Meet and beat

Soon after our first “date” (we didn’t know when we were going to meet that it was going to be a “date” that would ultimately lead to marriage), the person who is now my wife wrote a cute  blogpost titled “Karabath Series“.

In that she had written about “arranged louvvu”, and went on to write this:

First step is to keep your eyes open to delicious and nutritious tharkaris(potential marriage material girls/boys). Then, somehow through some network, make someone set you two up. Third, interact. with tact. Fourth, put meet. or beat. Fifth, this can go in three ways now. First, is a no. Definite no. Second, yes. Full yes. Third, Yes, but not yet. This is a lucrative possibility which gives super scope to put more meets, learn about each others funny faces, food tastes, sense of humour, patience, sense of dressing, chappliying, smells, etc

The fourth point is key, and it was amply clear to me after reading it that it was aimed at me. For a few days before this was written, we had met, and “put beat” (as they say in Bangalore parlance).

We had sort of been “google talk friends” for two years then, and “orkut friends” for three. I had been in the arranged marriage market, and I had out of the blue suggested that we meet. After a little song and dance about whether meeting would be appropriate or not, the discussion went on to where to meet.

This is when she mentioned we could “simply walk around Gandhi Bazaar together”. Things moved fast after that. We met in front of Vidyarthi Bhavan at 4 o’clock on the long weekend Monday, and then started walking. Two hours of walking around Basavanagudi later, we stopped at a Cafe Coffee Day (now closed) to sit for a bit and have coffee. Five years later I documented what we’ve now retrofitted as our “first date” here.

This is not a “personal” post. This is yet another post about how the world might change after the covid crisis. It just has a long preamble, that’s all.

One of the things that is going to suffer after the crisis is over is cafes. I’d written in my post on verandahs about how cafes have served well as good “third places” to meet people. That option is not going to be too much of an option going forward, for even after cafes reopen, people will be loathe to go there and sit in close proximity to strangers.

So how do we do “general catchups”? How do we do dates? How do we discuss business ideas with people? The solution for all this lies in what we ended up doing on our first date. I don’t claim we invented it. Well before we went on this date, journalist Shekhar Gupta had started this series on NDTV called “walk the talk”.

What do you do? You just meet at an agreed place, pick up something to munch on or drink, and start walking. You can take side roads to make sure there isn’t too much traffic. The length of the walk can vary based on how interesting you find each other, and how much time you have.

The best part of meeting someone while walking is that there are no awkward silences. Rather, since you aren’t looking at each other constantly, the silences won’t be awkward. When you run out of things to talk about, there will be some visual stimulus by something you walk by. What’s not to like?

The only issue with walking and talking is that it might be an excellent idea for Bangalore, but not so much for a lot of other cities. Delhi and Bombay, for example, are impossible to step outside in for at least the summer. Maybe in those places we’ll end up having heavily “air cooled” or heavily fanned outdoor places.

It’s not for nothing that the phrase “putting beat” (for aimlessly walking around) was invented in Bangalore.

 

 

Expertise

During the 2008 financial crisis, it was fairly common to blame experts. It was widely acknowledged that it was the “expertise” of economists, financial markets people and regulators that had gotten us into the crisis in the first place. So criticising and mocking them were part of normal discourse.

For example, most of my learning about the 2008 financial crisis came from following blogs written by journalists, such as Felix Salmon, and generalist academics such as Tyler Cowen or Alex Tabarrok or Arnold Kling, rather than blogs written by financial markets experts or practitioners. I don’t think it was very different for too many people.

Cut to 2020 and the covid-19 crisis, and the situation is very different. You have a bunch of people mocking experts (epidemiologists, primarily), but this is in the minority. The generic Twitter discourse seems to be “listen to the experts”.

For example, there was this guy called Tomas Pueyo who wrote a bunch of really nice blog posts (on Medium) about the possible growth of the disease. He got heavily attacked by people in the epidemiology and medicine professions, and (surprisingly to me)  the general twitter discourse backed this up. “We don’t need a silicon valley guy telling us epidemiology”, went the discourse. “Listen to the experts”.

That was perhaps the beginning of the “I’m not an epidemiologist but” meme (not a particularly “fit” meme in terms of propagation, but one that continues to endure). For example, when I wrote my now famous tweetstorm about Bayes’s theorem and random testing 2-3 weeks back, a friend I was discussing with it advised me to “get the thing checked with epidemiologists before publishing”.

This came a bit too late after I’d constructed the tweetstorm, and I didn’t want to abandon it, and so I told him, “but then I’m an expert on Probability and Bayes’s Theorem, and so qualified to put this” and went ahead.

In any case, I have one theory as to why “listen to the expert” has become the dominant discourse in this crisis. It has everything to do with politics.

Two events took place in 2016 that the “twitter establishment” (the average twitter user, weighted by number of followers and frequency of tweeting, if I can say) did not like – the passing of the Brexit referendum and the election of President Trump.

While these two surprising events took place either side of the Atlantic, they were both seen as populist movements that were aimed at the existing establishment. Some commentators saw them as a backlash “against the experts”. The rise of Trump and Brexit (and Boris Johnson) were seen as part of this backlash against expertise.

And the “twitter establishment” (the average twitter user, weighted by number of followers and frequency of tweeting, if I can say) doesn’t seem to like either of these two gentlemen (Trump and Johnson), and they are supposed to be in power because of a backlash against experts. Closer home, in India, the Modi government allegedly doesn’t trust experts, which critics blame for ham-handed decisions like Demonetisation and pushing through of the Citizenship Amendment Act in the face of massive protests (the twitter establishment doesn’t like Modi either).

Essentially we have a bunch of political leaders who are unpopular with the twitter establishment, and who are in place because of their mistrust of expertise, and multiplying negative with negative, you get the strange situation where the twitter establishment is in love with experts now.

And so when mathematicians or computer scientists or economists (or other “Beckerians“) opine on covid-19, they are dismissed as being “not expert enough”. Because any criticism of expertise of any kind is seen as endorsement of the kind of politics that got Trump, Johnson or Modi into power. And the twitter establishment (the average twitter user, weighted by number of followers and frequency of tweeting, if I can say) doesn’t like that.

Advertising

When I first joined Instagram in 2013 or 2014, the first thing that fascinated me about the platform was the quality of advertisements. At that point in time, all advertisements there looked really good, like the pictures that the platform was famous for helping sharing.

It wasn’t like the clunky ads I would see elsewhere on the internet, or even on Facebook – which mostly stuck out like a sore thumb in the middle of whatever content I was consuming at that point in time. Instagram advertisements looked so good that I actually paid them considerable attention (though I hardly clicked on them back then).

Over the years, as Facebook has gotten to know me better (I hardly use Facebook itself nowadays. But I use a lot of Instagram. For now I’ll believe Facebook’s claim that my WhatsApp information is all encrypted and Facebook doesn’t learn much about me through that), and the advertisements have gotten better and more relevant.

Over the last one year or so (mostly after I returned to India) I’ve even started clicking on some of the ads (yes they’ve become that relevant), giving Facebook even more information about myself, and setting off a positive feedback loop that makes the advertisements more relevant to me.

Over the years I’ve attended talks by privacy experts about the privacy challenges of this or that platform. “They’ll get all this information about you”, they say, “and then they can use that to send you targeted advertisements. How bad is that?”. If I think about all the problems with telling too much about myself to anonymous platforms or companies, receiving better targeted advertisements is the least of my worries.

As a consumer, better targeted ads means better information to me. Go back to the fundamentals of advertising – which is to communicate to the customer about the merits of a particular product. We think advertising can be annoying, but advertising is annoying only when the advertisements are not relevant to the target customer. 

When advertisements are well targeted, the customer gets valuable information about products that enables them to make better decisions, and spend their money in a better fashion. The more the information that the advertiser has about the end customer, the better the quality (defined in terms of relevance) the advertisements that can be shown.

This is the “flywheel” (can’t imagine I would actually use this word in a non-ironic sense) that Facebook and affiliated companies operate on – every interaction with Facebook or Instagram gives the company more information about you, and this information can be used to show you better targeted advertisements, which have a higher probability of clicking. Because you are more likely to click on the advertisements, the advertiser can be charged more for showing you the advertisement.

Some advertisers have told me that they elect to not use “too much information” about the customer while targeting their advertisements on Facebook, because this results in a much higher cost per click. However, if they look at it in terms of “cost per relevant click” or “cost per relevant impression”, I’m not sure they would think about it the same way.

Any advertisement shown to someone who is not part of the intended target audience represents wastage. This is true of all forms of advertising – TV, outdoor, print, digital, everything. It is no surprise that Facebook, by helping an advertiser advertise with better (along several axes) information about the customer, and Google, by showing advertisements after a customer’s intent has been established, have pretty much monopolised the online advertising industry in the last few years.

Finally, I was thinking about advertising in the time of adblockers. Thanks to extensive use of ad-blockers (Safari is my primary browser across devices, so ad blocking is effective), most of the digital advertisements I actually see is what I see on Instagram.

Today, some publication tried to block me from reading their article because I had my ad-blocker on. They made a sort of moral pitch that advertising is what supports them, and it’s not fair if I use an ad-blocker.

I think they should turn to banner ads. Yes. You read that right.

To the best of my knowledge, ad blockers work by filtering out links that come from the most popular ad exchanges. Banner ads, which are static and don’t go through any exchange, are impossible to block by ad-blockers. The problem, however, is that they are less targeted and so can have higher wastage.

But that is precisely how advertising in the offline versions of these newspapers works!

Something is better than nothing.

Verandahs

Both the houses that I grew up in (built in 1951 and 1984) had large verandahs through which we entered the house. Apart from being convenient parking spaces for shoes and bicycles (the purpose that the “hallway” in British homes also performs), these were also large enough to seat and greet guests that you weren’t particularly familiar with.

None of the other houses that I’ve lived in (as an adult, and most of them being apartments constructed in the last 20-30 years) have verandahs. Instead, you enter directly into the living room.

There might be multiple reasons for this. Like you don’t want to waste precious built up area on a separate room for guests that is likely to be sparingly used. Some people might consider a separate space to meet certain kinds of people who come home to be classist, and unbecoming of a modern home. Finally, over the last 20 years or so, not as many people come home as they used to earlier.

I’m completely making this up, but I think one reason that the number of people who come home is lower is that we now have more “third places” such as restaurants or bars or cafes to meet people. If you can meet your acquaintances for breakfast, or tea, or for a drink, there is less reason to call them home (or visit them). Instead, your home can be exclusive to people who you know very well and who you can invite into the fullness of your living room.

Now, I must confess that even before the covid-19 crisis, the wife and I had started missing a verandah, and have been furiously rearranging our large living-cum-dining room over the last year to create a “verandah like space”.

When government officials conducting the census come home, where do you make them sit? What about the painter or carpenter who has come to have a discussion about some work you want to get done? What about the guy from the bank who has come to get your signature on some random forms? Or the neighbour or relative who suddenly decides to pop in without being invited?

In either of the homes I grew up in, the verandah was the obvious place to seat and greet these people. You let people into your home, but not really. Now again, some people might think this is casteist or classist or whatever, but you don’t want to expose your private spaces to the world. With relatives and some acquaintances, though, it could get tricky, as seating someone in the verandah was too blatant an indication that they were not welcome, and could potentially cause offence.

In any case, the verandah was this nice middle place that was neither inside nor outside (Hiranyakashipu could have been killed in a verandah). Apart from seating the uninvited, verandahs meant that you could call acquaintances home, and the rest of the house could go on with its business completely ignoring that a guest had come.

In fact in my late teenage I had this sort of unspoken arrangement with my parents that I was free to call anyone home as long as I “entertained” them in the verandah. The family’s permission to invite someone would be necessary only if they were to come into the living room.

In any case, I think verandahs are going to make a comeback. As I wrote in my last post, the covid-19 crisis means that we are going to lose “third spaces” like restaurants or cafes or bars which were convenient places to meet people. And you don’t want to make a big deal of a formal invite home (including taking your family’s permission) to meet the sort of people you’ve been meeting on a regular basis in “third spaces”. A verandah would do nicely.

The only issue, of course, is that you can’t change the architecture of your home overnight, so verandahs may not make as quick a comeback as one would like. However, I think houses that are going to be constructed are going to start including a verandah once again (as well as a study). And people will start creating verandah-like spaces where they can.

One guy in my apartment works from home and gets lots of random visitors. He’s installed an artificial wall in his living room to simulate a verandah. Maybe that’s a sort of good intermediate solution?

Fulfilling needs

We’re already in that part of the crisis where people are making predictions on how the world is going to change after the crisis. In fact, using my personal example, we’ve been in this part of the crisis for a long time now. So here I come with more predictions.

There’s a mailing list I’m part of where we’re talking about how we’ll live our lives once the crisis is over. A large number of responses there are about how they won’t ever visit restaurants or cafes, or watch a movie in a theatre, or take public transport, or travel for business, for a very very long time.

While it’s easy to say this, the thing with each of these supposedly dispensable activities is that they each serve a particular purpose, or set of purposes. And unless people are able to fulfil these needs that these activities serve with near-equal substitutes, I don’t know if these activities will decline by as much as people are talking about.

Let’s start with restaurants and cafes. One purpose they serve is to serve food, and one easy substitute for that is to take the food away and consume it at home. However, that’s not their only purpose. For example, they also provide a location to consume the food. If you think of restaurants that mostly survive because working people have their midday lunch there, the place they offer for consuming the food is as important as the food itself.

Then, restaurants and cafes also serve as venues to meet people. In fact, more than half my eating (and drinking) out over the last few years has been on account of meeting someone. If you don’t want to go to a restaurant or cafe to meet someone (because you might catch the virus), what’s the alternative?

There’s a certain set of people we might be inclined to meet at home (or office), but there’s a large section of people you’re simply not comfortable enough with to meet at a personal location, and a “third place” surely helps (also now we’ll have a higher bar on people we’ll invite home or to offices). If restaurants and cafes are going to be taboo, what kind of safe “third places” can emerge?

Then there is the issue of the office. For six to eight months before the pandemic hit, I kept thinking about getting myself an office, perhaps a co-working space, so that I could separate out my work and personal lives. NED meant I didn’t execute on that plan. However, the need for an office remains.

Now there’s greater doubt on the kind of office space I’ll get. Coworking spaces (at least shared desks) are out of question. This also means that coffee shops doubling up as “computer classes” aren’t feasible any more. I hate open offices as well. Maybe I have to either stick to home or go for a private office someplace.

As for business travel – they’ve been a great costly signal. For example, there had been some clients who I’d been utterly unable to catch over the phone. One trip to their city, and they enthusiastically gave appointments, and one hour meetings did far more than multiple messages or emails or phone calls could have done. Essentially by indicating that I was willing to take a plane to meet them, I signalled that I was serious about getting things done, and that got things moving.

In the future, business travel will “become more costly”. While that will still serve the purpose of “extremely costly signalling”, we will need a new substitute for “moderately costly signalling”.

And so forth. What we will see in the course of the next few months is that we will discover that a lot of our activities had purposes that we hadn’t thought of. And as we discover these purposes one by one, we are likely to change our behaviours in ways that will surprise us. It is too early to say which sectors or industries will benefit from this.

Tests per positive case

I seem to be becoming a sort of “testing expert”, though the so-called “testing mafia” (ok I only called them that) may disagree. Nothing external happened since the last time I wrote about this topic, but here is more “expertise” from my end.

As some of you might be aware, I’ve now created a script that does the daily updates that I’ve been doing on Twitter for the last few weeks. After I went off twitter last week, I tried for a couple of days to get friends to tweet my graphs. That wasn’t efficient. And I’m not yet over the twitter addiction enough to log in to twitter every day to post my daily updates.

So I’ve done what anyone who has a degree in computer science, and who has a reasonable degree of self-respect, should do – I now have this script (that runs on my server) that generates the graph and some mildly “intelligent” commentary and puts it out at 8am everyday. Today’s update looked like this:

Sometimes I make the mistake of going to twitter and looking at the replies to these automated tweets (that can be done without logging in). Most replies seem to be from the testing mafia. “All this is fine but we’re not testing enough so can’t trust the data”, they say. And then someone goes off on “tests per million” as if that is some gold standard.

As I discussed in my last post on this topic, random testing is NOT a good thing here. There are several ethical issues with that. The error rates with the testing means that there is a high chance of false positives, and also false negatives. So random testing can both “unleash” infected people, and unnecessarily clog hospital capacity with uninfected.

So if random testing is not a good metric on how adequately we are testing, what is? One idea comes from this Yahoo report on covid management in Vietnam.

According to data published by Vietnam’s health ministry on Wednesday, Vietnam has carried out 180,067 tests and detected just 268 cases, 83% of whom it says have recovered. There have been no reported deaths.

The figures are equivalent to nearly 672 tests for every one detected case, according to the Our World in Data website. The next highest, Taiwan, has conducted 132.1 tests for every case, the data showed

Total tests per positive case. Now, that’s an interesting metric. The basic idea is that if most of the people we are testing show positive, then we simply aren’t testing enough. However, if we are testing a lot of people for every positive case, then it means that we are also testing a large number of marginal cases (there is one caveat I’ll come to).

Also, tests per positive case also takes the “base rate” into effect. If a region has been affected massively, then the base rate itself will be high, and the region needs to test more. A less affected region needs less testing (remember we only  test those with a high base rate). And it is likely that in a region with a higher base rate, more positive cases are found (this is a deadly disease. So anyone with more than a mild occurrence of the disease is bound to get themselves tested).

The only caveat here is that the tests need to be “of high quality”, i.e. they should be done on people with high base rates of having the disease. Any measure that becomes a metric is bound to be gamed, so if tests per positive case becomes a metric, it is easy for a region to game that by testing random people (rather than those with high base rates). For now, let’s assume that nobody has made this a “measure” yet, so there isn’t that much gaming yet.

So how is India faring? Based on data from covid19india.org, until yesterday India had done (as of yesterday, 23rd April) about 520,000 tests, of which about 23,000 people have tested positive. In other words, India has tested 23 people for every positive test. Compared to Vietnam (or even Taiwan) that’s a really low number.

However, different states are testing to different extents by this metric. Again using data from covid19india.org, I created this chart that shows the cumulative “tests per positive case” in each state in India. I drew each state in a separate graph, with different scales, because they were simply not comparable.

Notice that Maharashtra, our worst affected state is only testing 14 people for every positive case, and this number is going down over time. Testing capacity in that state (which has, on an absolute number, done the maximum number of tests) is sorely stretched, and it is imperative that testing be scaled up massively there. It seems highly likely that testing has been backlogged there with not enough capacity to test the high base rate cases. Gujarat and Delhi, other badly affected states, are also in similar boats, testing only 16 and 13 people (respectively) for every infected person.

At the other end, Orissa is doing well, testing 230 people for every positive case (this number is rising). Karnataka is not bad either, with about 70 tests per case  (again increasing. The state massively stepped up on testing last Thursday). Andhra Pradesh is doing nearly 60. Haryana is doing 65.

Now I’m waiting for the usual suspects to reply to this (either on twitter, or as a comment on my blog) saying this doesn’t matter we are “not doing enough tests per million”.

I wonder why some people are proud to show off their innumeracy (OK fine, I understand that it’s a bit harsh to describe someone who doesn’t understand Bayes’s Theorem as “innumerate”).

 

Rewarding Inefficiency

As the lockdown goes on and we have to spend tonnes of effort for things that we took for granted, there are some things I’m thankful I don’t have to spend effort for.

For example, ever since we returned to India a year ago, we’ve got milk delivered to the door every morning, and that continues. We buy our vegetables from this guy who drives a small truck in front of our road every other day (the time at which he arrives is less certain, but he maintains his thrice-a-week schedule).

For eggs, and as backup for vegetables, there is this “HOPCOMS” (a government-run fruits and vegetables shop) 100 metres from where I stay. The thing is so empty most of the time that I wonder if it would continue to exist if it had a profit motive.

It’s only for our staples, toiletries and other groceries that we have to visit organised stores, and in that too, I patronise this “independent supermarket” run by an enterprising bunch of Mallus rather than a chain. Plenty of other kinds of redundancy exists in the area where we live – there are a few family-owned grocers who don’t stock any “long tail stuff” but can supply the staples. And so forth.

This is very different from the situation in London, where I lived for two year, where for pretty much everything you go to the supermarket. If you are looking for “regular” stuff, you go to the little Tesco at the corner. If you want long tail stuff, you walk farther to the large-format Tesco. Bread, dairy, fruits and vegetables, groceries – for everything you go to Tesco. There were “unbranded” retail stores around as well (“off-licenses”, I think, they were called), but pretty much nobody ever went there.

It is the time of crisis when you start appreciating redundancy and inefficiency. All the “local supply chains” that we’ve relied upon continue to be reliable (the only exception being bread – all local bakeries are shut). It’s only for staples and toiletries that one needs to go to the supermarket.

Actually, not really, unless you are looking for long tail stuff. On my way back from the supermarket last Wednesday, I drove past one of the small family-owned groceries around here. There was a line one person long there. In other words, being a rather “inefficient” system around here, redundancy exists, and it is invaluable at crisis time.

Contrast this to a place like London, or even Gurgaon (or Gurgaon-like localities in other cities in India), where most shopping is done in branded chain stores. In that kind of scenario, at the time of crisis, there is no way out. The overoptimised and stretched (but “efficient”) supply chains mean that things come to a halt. You have no option but to regularly go to the supermarket and line up, and hope that their supply doesn’t run out.

My shopping habits apart, the larger question I’m wondering about is – once the crisis is over, how do we incentivise inefficiency? Clearly there are benefits to come out of inefficiency, in terms of slack in the system and greater resilience at the time of stress. However, these benefits are seldom seen in normal times, thanks to which businesses that push tail risks under the carpet can deliver super-normal returns and drive the more careful ones out of business.

We don’t know when the next such crisis will hit. It is highly likely that the next crisis will be nothing like this crisis, and we have no clue what it will be like. So how can we be prepared and have enough inefficiency in the system that when it comes around we are resilient?

Right now I have no answers.

Simulating Covid-19 Scenarios

I must warn that this is a super long post. Also I wonder if I should put this on medium in order to get more footage.

Most models of disease spread use what is known as a “SIR” framework. This Numberphile video gives a good primer into this framework.

The problem with the framework is that it’s too simplistic. It depends primarily on one parameter “R0”, which is the average number of people that each infected patient infects. When R0 is high, each patient infects a number of other people, and the disease spreads fast. With a low R0, the disease spreads slow. It was the SIR model that was used to produce all those “flatten the curve” pictures that we were bombarded with a week or two back.

There is a second parameter as well – the recovery or removal rate. Some diseases are so lethal that they have a high removal rate (eg. Ebola), and this puts a natural limit on how much the disease can spread, since infected people die before they can infect too many people.

In any case, such modelling is great for academic studies, and post-facto analyses where R0 can be estimated. As we are currently in the middle of an epidemic, this kind of simplistic modelling can’t take us far. Nobody has a clue yet on what the R0 for covid-19 is. Nobody knows what proportion of total cases are asymptomatic. Nobody knows the mortality rate.

And things are changing well-at-a-faster-rate. Governments are imposing distancing of various forms. First offices were shut down. Then shops were shut down. Now everything is shut down, and many of us have been asked to step out “only to get necessities”. And in such dynamic and fast-changing environments, a simplistic model such as the SIR can only take us so far, and uncertainty in estimating R0 means it can be pretty much useless as well.

In this context, I thought I’ll simulate a few real-life situations, and try to model the spread of the disease in these situations. This can give us an insight into what kind of services are more dangerous than others, and how we could potentially “get back to life” after going through an initial period of lockdown.

The basic assumption I’ve made is that the longer you spend with an infected person, the greater the chance of getting infected yourself. This is not an unreasonable assumption because the spread happens through activities such as sneezing, touching, inadvertently dropping droplets of your saliva on to the other person, and so on, each of which is more likely the longer the time you spend with someone.

Some basic modelling revealed that this can be modelled as a sort of negative exponential curve that looks like this.

p = 1 - e^{-\lambda T}

T is the number of hours you spend with the other person. \lambda is a parameter of transmission – the higher it is, the more likely the disease with transmit (holding the amount of time spent together constant).

The function looks like this: 

We have no clue what \lambda is, but I’ll make an educated guess based on some limited data I’ve seen. I’ll take a conservative estimate and say that if an uninfected person spends 24 hours with an infected person, the former has a 50% chance of getting the disease from the latter.

This gives the value of \lambda to be 0.02888 per hour. We will now use this to model various scenarios.

  1. Delivery

This is the simplest model I built. There is one shop, and N customers.  Customers come one at a time and spend a fixed amount of time (1 or 2 or 5 minutes) at the shop, which has one shopkeeper. Initially, a proportion p of the population is infected, and we assume that the shopkeeper is uninfected.

And then we model the transmission – based on our \lambda = 0.02888, for a two minute interaction, the probability of transmission is 1 - e^{-\lambda T} = 1 - e^{-\frac{0.02888 * 2}{60}} ~= 0.1%.

In hindsight, I realised that this kind of a set up better describes “delivery” than a shop. With a 0.1% probability the delivery person gets infected from an infected customer during a delivery. With the same probability an infected delivery person infects a customer. The only way the disease can spread through this “shop” is for the shopkeeper / delivery person to be uninfected.

How does it play out? I simulated 10000 paths where one guy delivers to 1000 homes (maybe over the course of a week? that doesn’t matter as long as the overall infected rate in the population otherwise is constant), and spends exactly two minutes at each delivery, which is made to a single person. Let’s take a few cases, with different base cases of incidence of the disease – 0.1%, 0.2%, 0.5%, 1%, 2%, 5%, 10%, 20% and 50%.

The number of NEW people infected in each case is graphed here (we don’t care how many got the disease otherwise. We’re modelling how many got it from our “shop”). The  right side graph excludes the case of zero new infections, just to show you the scale of the problem.

Notice this – even when 50% of the population is infected, as long as the shopkeeper or delivery person is not initially infected, the chances of additional infections through 2-minute delivery are MINUSCULE. A strong case for policy-makers to enable delivery of all kinds, essential or inessential.

2. SHOP

Now, let’s complicate matters a little bit. Instead of a delivery person going to each home, let’s assume a shop. Multiple people can be in the shop at the same time, and there can be more than one shopkeeper.

Let’s use the assumptions of standard queueing theory, and assume that the inter-arrival time for customers is guided by an Exponential distribution, and the time they spend in the shop is also guided by an Exponential distribution.

At the time when customers are in the shop, any infected customer (or shopkeeper) inside can infect any other customer or shopkeeper. So if you spend 2 minutes in a shop where there is 1 infected person, our calculation above tells us that you have a 0.1% chance of being infected yourself. If there are 10 infected people in the shop and you spend 2 minutes there, this is akin to spending 20 minutes with one infected person, and you have a 1% chance of getting infected.

Let’s consider two or three scenarios here. First is the “normal” case where one customer arrives every 5 minutes, and each customer spends 10 minutes in the shop (note that the shop can “serve” multiple customers simultaneously, so the queue doesn’t blow up here). Again let’s take a total of 1000 customers (assume a 24/7 open shop), and one shopkeeper.

 

Notice that there is significant transmission of infection here, even though we started with 5% of the population being infected. On average, another 3% of the population gets infected! Open supermarkets with usual crowd can result in significant transmission.

Does keeping the shop open with some sort of social distancing (let’s see only one-fourth as many people arrive) work? So people arrive with an average gap of 20 minutes, and still spend 10 minutes in the shop. There are still 10 shopkeepers. What does it look like when we start with 5% of the people being infected?

The graph is pretty much identical so I’m not bothering to put that here!

3. Office

This scenario simulates for N people who are working together for a certain number of hours. We assume that exactly one person is infected at the beginning of the meeting. We also assume that once a person is infected, she can start infecting others in the very next minute (with our transmission probability).

How does the infection grow in this case? This is an easier simulation than the earlier one so we can run 10000 Monte Carlo paths. Let’s say we have a “meeting” with 40 people (could just be 40 people working in a small room) which lasts 4 hours. If we start with one infected person, this is how the number of infected grows over the 4 hours.

 

 

 

The spread is massive! When you have a large bunch of people in a small closed space over a significant period of time, the infection spreads rapidly among them. Even if you take a 10 person meeting over an hour, one infected person at the start can result in an average of 0.3 other people being infected by the end of the meeting.

10 persons meeting over 8 hours (a small office) with one initially infected means 3.5 others (on average) being infected by the end of the day.

Offices are dangerous places for the infection to spread. Even after the lockdown is lifted, some sort of work from home regulations need to be in place until the infection has been fully brought under control.

4. Conferences

This is another form of “meeting”, except that at each point in time, people don’t engage with the whole room, but only a handful of others. These groups form at random, changing every minute, and infection can spread only within a particular group.

Let’s take a 100 person conference with 1 initially infected person. Let’s assume it lasts 8 hours. Depending upon how many people come together at a time, the spread of the infection rapidly changes, as can be seen in the graph below.

If people talk two at a time, there’s a 63% probability that the infection doesn’t spread at all. If they talk 5 at a time, this probability is cut by half. And if people congregate 10 at a time, there’s only a 11% chance that by the end of the day the infection HASN’T propagated!

One takeaway from this is that even once offices start functioning, they need to impose social distancing measures (until the virus has been completely wiped out). All large-ish meetings by video conference. A certain proportion of workers working from home by rotation.

And I wonder what will happen to the conferences.

I’ve put my (unedited) code here. Feel free to use and play around.

Finally, you might wonder why I’ve made so many Monte Carlo Simulations. Well, as the great Matt Levine had himself said, that’s my secret sauce!

 

Why Border Control Is Necessary

India is shutting down its domestic flights today in order to stop the spread of Covid-19. This comes a day after shutting down the national railways and most inter-city buses. States and districts have imposed border controls to control the movement of people across borders.

The immediate reaction to this would be that this is a regressive step. After a few decades of higher integration (national and international) this drawing of borders at minute levels might seem retrogade. Moreover, the right of a citizen to move anywhere in India is a fundamental right, and so this closing of borders might seem like a violation of fundamental rights as well.

However, the nature of the Covid-19 bug is that such measures are not only permissible but also necessary. The evidence so far is that it has a high rate of transmission between people who meet each other – far higher than for any other flu. The mortality rate due to the illness the bug causes is also low enough that each sick person has the opportunity to infect a large number of others before recovery or death (compared to this, diseases such as Ebola had a much higher death rate, which limited its transmission).

So far no cure for Covid-19 has been found. Instead, the most optimal strategy has been found to prevent infected people from meeting uninfected people. And since it is hard to know who is infected yet (since it takes time for symptoms to develop), the strategy is to prevent people from meeting each other. In fact, places like Wuhan, where the disease originated, managed to stem the disease by completely shutting down the city (it’s about the size of Bangalore).

In this context, open borders (at whatever level) can present a huge threat to Covid-19 containment. You might manage to completely stem the spread of the disease in a particular region, only to see it reappear with a vengeance thanks to a handful of people who came in (Singapore and HongKong have witnessed exactly this).

For this reason, the first step for a region to try and get free of the virus is to “stop importing” it. The second step is to shut down the region itself so that the already infected don’t meet the uninfected and transmit the disease to them.

Also, a complete shutdown can be harmful to the economy, which has already taken a massive battering from the disease. So for this reason, the shutdown is best done at as small a level as possible, so that the overall disruption is minimised. Also different regions might need different levels of shutdown in order to contain the disease. For all these reasons, the handling of the virus is best done at as local a level as possible. City/town better than district better than state better than country.

And once the spread of the disease has been stopped in a region, we should be careful that we don’t import it after that, else all the good work gets undone. For this reason, the border controls need to remain for a while longer until transmission has stopped in neighbouring (and other) regions.

It’s a rather complex process, but the main points to be noted are that the containment has to happen at a local level, and once it has been contained, we need to be careful to not import it. And for both these to happen, it is necessary that borders be shut down.

The future of work, and cities

Ok this is the sort of speculative predictive post that I don’t usually indulge in. However, I think my blog is at the right level of obscurity that makes it conducive for making speculative predictions. It is not popular enough that enough people will remember this prediction in case this doesn’t come through. And it’s not that obscure as well – in case it does come through, I can claim credit.

So my claim is that companies whose work doesn’t involve physically making stuff haven’t explored the possibilities of remote work enough before the current (covid-19) crisis hit. With the gatherings of large people, especially in air-conditioned spaces being strongly discouraged, companies that hadn’t given remote working enough thought are being forced to consider the opportunity now.

My prediction is that once the crisis over and things go back to “normal”, there will be converts. Organisations and teams and individuals who had never before thought that working from home would have taken enough of a liking to the concept to give it a better try. Companies will become more open to remote working, having seen the benefits (or lack of costs) of it in the period of the crisis. People will commute less. They will travel less (at least for work purposes). This is going to have a major impact on the economy, and on cities.

I’m still not done with cities.

For most of history, there has always been a sort of natural upper limit to urbanisation, in the form of disease. Before germ theory became a thing, and vaccinations and cures came about for a lot of common illnesses, it was routine for epidemics to rage through cities from time to time, thus decimating their population. As a consequence, people didn’t live in cities if they could help it.

Over the last hundred years or so (after the “Spanish” flu of 1918), medicine has made sufficient progress that we haven’t seen such disease or epidemics (maybe until now). And so the network effect of cities has far outweighed the problem of living in close proximity to lots of other people.

Especially in the last 30 years or so, as “knowledge work” has formed a larger part of the economies, a disproportionate part of the economic growth (and population growth) has been in large cities. Across the world – Mumbai, Bangalore, London, the Bay Area – a large part of the growth has come in large urban agglomerations.

One impact of this has been a rapid rise in property prices in such cities – it is in the same period that these cities have become virtually unaffordable for the young to buy houses in. The existing large size and rapid growth contribute to this.

Now that we have a scary epidemic around us, which is likely to spread far more in dense urban agglomerations, I imagine people at the margin to reconsider their decisions to live in large cities. If they can help it, they might try to move to smaller towns or suburbs. And the rise of remote work will aid this – if you hardly go to office and it doesn’t really matter where you live, do you want to live in a crowded city with a high chance of being hit by a stray virus?

This won’t be a drastic movement, but I see a marginal redistribution of population in the next decade away from the largest cities, and in favour of smaller towns and cities.It won’t be large, but significant enough to have an impact on property prices. The bull run we’ve seen in property prices, especially in large and fast-growing cities, is likely to see some corrections. Property holders in smaller cities that aren’t too unpleasant to live in can expect some appreciation.

Oh, and speaking of remote work, I have an article in today’s Times Of India about the joys of working from home. It’s not yet available online, so I’ve attached a clipping.