drawing my attention to the P.E.I. success story.

I am, as always, grateful to my friend Dr. Ashish Kumar Dawn for many insightful comments



I have spent over 30 years in academia and industry exploring how to use mathematical methods to solve real world problems