Modelling a Pandemic

Summary

Inspired by the observed differences between actual Covid-19 data and the predictions of the classic "SIR" model, I built a detailed pandemic model. It's a person-by-person simulation, for up to 50 million people, rather than a mathematical model. It uses the tricks I've accumulated writing high-performance network software to do this at reasonable speed. The results closely match actual data, and allow control over variables like vaccination, social distancing and self isolation. Skip to the last section to see the results. The source code is available on Github.

Background

Soon after the Covid 19 pandemic started, Mark Handley at UCL in London started a website showing the development in the number of cases and deaths in various countries and places around the world, which I followed with great interest.

Out of curiosity, I put together a simple simulation based on the SIR model of infectious transmission. This is the basis of much of epidemiology, and yet it quickly struck me that the curves it generates didn't correspond at all with Mark's. Using a log/linear scale (i.e. the Y-axis is logarithmic), SIR gives a straight line up until very close to saturation, where nearly all of the population have been infected. This corresponds to the now much-discussed "R0" number, i.e. the number of next-generation victims who will be infected by a single sick person.

Yet Mark's graphs weren't like that. No matter which country or area, nor which policies were being followed there, they all showed a gradual reduction in the slope. This was true for Lombardy and for much less afflicted places. It was true for Spain, which quickly enforced a very strict lockdown, and for Belarus, which never edicted anything at all. Even knowing exactly when lockdowns were put in place, it was difficult or impossible to see an inflection in the curve.

It was easy enough to come up with a mathematical model which closely described these curves. It is sufficient for the "R0" number to decrease slowly over time, to get a close match. The resulting curves perfectly matched the actual data from Lombardy.

So, why is reality different from the this nearly one century old model? It doesn't take long to see an obvious weakness. The math behind the model is simple:

    infected on day n+1 = constant * infected on day n * susceptible on day n

where the constant is closely related to our old friend R0. It's a simple differential equation, which indeed predicts the exponential growth everyone talks about.

But wait a moment. This supposes that every infected person is equally likely to infect every susceptible person. Is this realistic? Suppose Bob, living in New York, get sick. Alice lives in Los Angeles with her vulnerable elderly mother. She gets sick too. Which of them is more likely to infect Alice's mother? Or Bob's drinking buddy? In fact, the SIR equation only makes sense when applied to relatively intimate groups of people - families or close friends, for example. For larger communities, it needs to take into account also the probability of contact between individuals.

Herd Immunity

Everyone is now familiar with the concept of "herd immunity". If enough people are immune, a single infected person can no longer infect enough for the outbreak to grow. R (not R0 any more) has fallen below 1. It's widely stated that herd immunity needs to be somewhere around 60% to be effective, depending on the value of R0.

But again, this assumes that everyone is equally likely to infect everyone else - that herd immunity will not protect New Yorkers from each other if it has not yet reached the necessary level in Idaho. This obviously makes no sense. That situation may be bad news when an infected New Yorker visits Idaho, but New Yorkers will be protected from each other.

People tend to operate in clusters: families, groups of friends, close colleagues. Within such a cluster, transmission is high: if one person in a nuclear family, or one person in a small office, gets sick, the others will all be heavily exposed and most likely will either get sick or develop an immune response. Hence the admonition, common even before Covid, for sick people to stay home from work.

Once all the people in such a cluster have been exposed, the cluster has a localised form of herd immunity, regardless of what is going on in the wider world. An infected stranger visiting an exposed family, for example, poses no risk.

Thinking along these lines led me to the idea of "fractal herd immunity" - that there can be herd immunity at a local level, or in a larger community, without it applying globally. There is leakage between clusters - the nuclear family goes to visit the parents and cousins, close colleagues are part of  a larger company. Friendships especially are "leaky", it's common enough that my friends have friends who I don't know, or barely.

Building a Model

I wanted to develop a model to test this idea and see if the results look like reality. I didn't see any mathematical way to do this, so I built a simulation. Each person in the population is simulated, with day-by-day exposure to the infected people around them.

The model creates cities, and populates them according to a realistic distribution - a few big cities, and lots of small ones. Each person is allocated to each of four different clusters: family, friends, work and the local community. The latter corresponds to things like shopping. Clusters are randomly sized; for example, the family cluster can be anything from 1 (people living alone) to 8, with a bias towards smaller sizes.

Influence is a parameter for each cluster. In a family, people are in close proximity. This is taken as an influence of 1. The community cluster has a much smaller influence, but the clusters are a lot bigger. Cluster size is extremely important, because transmission increases as the square of cluster size: more people are exposed to more infected people. This is why large gatherings have been such an effective way to spread Covid, like the religious groups in north-east France and Korea.

Infection has to get between clusters. Partly this is done by grouping them into larger clusters, with reduced influence between the members. So a sick person in one family cluster has a small chance of infecting someone in an adjacent cluster, just as if they visited another part of the family.

Most cluster memberships and relationships are within the same city, but there are also ways for infection to travel between cities. This can be via cluster membership, for example when a family's relations are in another city, or when an office is part of a larger company based elsewhere. It can also be through explicit travel. Each person is randomly assigned a mobility, which is the probability that they will visit another city on any given day.

The model has a few higher-level parameters that control it, and a lot of detailed ones that are manipulated by the higher level ones. For example:

• population: the total number of people - the model can handle 50 million, and gives rapid results for 3 million
• infectiousness:  the R0 value for the infection
• auto-immunity: the number of people who, when exposed, will develop immunity without becoming sick or infectious
• distancing: the extent to which people's behavior is modified by social distancing
• vaccination: the number of people who are immune at the start due to prior vaccination 

Results

The results can be presented either as a simple graph, showing the number infected and total infected as some parameter is changed, or as a rather fetching animation where each city is shown as a "bubble" gradually changing color as people are infected and either become immune or recover (or die). Here are some examples.

Social Distance

This chart shows the effect of varying "social distance", i.e. reducing interaction with friends, work and the local environment, and reducing travel between cities. Zero means business as usual. 1 is Wuhan style - everyone at home except truly essential workers, no travel. It is modelled by varying the level of interaction between people and the groups they belong to. At distance equal to 1, the family group is unchanged, friends drops to zero, work to 20% (allowing for some essential workers), and travel to 10%. Intermediate values of distance set intermediate values of interaction.

Somewhere around 0.8 or 0.9 is what was achieved in the UK or California, with less travel and contact, but still some, and some people trying to disregard the restrictions altogether. This level very substantially "flattens the peak", as well as reducing the total number infected. The chart also shows that anything less than 0.5 has no impact.

R0 - the Infection Ratio

This chart shows the effect of different values of R0, the number of people infected by each infectious person (using a log scale for the Y-axis). At 1.0, the infection dies out slowly. In some simulations, depending on the randomness, it lingers for a long while without growing much. At 1.2, the infection grows very, very slowly. This is a consequence of the local immunity effect - with the traditional SIR model, it would grow very quickly. Covid-19 supposedly has R0 in the range 2.5-3.

Vaccination

This chart shows the effect of vaccination. Just 20% vaccination halves the total number of people infected, and the size of the peak. At 50%, the infection is wiped out. This percentage is a product of the number of people vaccinated, and the effectiveness of the vaccine. So if 50% of people get vaccinated, and the vaccine is 80% effective, that corresponds to 0.4 on this chart.

Watching the Pandemic

The simulation can also show graphically how the pandemic spreads. The picture above is at day 100 with some typical parameters. Each blob is a city (some large cities are drawn on top of their smaller neighbors). The red ring corresponds to current infections, the blue outer circle to those who are still susceptible. The inner green circle is those who are no longer susceptible - recovered, asymptomatically immune, or vaccinated. The small black dot in the middle corresponds to deaths. Clicking here will show the complete evolution of the pandemic (select 1080p for best results).

Life on the Ocean Wave - Riding the Hovercraft

One day I will write a guidebook to nostalgia, called "101 Things You Can't Do Any More". In pride of place, along with crossing into East Berlin and flying on Concorde, will be the hovercraft journey across the English Channel (La Manche pour mes lecteurs français).

Since 1994 crossing the channel has been a dull business. You drive straight off the M20 from London into a vast car park, from which you are shepherded into a tunnel. You stop behind the car in front, like any other traffic jam, turn the engine off, and sit there for half an hour or so. You are vaguely aware of movement, but only just, as you listen to the car stereo or read a book. Then the car in front moves, you follow it, and you are on the A1 headed for Paris. It's efficient, relatively inexpensive, and of absolutely no interest at all.

The story behind this dull half hour is a fascinating one, of over a century of political and financial wrangling which led, finally, to the construction of the Channel Tunnel. While you are sitting there, bored, you are on a train travelling at 100 miles per hour through one of man's most extraordinary civil engineering achievements. But the whole point of it is that you don't need to be aware of any of this.

Until 1994, there was no way to travel with a car between England and France without being firmly aware of the 22 miles of open water that have protected England and Continental Europe from each other since 1066 AD. In Victorian times it was a serious adventure, tossed about on the waves in a sailing boat or later a steamship. Turner, the English artist, was inspired by it to produce some extraordinary paintings, even strapping himself to the mast of a channel boat during a violent storm for the experience.

It could be hazardous in many ways. It certainly was for Rudolf Diesel, inventor of the eponymous and omnipresent engine. After the German Navy had expressed no interest in his invention he took the steamer to Harwich to try and sell it to the British. One has to suppose that the Germans suddenly woke up to their mistake, because he disappeared en route, his body never to be found.

My own first Channel crossing by car was in about 1979. It was long and boring. The shortest crossing, the 22 miles between Dover and Calais, took a couple of hours, with another hour or so at each end of waiting, embarkation and disembarkation. The crossing itself was spent staring at the sea, resisting the limited attractions of the greasy fast food and fizzy beer available on board.

There were other, longer routes. For one summer holiday we took our car on the ferry between Southampton and Le Havre. That was an overnight trip, tucked up in a narrow berth in a tiny cabin. While waiting for the return ferry we got chatting to the driver of the car in front, who was struggling with a stuck-open window in his Lancia. He told us he was a fashion designer. A year later his name, David Emanuel, became famous as the creator of Princess Diana's wedding dress, but at the time he was just a thoroughly nice bloke.

From 1989, after I met Isabelle and started our long-distance relationship between England and France, I needed to cross back and forth more often. By then the hovercraft was an option. (You were wondering when I'd get to it, weren't you?) It offered a crossing in just 40 minutes and since it was smaller, a lot less time was spent messing about at either end. This more than made up for the extra cost.

My first trip was unforgettable. The sea was choppy, and with every wave we ploughed up high in the air then crashed down into the void between the peaks. Unlike the ferries you had to remain seated the whole time, in airliner-like seats stretched across the width of the cabin. I spent the whole journey staring fixedly but unfocussed at the horizon, trying to keep my breakfast inside me.

Afterwards I made a visit to the men's room. Next to me were two colleagues, one regaling the other with how much worse it could have been. "Remember that bit where it felt like we were just hanging in space?" His buddy groaned in response. "Well, last time, those were the good bits."

It was a fantastic way to travel though. You stood on the edge of the beach at Ramsgate or Calais watching the giant, roaring monster slither gently up the sand then sink gradually onto its giant rubber skirt as the engines stopped. Compared to a ferry it was tiny, with room for maybe 40 cars, all firmly tied down en route.

The hovercraft did not deal well with rough seas. At least, I think the machine itself did, but there was a limit to what you could ask passengers to put up with. This was brought home to me on my most memorable trip, in April 1990, taking my children on a spring break to Paris, Toulouse and Hossegor.

It was memorable for many reasons. My car's wheels had been stolen a couple of weeks earlier, and the replacements were on long back-order. In place of my beloved Golf GTi, the insurance was paying for that pinnacle of British luxury motoring, the Rover 827. The adventure started long before we got near water. We had stopped off for tea at my parents' house in Romford, more or less on the way to Ramsgate. When it was time to leave, somebody - we will be discreet here - revealed that they had locked the car keys in the trunk. It has been a source of family amusement ever since, but at the time it was not funny at all. Eventually the RAC showed up.

"Have it open in no time, guv. What car is it?" said the smiling mechanic.

"A Rover 827."

His faced dropped. "Blimey, they're nearly impossible. I'll 'ave a go anyway." That was just the kind of reassurance I was looking for. After half an hour of fiddling about with long thin bits of metal, he finally got the door open, and we set off for Ramsgate.

As it turned out, none of this mattered. We arrived to see a big handwritten sign, "Hovercraft cancelled due to bad weather, please go to ferry terminal at Folkestone". We drove the 20 miles or so down the coast in what was indeed terrible weather, the gale-swept rain swirling around the car. Upon arrival we learned that the ferry too was running hours late. We filled in the time with a visit to McDonalds, and finally boarded the ferry around 10pm - when we should already have been well on our way down the A1 to Paris. We climbed up from the car deck, and waited to set sail. And waited, and waited, and waited.

Finally I went back to the car deck, and found a loader who explained the delay to me. The waves were huge even inside the harbour, and the ferry had sunk into the trough of one just as a bus was crossing onto the ramp. The ramp crashed into the bottom of the bus, severing the brake lines and locking the brakes firmly on.

"Normally if that happens someone crawls underneath and releases them by hand. But not tonight," said my interlocutor, gesturing at the bus which was tossing around crazily as the boat did the same. Instead they had to tow it off, wheels locked, with the giant tractors used for container trucks. The first effort snapped a rope the size of a man's arm. Eventually they got it off with an even thicker one.

I whiled away the time by wandering around the open deck in the gale and blowing rain. I read the notice explaining how to launch a lifeboat. I have to suppose that the sailors were trained and knew the procedure, so this was just in case the passengers had to do it themselves. It made the instructions for Chinese consumer electronics look positively lucid. I didn't understand a single substantive word. It read something like the following.

1. Unsprurl the flangling ropes.
2. Diswangle the grotling clips.
3. Under no circumstances allow the wribbits to contact the ortlers.
4. Bringle the yarling cords.

And so on and so on. Eventually we set sail, and after a rough crossing during which we all slept soundly and several hours driving, we arrived in Paris at about 5am.

Our trip was wonderful. We explored Paris together, had an Easter Egg hunt at Isabelle's mother's house outside Toulouse, and paid the first of many, many visits to Hossegor on France's Atlantic coast. On the way back we spent another night in Paris, creating another family memory. We had to be up very early for the return trip to Calais. I went out to buy croissants. My daughter, about 7 at the time and very grumpy at her early awakening, simply stared at hers.

"What's wrong?" I asked.

"My croissant is too bumpy!" she complained.

Despite bumpy croissants, we made it uneventfully to Calais and could watch the monster machine arrive on the beach, where the photo at the top was taken. The sea was perfectly calm, one of the best hovercraft trips I ever did.

I missed them when the tunnel opened, a few years later. The hovercraft is a brilliant invention, even without its famous contribution to the Hungarian-English phrasebook ("My hovercraft is full of eels"). But somehow it is never quite the right tool for the job, and there is hardly anywhere in the world where you can still ride them. Still, it was fun while it lasted.

My Dad's War

My Dad, December 1940 - 29 years old

In 1940, soon after the declaration of war against Germany, my Dad was conscripted into the British Army. In that he was just like every able-bodied male, of suitable age and not in an essential job like the railways.

War is hell, as has been said before. For so many, even if they escaped with their lives, it was a traumatic, life-changing experience - and not in a good way. But for some it was the greatest experience of their lives, working together in a common purpose. I'm quite jealous of the people at Bletchley Park, constantly struggling with new ways to break the German codes, knowing that an hour shaved off the time could save hundreds of lives.

One of my favourite books is Most Secret War, by Reg Jones. He led the efforts to develop hi-tech (for the time) aids to beating the Germans, and to understand and defeat their technology. Just one example was their use of intersecting radio beams to bomb British cities accurately. Once understood, it was a simple matter to broadcast a stronger signal on a slightly different alignment, resulting in thousands of tons of German bombs falling on open countryside instead of devastating a town and killing hundreds of people.

Yet there was a human side too. Jones had to live through the blitz just like everyone else. He mentions an occasion when they expected a big raid on their neighbourhood. Prudently he filled the bath beforehand, ensuring a water supply even if, as happened, the pipes were destroyed by the bombs. Imagine his shock when he discovered his wife, wondering why on earth he had left the bath full, had emptied it shortly before the bombs fell.

My Dad was selected for the Artillery. He was sent off to a remote training camp in North Wales to learn to be a wireless (radio) operator. He was taught Morse Code, and the basics of radio operation. No doubt he expected to be sent to a battlefield somewhere, sending reports and receiving instructions under bombardment as his squad-mates in turn bombarded the Germans.

He never talked about exactly what happened. He was a very social, personable chap, who made friends very easily with a straightforward, natural charm. Maybe it was that, or maybe he really was talented. But whatever the reason, the camp commander decided that he could best serve his country by teaching other people how to communicate under bombardment, instead of doing it himself.

And so for the next five years my Dad was stationed just outside Llandudno, teaching other men Morse Code. It's hard to imagine anywhere more remote or distant from the industrial heartland, except maybe the Scottish Highlands. He admitted to having seen just one enemy plane, a German bomber which had got lost and subsequently crashed into the Irish Sea. The contrast with my mother, too young to serve and living at home in South London with her family, couldn't be greater. Bombs were part of her daily life, met with typical British stoicism: "If it's got my number on it, it's for me". She was more concerned about being home before her mother's imposed deadline than she was about being hit by a bomb.

He may have been far from the action, but he was still a soldier in uniform, admired by the people who remained on the farms and in the villages. Even with strict rationing, the local country people weren't short of eggs, chickens, milk or butter. So, "Here Reg, take a couple of eggs for your breakfast" happened often enough.

Without a shadow of a doubt, World War II was the highlight of my Dad's life. He had good friends, an easy enough life, the respect of everyone for a serving soldier - and what he was doing was genuinely valuable for the war effort. That it involved absolutely no risk at all certainly made it more pleasant.

He made friends easily, but they were mostly superficial - good mates, but no more. There was one exception, Bert. They served together in North Wales for the entire duration of the war. He often spoke of him, and in the tradition of the times they exchanged Christmas cards, but no more. Bert lived a long way off for the times, somewhere near Birmingham in the Midlands.

And yet... one day with my mother he visited a park quite a way off, in Barking. Why they went there I have no idea. And strolling through the park, over a hundred miles from home, was Bert, with his family. It's an extraordinary coincidence, worthy of a Thomas Hardy novel. They shook hands, chatted for a while about the old times... and never saw each other again.

Even for my Dad, the war wasn't without unfortunate consequences. He had married in the late 1930s, setting up home in a flat in Kilburn in grimy north-western inner London where my half-sister was born. When he went off to the Army his wife moved to the Suffolk countryside to live with her mother. It was an area that was crammed full of airbases, as close as possible for launching nightly raids on Germany. The airbases were in turn crammed full of airmen, British and American, and all the supporting staff they needed.

As the locals said, "The problem with the Americans is that they're overpaid, over-sexed, and over here." That was very unfair, considering that they were dying by hundreds every day in poorly conceived daylight bombing raids. And anyway it wasn't an American who stole my Dad's wife, it was a fellow Brit. From my point of view, this was an excellent thing - otherwise I would not have come into existence. In fact things worked out well all round - her second marriage was long-lasting, and my father made a happy second marriage too, as these things go.

It was a common enough problem after the war, and the Army set up special divorce courts to deal with it. My Dad told the story of leaving the court, after his divorce had been approved, along with a fellow serviceman who said, "Best day of my life, I'm finally rid of her. Let me buy you a drink."

My Dad's post-war life was uneventful, and successful enough in a very modest way. He became a salesman to the clothing industry, which lasted until he retired at 67. But I don't think anything after 1945 came close to his wartime experience.

Lighting up Shiny, the Wismar Railbus

In the 1920s, road competition was really beginning to hurt rural railways everywhere in the world. The economics of running a steam engine, trailing a handful of elderly carriages behind it for three or four journeys per day, had never been good. Now they were terrible. The railway companies looked to modern technology for a solution. A diesel powered railbus could be operated by one man, requiring almost no routine maintenance - unlike a steam locomotive which took several hours of preparation every day. And as a bonus, it offered the same level of comfort as the road competition, rather than the hard seats and general decay of carriages that were often 50 years old. More frequent (well, less infrequent) services could be run, as well.

All over the world various different railbus designs appeared. Another of their advantages was that they run readily in either direction. Nowadays, we take it for granted that there will be a driving cab at either end. But that wasn't obvious in the beginning. For one thing it takes up space that could otherwise be used for passengers or freight. For another, operating the engine and transmission from a distance requires some kind of linkage. An electric or pneumatic system sounds ideal, but it had to be maintained in the field by steam locomotive engineers whose most subtle tool was a coal hammer. And mechanical linkages were hard to keep working. (When I was a teenager, I travelled all across France on a bus with a rear-engine, unknown in England at that time. Every gearchange was an adventure, as the driver struggled with the worn-out mechanical linkage to try and persuade the gearbox, 12 metres away at the back of the bus, to engage the right gear, or at least some gear).

So other solutions to the problem were developed. The French were especially creative. Some early railcars had a cab at one end only, next to the engine, and a kind of mini-turntable under the bus. At the terminus the crew would crank a handle until the bus was resting on the turntable, push the bus around 180 degrees, then retract the turntable. A much more widely-used idea was to put the driver in a turret on the roof. He sat sideways with the controls in front of him. The most common railbuses in the 1950s had the turret in the middle and offset to the side. They were called Picassos, after the painting with the girl's nose to one side of her face. The poor drivers must have suffered terribly from stiff necks, having to look sideways the whole time.

In Germany another ingenious, if improbable, solution emerged. In 1932 the Wismar company produced a railbus which had a completely independent engine and gearbox at each end. Whichever end the driver was sitting, he simply started the corresponding engine and drove from there. At the terminus he stopped that engine and put the gearbox in neutral, walked to the other end, and used the opposite engine. This made it possible to use readily-available Ford engines and transmissions, rather than developing something specific for railway use - making their product a lot cheaper. The resulting vehicle looked very odd, like a pig with a snout at each end. For all that, they were the salvation of many little rural lines. There are several still running today on preserved railways in Germany.

LGB made a model of this odd vehicle, and when I built the garden railway I really had to have one. We called him "Shiny", from the German name "schienenbus" (meaning railbus). At the time I added a DCC decoder in the simplest way possible. And Shiny trundled reliably around the railway, just as happy in either direction just like its prototype.

There are two ways to go about installing a DCC decoder. The simplest is just to put it as a "bump in the wire" between the track power and the motor. Sometimes with older locos, this means separating the track power from the motor, but otherwise it's easy. The disadvantage, though, is that nothing works if the train isn't moving - in particular, the lights. That's what I did for Shiny.

The more complicated alternative is to wire the lights, and any other accessories, to the corresponding outputs of the decoder. This works perfectly, but it's complicated. All LGB locos have a fairly elaborate circuit board to operate lights and the rest from the track power, using strange proprietary connectors. I have replaced them in some engines, but it's a lot of work. The little railbus would be especially difficult, because of its headlights and taillights that change according to the direction of travel.

But I really did want the lights to work when the train is stationary. It just looks so much better at night or in the twilight. And I really wasn't ready to build a replacement for the internal wiring. So I thought of a third approach.

The idea is very simple: separate the motor from the lighting circuit. Connect the decoder output to the motor as usual, but create a fake always-on motor feed for the lighting circuit. This is powered from the lighting power on the decoder, which is always on, via a polarity-switching relay, whose output is taken to the lighting circuit. The relay is bistable, i.e. it remembers its position even without power. It is controlled by the polarity of the actual motor feed, via a couple of diodes. So when the motor runs in the forward direction, the relay switches to the same polarity, and provides full-power  forward voltage to the lighting circuit - which continues even when the motor is turned off and the train is no longer moving. When the train direction is changed, the relay switches to follow it.

Using a relay makes this very easy. It could be done using an H-bridge chip, but that would also require some electronics to remember the last setting - much harder than just soldering a relay onto the board.

I chose to feed the fake power from the always-on auxiliary supply on the decoder, rather than from the lighting output. This means the lights cannot be switched off. I prefer this - in daylight they are invisible anyway, and at night I always want them on.

While I was buying the parts for this, I also noticed on eBay some seated LGB figures, some of whom are now installed in Shiny. I'm sure they're much happier now they can read while the train is stopped at a station or in the sidings.

Berlin, Before and After

My first visit to Berlin was in 1983, in the depths of the Cold War. It was the Berlin of black-and-white movies, of Michael Caine in Funeral in Berlin and the Len Deighton spy novels. In retrospect it feels like Berlin itself was in black-and-white.

I was there for a standards meeting hosted by the German national standards body, DIN. Their headquarters was at the eastern side of West Berlin, overlooking the Zoo. Oddly the best view, of the Bradenburger Tor, was visible only from the mens' room (and also, I'm told, from the ladies' room).

The centre of Berlin was the Ku-Damm, a shopper's paradise like London's Oxford Street, dominated by the broken, blackened stump of the bombed Kaiser Wilhelm Church. Even then it had a slightly tacky feel to it. The original centre of Berlin, before 1939, was Unter den Linden, but after 1945 this was in the eastern sector, inaccessible and decaying like the rest of the East.

I was with a group of friends and colleagues, as always at these meetings. One, an American, was fascinated by the divided city, but his security clearance made a visit to the East out of the question. We spent our free time getting as close as possible without actually going there. We took the subway (U-Bahn) line that passed under the East, passing at full speed through the barely visible ghosts of stations that had been closed for decades.

One evening we visited a remote truck parking lot by the Wall. It was very spooky, and then afterwards we tried to take the S-Bahn, the surface suburban train which has been a vital part of Berlin's transport system for well over a century. But some twisted part of the agreements over the city meant that even though more than half of it was in the West, it was operated by the East Berlin transport company. As a result it had been boycotted by the westerners for several years, and the services reduced to the point where it was just the phantom of a transport system. Late at night the trains ran about once an hour. We hung around, the only people on the lonely platform, our breath fogging in the chilly night air, until finally someone showed some common sense and we walked back to our hotel.

Another must-see was Checkpoint Charlie, by then the only open road crossing into the East in an undistinguished urban street. It was there that Isabelle, long before I knew her, took a bus tour and had her copy of Le Monde confiscated - it wouldn't do for the liberated people of the German Democratic Republic to see such degenerate filth. But much to her surprise, in a typically German organised way, she was reunited with it when she re-entered the West.

I took a bus tour myself in 1983. We were taken to the Soviet war memorial in Treptower Park, a monument to the twenty million Russians who died during the war with Germany - though many at the hands of their own government. We passed a shop with a long queue outside, which was a cue for the guide to explain to us that there were no shortages of anything in the Democratic Republic.

Even getting to and from Berlin was surreal. The post-1945 treaty decreed that Lufthansa, the German airline, was not permitted to serve Berlin. In fact only three airlines were, one for each of the western powers: British Airways, Air France, and Pan Am. The latter had a fair-sized European operation to serve Berlin, mainly from other airports in Germany. There were very few direct flights from London, and every trip I made to Berlin involved a change in some north German airport - Hannover, Hamburg or Bremen. The official air corridors had been approved in the days of piston airliners like the DC3, so they were at abnormally low altitudes for jets - 11,000 feet or so. They gave spectacular views over the rather dull Prussian countryside.

---

In 1986 we had a two-week meeting at DIN, with a spare weekend. My friend Peter and I decided to spend an evening in the East. We thought it would be good to see the main railway station (Hauptbahnhof) figuring that it must be a hive of activity.

First though we had to cross the border. We took the S-Bahn to Friedrichstrasse, in the heart of the East but still functionally part of the West. The platforms were divided by high walls, and to cross we had to descend into the bowels of the station to a very unwelcoming customs post. We changed money into Reichsmarks, the currency of the East - far more than we could hope to spend in one evening, which was their idea. And then we continued on another S-Bahn train to the Hauptbahnhof.

It was a huge disappointment. Where we'd expected to see packed trains to any number of exotic and inaccessible destinations, there was just one - going, as I recall, to Prague. None to Moscow, or Warsaw, or indeed anywhere else at all. The only thing to do was to find somewhere for dinner.

Good restaurants in East Berlin didn't exist. We chose what our guidebook (no TripAdvisor in those days) said was one of the best. It was right on Alexanderplatz, the centre of the city, and specialised in Moravian cuisine, which is to say Czech. It was a huge hangar of a place, but even so we had to share a table. Our table partners were what appeared to be - which was later confirmed - a young Czech guy and his mother. During the meal we politely ignored each other, but once we had finished eating things turned a little weird.

Our new friend spoke excellent English even though it was the first time he'd ever spoken to a real native speaker. He started to tell us how much he disliked Berlin, how sad he found it compared to Prague. Back then even travelling between Iron Curtain countries was difficult, but going outside them was essentially impossible. He waxed eloquent on his theme.

"I mean, what right does some Ivan in Moscow have to tell the Germans how to live their lives?" he proclaimed.

My friend was trying to hide under the table. He'd probably had some minor involvement with the security services, and was certainly paranoid about being in the East at all. He was convinced we had been found by an agent provocateur. His relief when we finally left was tempered only by his conviction that we would be seized by Stasi agents and left to rot in a Communist gaol before we could make it back to the West.

Luckily this didn't happen, and I got to spend the weekend with my then-wife. It was the first time i'd ever been in Germany at the weekend. We spent a lazy Saturday morning, and started to wander around the shops on the Ku-Damm after lunch. She was about to try something on, when suddenly we were hurriedly ushered out of the shop. We didn't understand - was there a fire or something? But no, nothing like that - German shops still closed at 2pm on Saturday, as we quickly realised when we saw that everything else was shut too.

On Sunday we visited East Germany itself, with a bus trip to Potsdam. Before 1939, and again now, this was a very upmarket suburb, like Versailles is to Paris. Very much like it, because in 1745 Frederick the Great of Prussia built a palace there, Sans Souci, inspired by Versailles. This was the principal destination of our trip.

Central Potsdam, 1986

But first we had to cross the border, at a truly vast parking lot on the highway. We spent a long time there, and when we finally got to the head of the queue our bus was comprehensively searched, inside and out, including mirrors on long poles underneath. Though it seems very unlikely that anyone would want to be smuggled into the glorious DDR.

The town centre was completely deserted. Only the occasional Trabant pottered smokily through its streets. I haven't been there since but I'm sure it's a very different place now.

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On 3rd October 1990 East Germany, and with it East Berlin, ceased to exist. I was at an international meeting at the time, though it happened to be in Sydney, Australia, and coincidentally also on my honeymoon. At midnight, German time - which was 8am for us - the head of the German delegation served sekt to everyone present. It was an emotional moment.

The next meeting had long been scheduled in Berlin, the following June. But instead of meeting at the DIN headquarters, we were hosted at the Academy of Sciences in the heart of the former East. There were still no decent hotels there, and for various reasons I had driven from England. So every morning and evening we made what just one year earlier would have been an inconceivable journey, driving through Potsdamer Platz which until recently had the Wall running through the middle. The roads were still crowded with the "Trabbi", the awful tiny car whose design dated from the early 1950s that was an almost unattainable luxury for the Osties. Being surrounded by them in a traffic jam, with their stinking, erratically noisy two-stroke engines belching unburned fuel and oil, was an unforgettable experience.

Naturally very little had changed in the few months since reunification. East Berlin was a grim, grey place, exactly as in the Cold War era movies. There were no shops, but the Pergamon Museum was fascinating. The German telephone company had made special, urgent arrangements to install a temporary telephone line at the meeting site - in the days of the East, even the Academy of Sciences didn't have a single telephone.

We made the most of the experience. With my friend Peter - this time in no danger of being arrested by the Stasi - we took the S-Bahn to Schönefeld, East Berlin's airport. There wasn't much to see - although it is far larger than Tegel, its western counterpart, there was little going on there. It is the only time I have ever seen a Tupolev 134, the small twin-engine jet that was the mainstay of East Germany's airline, Interflug. Now Schönefeld is the site of Berlin's new airport, Brandenburg, of which more later.

The Harzquerbahn in 1990

We took advantage of a free day, and my car, to visit the Harzquerbahn, a narrow gauge railway about 100 km away. It was still a much-used part of the transport infrastructure, not a preserved line for enthusiasts. It was operated by enormous narrow gauge steam engines with a 2-10-2 wheel arrangement - meaning a lot of wheels. It was extremely impressive to see it in operation.

One afternoon Isabelle and I drove around the East, including a stop at the iconic Bornholmerstrasse Bridge, where hostages were exchanged during Cold War days. Its enormous span covers a huge S-Bahn junction just north of the city centre. We also managed a trip to Potsdam and Sans Souci, by now already waking up from the DDR times.

I thoroughly enjoyed that trip, with fond memories of gemützlich restaurants and bars in the evening and the warm atmosphere that cold climates generate.

A typical grim DDR scene in Halle

When the meeting was over we took a circuitous route home, spending a night in Heidelberg well to the south of Berlin before heading back to England. Our route took us close to Halle, a city then completely unchanged from its DDR days, complete with Czech built trams, the buildings still blackened by soot as they had been in 1945. The visit left us short of time, so I took advantage of my nearly-new VW Golf GTi and the speed-unlimited autobahn. The car handled superbly at 200 km/h but every now and then one Trabbi would pull out to pass another, a barely visible speck almost at the horizon. At a closing speed of 150 km/h I was on top of it almost before my foot hit the brake pedal. It was a salutory experience.

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I visited Berlin again nearly 15 years later. By then all memory of the DDR had disappeared, at least from the city centre. Unter den Linden was once again the vibrant heart of the city, with luxury hotels springing up everywhere. Potsdamer Platz, where we had sat in traffic surrounded by stinking Trabbis, is now home to vast modern high-rise offices. Meanwhile the Ku-Damm had become tawdrier than ever, a forgotten monument to shabby 1960s architecture and the Cold War.

I also saw an excellent illustration of the weakness of the German way of doing things. The S-Bahn, historically the most important part of Berlin's transport, was being renovated and rebuilt, reverting to its pre-1939 glory. In Germany things usually work extraordinarily well. But if they don't, they don't work at all. And so it was with the S-Bahn. I planned a journey one evening to travel on stretches which had hitherto been impossible, but it turned into an exercise in frustration and long cold waits on lonely platforms, reminiscent of that first trip twenty years earlier.

Speaking of things that go badly in Germany, it's impossible not to mention Brandenburg Airport. I haven't been back to Berlin since that trip in 2003, but Isabelle was there for a meeting in 2011. She arrived, as always, at the cramped Tegel airport. But just one week later it was to close, and after a miraculous 24-hour move all the airlines would be at Brandenburg, the gleaming new airport to the southeast.

And then, barely a week before it was due to open, it was suddenly declared unsafe. Among the many problems which emerged, the architects had decided that the traditional smoke evacuation scheme via the roof would spoil the appearance of the building. Instead they had devised a complex scheme for evacuating smoke via huge subterranean ducts. Sadly this did not take into account the well known propensity of smoke to rise. Now, over 10 years later, there has been a succession of opening dates which have come and gone. The most recent is later this year, but it remains to be seen whether that happens. In the meantime it has resulted in the premature end of several careers, and even one murder of a whistleblower. When things go badly in Germany, they go very badly indeed.