While I applaud the fact that there are very few partisan voices in Canada, and that governments at all levels constructively cooperate with each other, I cannot help but wonder if the measures taken are sufficient to fight this demon of a virus, COVID-19.

• 11:23 AM: À compter de lundi midi, les Canadiens ayant des symptômes de la COVID-19 ne pourront plus prendre des vols intérieurs ou le train
• 11:38 AM: Justin Trudeau affirme qu’Ottawa n’envisage pas de fermer les frontières interprovinciales

My question is… why exactly do we still have non-essential travel within Canada? And why exactly are the interprovincial borders still open?

This virus will not be beaten with half-measures. If we are not able to bring down the infection rate, soon an extremely large number of people will become simultaneously sick, completely overwhelming the intensive care capacity of our health care system. Which means that a great many people who could survive with adequate medical care will die.

SIR model prediction based on US data as of March 28, 2020.

See this simple simulation of the US situation that I put together, using the simplest epidemiological model. If its predictions come true, at one point in late April more than 20% of America’s population will be sick. If 5-10% of these patients require intensive care, that is up to 6 million people or more, only a small fraction of which will receive the care that they will need to stay alive. The rest will die. The same thing can happen here in Canada if we don’t take the necessary measures.

Ottawa looks like a ghost town these days. Here are a few images from this morning’s “rush hour”:

The one good thing about this is that when you actually have to go somewhere, it has never been this easy.

Oh, and gas is cheaper than… well, pretty much cheaper than it has ever been in my experience, since I moved to Ottawa in 1987.

Two weeks, or to be precise, fifteen and a half days ago, I was walking the streets of downtown Vienna, enjoying a bright late winter day, eating a bit of authentic Viennese street food and a fabulous slice of cake in a Vienna coffee house. The next day, I boarded a flight at a busy Vienna Airport. To be sure, some signs were already present that not everything was normal. The plane had fewer passengers than usual, especially in business class. There was news of Lufthansa grounding all their A380 superjumbos, and when I asked our pilot about this, he just shook his head, not knowing what the future would bring. But all this felt distant; the world around us, by and large, still felt normal, busy as usual, with people lining up at checkpoints, roadways busy with traffic, airplanes landing and departing at regular intervals.

Today, fifteen days later, we visited our favorite deli store in a nearly completely deserted Byward Market in downtown Ottawa. I literally could have parked in the middle of the street. The store was open (we phoned ahead to make sure) but deserted as well. All the good food there… will it ever sell? Will they at least get a chance to donate some of it, e.g., to the Food Bank or to a nearby shelter? Will they be able to stay open? Will they be able to stay in business?

I don’t know what hit me more, this store or the Web site of Vienna Airport. You know, the same airport where I stood in line, two weeks ago, to go through customs and security.

Not much of a chance of a lineup today.

How will our world recover from this?

My wife and I went on a shopping spree.

No, we didn’t win the lottery. But apart from our desire to support our local economy in times of crisis, we were also rather worried that our favorite deli store in the Byward Market may be forced to close for an indefinite period of time.

So we stocked up on things. That said, I hope they are able to stay open. I hope they are able to stay in business. Other deli stores have shut their doors. I hope Continental remains open and that the owner and employees stay healthy.

In the meantime, I thank them for serving us.

Working from home is easier for some than for others.

Members of a symphony orchestra have to get a little more creative than most of us, but that didn’t stop members of the Danubia Symphony Orchestra of Óbuda, from Budapest, Hungary:

Nicely done!

Looking at papers presenting predictions about the COVID-19 outbreak, one thing is evident: Things are going to get a lot worse before they get better. Today, we passed the 200,000 mark for confirmed infections worldwide, and the curve continues its super-exponential rise for the time being. We are quite a long way away from “flattening” the curve, and that means that millions will get infected, health care systems will be overwhelmed even in the most advanced industrialized societies, and some of us who could be saved, will die, because there will not be enough hospital beds, respirators, medication, or health care professionals available to help.

Yet… I cannot help but wonder if this calamity is, perhaps, a blessing in disguise. Here is why.

This is the year 2020, when we celebrate the 75th anniversary of the end of one of the most devastating wars in history. Back when I was a young child, growing up watching the Spaceship Orion (Europe’s answer to Star Trek, with, ahem, slightly inferior production values) on our black-and-white television, I don’t think there was a sensible adult anywhere in Moscow or Washington, Ottawa or Budapest, who was not quite certain that by the year 2000, the world would have lived through an even more devastating world war.

Yet WW3 never happened. Instead, here we are, after 75 years of unprecedented peace and prosperity, a Golden Age that brought benefits to more people than at any time in the history of humanity. It is not unreasonable to worry that this Golden Age would not last forever, that eventually, it would crumble, just as the old world order that characterized Western civilization between 1849 and 1914 crumbled when the “lights went out all over Europe” in August 1914.

But imagine… for one moment, imagine what would have happened if the last global pandemic, the Spanish Flu, hit the world not in 1918 but in 1913. Imagine towns and cities shutting down, borders closed, but also nations helping each other, exchanging medical information, improving their communication, all in an at first haphazard, but later increasingly coordinated effort to overcome this scourge. And eighteen months later, when the last wave of infections subsides, global euphoria: A new fraternity of nations who, using the powers of modern science and working together, overcame this challenge and preserved our shared civilization.

And… no Great War. No collapse of the old world order. Instead, countries that previously seemed incapable of reforming themselves, now willing to take the necessary steps, as Russia, Austria-Hungary and Imperial Germany transition to constitutional monarchies, and a new, modern Europe emerges without the devastation of war, without the horrors of the Holocaust… all because of the pandemic that hit the continent before it had a chance to go berserk on its own.

So perhaps… perhaps COVID-19 is our era’s Spanish Flu and it is hitting us in our equivalent of 1913, before our next Great War, instead of devastating us after years of horrific warfare. Perhaps COVID-19 is what our societies need to preserve the values of our existing world order even as we reform it and ensure its survival for decades to come.

Is this a pipe dream? Perhaps. Then again… just thinking about this possibility made me feel substantially less apprehensive about the coming months, despite all my concerns, despite knowing that the worst is yet to come.

There are photos of empty store shelves circulating on the Internet, promoted in particular by Americans supporting Donald Trump, as examples of what stores would look like under socialism.

No, my friends, this is what stores looked like under socialism. Socialism that I experienced first-hand, not some abstraction. And it wasn’t pleasant. But the stores were… well, see for yourself. This is no propaganda photo, but a picture from the collection of my late father-in-law, who was a professional photographer. (The hand-written blue arrow is there to point out that under a sign advertising first-class poultry, there are meats hanging that definitely don’t appear to have come from any chicken):

In contrast, and contrary to what the poster tweeted, the following is a picture of Trumpian capitalism in a moment of crisis:

In fact, as some commenters pointed out, a centrally planned command economy in a police state may be better able to cope with a crisis of this nature than market capitalism, even with competent political leadership.

A Trumpist friend of mine (yes, I have Trump-supporting friends; I refuse to let politicians, left or right, to make me distrust my neighbor just because our political opinions differ) made a disparaging comment about Justin Trudeau, calling him xenophobic on account of Canada shutting its borders to foreigners.

No, my friend, that is not xenophobic. If you want to know why I call the American president a xenophobic asshole (again, forgive my language, dear readers, but I am done being nice to that boneheaded moron), here is a perfect example:

Yes, this is a tweet by a xenophobic schmuck.

Businesses appear to be somewhat freaked out by the COVID-19 pandemic. The good news is that many of these businesses choose to act responsibly, in the public interest, as opposed to trying to turn a global health crisis into short-term profiteering.

Several newspapers and magazines made their COVID-19 coverage accessible even for non-subscribers. In Canada, CBC Newsworld is now carried for free by several cable providers. One of the largest GIS software firms, ESRI, is making tools available for free online.

Even smaller firms follow suit. There is StarNet, makers of X-Win32 and FastX, popular software packages that can be used to access UNIX/Linux servers remotely from Windows workstations. They, too, are now offering free 6-month FastX licenses to anyone, to help facilitate work-from-home arrangements. I have liked this company ever since I first became familiar with their products back in the 1990s; now I like them even more (hence my decision to use their product logo to illustrate this post.)These steps, taken by businesses large and small, give me hope, even as I watch that compulsive liar of an infantile US president who cannot even get his story straight and his opposition who think that the impact of the COVID-19 crisis on Trump’s presidency is more important than the number of people the pandemic kills; or as I watch Canadian opposition politicians (looking at your Twitter feed, Andrew Scheer!) who use even COVID-19 as a cheap excuse for Trudeau-bashing. Can you please put this partisan shit aside, follow the lead of the aforementioned businesses, and start acting like, you know, grown-ups?

Trump is incompetent. America’s most Stable Genius is probably the most boneheadedly incompetent president in my lifetime, if not in the entire history of the great United States.

Take his announcement last night of the travel ban from Europe. First, let me state that the policy is, I believe, the right one: restricting international travel is the single biggest thing governments can do to slow the spread of a communicable illness. Despite being Draconian, despite inconveniencing hundreds of thousands if not millions of people, it was therefore the sanest thing to do, and I am glad that for a change, Trump listened to smart people in his administration.

Unfortunately, Trump obviously thinks life is a reality show, where bending the truth for the sake of maximizing entertainment value is not only acceptable but expected behavior. Which is why, if you only listened to Trump’s televised speech, without actually bothering to fact check it against the Web sites of the White House or the Department of Homeland Security, you could have come to the false conclusion that there might be a rush on airports as desperate Americans try to get home on one of the last few flights from the continent, or that trans-Atlantic trade is about to be shut down. Neither of which is the case, actually; US citizens can still return home and trans-Atlantic trade continues. The actual ban affects aliens who have spent any time in the Schengen zone within the past two weeks (like me; I presume I therefore cannot travel to the United States for the next couple of weeks, as I am not a US citizen or resident and I just returned from the Schengen zone this Monday.)

And Trump is also a hatemongerer, who feeds off dividing people. I cannot think of any US president in my lifetime: Kennedy, Johnson, Nixon, Ford, Carter, Reagan, Bush Sr., Clinton, Bush Jr., Obama — who would have presented the coronavirus thing as anything other than a global threat to humanity, a shared responsibility, not as an “us vs. them” affair, blaming China for the “foreign virus”, blaming Europe for not taking measures similar to those taken by the US (which is not even true, but that’s besides the point.) But Trump? As I said, like a leech or a vampire, he feeds off hate and distrust.

And then consider the following: This smartest president ever, this “stable genius” as he once characterized himself, actually disbanded his own National Security Council’s Global Health Unit, because, according to Mr. Stable Genius, it’s something that “you can never really think is going to happen.” Well, Mr. Stable Genius, I can offer a few names who actually did think that something like COVID-19 might happen: the aforementioned Messrs. Kennedy, Johnson, Nixon, Ford, Carter, Reagan, Bush Sr., Clinton, Bush Jr. and Obama… and that’s just in my lifetime.

You know, Mr. Stable Genius, I am trying to give you credit for finally listening to people who, unlike you, actually know what they are doing. But what I really feel… I hesitate to use profanity in my blog, but in this case I will make a rare exception, with apologies to my readers: I cannot wait until you just get the fuck out of that White House and return to obscurity as a failed rich boy, a crooked real estate villain, a reality TV has-been. The sooner you fuck off, the better we all are, Americans and other citizens, Republicans and Democrats alike.

PS: To my Republican-leaning friends who still defend this idiot and think that my criticism is evidence of me suffering from Trump Derangement Syndrome: Please look at the facts. Please recognize that this is not about “us vs. you”, not about liberals vs. conservatives, not about The Donald vs. Hillary, not about trying to undo an election. I understand why you voted for Trump and I accept that he actually delivered on a number of fronts, meeting or even exceeding your expectations. That does not make him any less dangerous, as he turns us against each other, makes us distrust each other more than we distrust actual enemies, and takes steps that reek of colossal incompetence. Like that speech last night. And before you dismiss all that, here is one number for you to ponder: 21,200.62. That’s the DJIA tonight, down from 27090.86 just eight days ago. That’s nearly 25% of the investments and retirement savings of millions of Americans and others, wiped out. In a market driven mostly by middle-aged white men. Trump’s primary voting base. Do they suffer from Trump Derangement Syndrome, too, when they conclude that his speech did more harm than good, driving markets down at an unprecedented pace?

I returned from a brief trip to Hungary yesterday.

My return flight was a bit eerie. Here is a picture of a part of the business class section of this Austrian Airlines 767:

It was not quite this empty (I tried to avoid photographing any passengers, for obvious privacy reasons) as there were a few passengers there, but only a few. Most reservations were canceled.

Is this dramatic response to the coronavirus justified? Parts of China, all of Italy under quarantine? Schools, public gatherings canceled around the world? A cruise ship industry in crisis, a global airline industry poised to lose hundreds of billions of dollars? Planes flying empty just to maintain the respective airlines’ claims on lucrative routes, or planes not flying at all, like the A380 fleet of Lufthansa?

Meanwhile, as Trump himself is fond to point out, the number of conformed coronavirus infections (most of which result in a mild illness, nothing more) worldwide is dwarfed by the number of influenza deaths this flu season.

Of course the flu is (more or less) predictable. The coronavirus is not. And its fatality ratio is much higher.

Even so, I have to admit that I wonder if the cure is causing more harm than the disease.

Then again… if we are just one minor mutation away from a Spanish Flu like pandemic, perhaps the drastic steps are justified. After all, at least some folks are criticizing the WHO for not going far enough, for failing to declare a global pandemic.

No matter what, flying back home in the time of coronavirus was an eerie experience. It was a bit like something straight out of the first episode of a science-fiction television series.

And yes, I was using my limited supply of hand sanitizer quite liberally. After all, you can never be certain…

A terrible sickness is upon us.

As of mid-January, just in the great United States 13 to 18 million people have been inflicted. Nearly 6 million required medical visits, and some 120,000 have been hospitalized. Worse yet, though the numbers are uncertain, somewhere between 6,600 and 17,000 people died. And that’s nearly two week old data; since then, I am sure there have been more victims.

Oh, you thought I was talking about the coronavirus outbreak that leads the evening newscast?

No. I am talking about the flu. Specifically, the 2019-2020 flu season, with data from the Centers for Disease Control.

As for the coronavirus, there have been a grand total of two confirmed cases so far in the US. None in Canada.

And that sums up the problem that I see with how we are being informed nowadays. Things that are exceptional and sensational lead newscasts. Things that are mundane are left forgotten, even when they are orders of magnitude more likely to affect you.

That is not to say that I disregard the threat that the coronavirus represents, or that I blindly criticize the response of authorities (in China and elsewhere) who are trying to contain a virus before it becomes more widespread. But keeping things in perspective is important.

Today, I answered a question on Quora about the nature of $$c$$, the speed of light, as it appears in the one equation everyone knows, $$E=mc^2.$$

I explained that it is best viewed as a conversion factor between our units of length and time. These units are accidents of history. There is nothing fundamental in Nature about one ten millionth the distance from the poles to the equator of the Earth (the original definition of the meter) or about one 86,400th the length of the Earth’s mean solar day. These units are what they are, in part, because we learned to measure length and time long before we learned that they are aspects of the same thing, spacetime.

And nothing stops us from using units such as light-seconds and seconds to measure space and time; in such units, the value of the speed of light would be just 1, and consequently, it could be dropped from equations altogether. This is precisely what theoretical physicists often do.

But then… I commented that something very similar takes place in aviation, where different units are used to measure horizontal distance (nautical miles, nmi) and altitude (feet, ft). So if you were to calculate the kinetic energy of an airplane (measuring its speed in nmi/s) and its potential energy (measuring the altitude, as well as the gravitational acceleration, in ft) you would need the ft/nmi conversion factor of 6076.12, squared, to convert between the two resulting units of energy.

As I was writing this answer, though, I stumbled upon a blog entry that discussed the crazy, mixed up units of measure still in use worldwide in aviation. Furlongs per fortnight may pretty much be the only unit that is not used, as just about every other unit of measure pops up, confusing poor pilots everywhere: Meters, feet, kilometers, nautical miles, statute miles, kilograms, pounds, millibars, hectopascals, inches of mercury… you name it, it’s there.

Part of the reason, of course, is the fact that America, alone among industrialized nations, managed to stick to its archaic system of measurements. Which is another historical accident, really. A lot had to do with the timing: metric transition was supposed to take place in the 1970s, governed by a presidential executive order signed by Gerald Ford. But the American economy was in a downturn, many Americans felt the nation under siege, the customary units worked well, and there was a conservative-populist pushback against the metric system… so by 1982, Ronald Reagan disbanded the Metric Board and the transition to metric was officially over. (Or not. The metric system continues to gain ground, whether it is used to measure bullets or Aspirin, soft drinks or street drugs.)

Yet another example similar to the metric system is the historical accident that created the employer-funded healthcare system in the United States that American continue to cling to, even as most (all?) other advanced industrial nations transitioned to something more modern, some variant of a single-payer universal healthcare system. It happened in the 1920s, when a Texas hospital managed to strike a deal with public school teachers in Dallas: For 50 cents a month, the hospital picked up the tab of their hospital visits. This arrangement became very popular during the Great Depression when hospitals lost patients who could not afford their hospital care anymore. The idea came to be known as Blue Cross. And that’s how the modern American healthcare system was born.

As I was reading this chain of Web articles, taking me on a tour from Einstein’s $$E=mc^2$$ to employer-funded healthcare in America, I was reminded of a 40-year old British TV series, Connections, created by science historian James Burke. Burke found similar, often uncanny connections between seemingly unrelated topics in history, particularly the history of science and technology.

The other day, I came across a wonderfully false analogy from a conservative writer. In an attempt to explain why conservatives despise Planned Parenthood in the United States, he asked how people on the opposite end of the ideological spectrum would feel if gay conversion therapy was offered in publicly financed clinics throughout the country.

I felt compelled to respond. Because if “gay conversion therapy” actually worked, I personally would have absolutely no objections to such clinics being offered to any gay person wishing to change their sexual orientation, even funded by government.

As things stand, however, “gay conversion therapy” is bogus, junk science, as nonsensical as creationism or belief in a flat Earth, almost as harmful as anti-vaxxers. Its real purpose is not to “cure” gays (which it cannot do) but to perpetuate bigotry and the marginalization of homosexuals in certain religious communities.

For this false analogy to work, abortions would have to be junk science, too, with clinics not actually being able to terminate unwanted pregnancies, but successfully perpetuating bigotry and hatred towards women with such pregnancies. But that is not what abortion clinics do. Rather, for better or for worse, they deliver exactly what they promise: ending unwanted pregnancies. This may be found objectionable on moral or religious grounds, but again, to draw the proposed analogy you would have to show how folks opposed to “gay conversion therapy” actually want gays to remain gay against their will on moral or religious grounds.

Because that’s what abortion opponents want: They want pregnant women to remain pregnant against their will.

Fair warning: This post contains some adult language.

In case there has been any doubt: Republicans have gone completely bonkers, and it is now official.

According to The Washington Post, the Centers for Disease Control and Prevention, America’s leading public health institute, is no longer allowed to use the following terms in its budget documents:

• vulnerable,
• entitlement,
• diversity,
• transgender,
• fetus,
• evidence-based,
• science-based.

Dear Republicans, dear followers of the orange person in the White House: Are you out of your fucking minds? Have you gone completely bonkers? Truly gone fishing? Are you bat shit crazy? Totally demented?

I mean, what kind of an idiot does this childish shit? You are worse than Soviet political commissars from the Stalin era. OK, you are not sending anyone to the Gulag (yet?) but your retarded drive for ideological purity is like a caricature of itself.

I mean… you are insane. Certifiably. This is not politics anymore. This is not left vs. right, transgender rights vs. traditional families. You are clearly deranged psychopaths.

I am secretly hoping that the news turns out to be false, but despite accusations of “fake news” and the like, I know The Washington Post to be a responsible news organization and I think it is a safe bet that this story was vetted.

In case anyone is wondering why my blog has been sitting idle for the past two weeks…

It’s a damn cold.

I haven’t had a cold or a flu in years. In fact, I was beginning to think that I might have become immune.

Er… nope.

Nearly two weeks ago, my wife began to feel sick. The usual: a bit of a cough, a bit of a runny nose, and a fairly high temperature, actually. The next morning when I woke up, I felt perfectly fine. Until I coughed a little, that is. And it felt like a sharp knife stabbing me in the middle of my chest. “Damn,” I said to myself, “I caught it.”

And caught it I did. I was sick for many days. Something that has not happened to me in decades: I even stayed in bed for half a day a couple of times.

OK, now I am on the mend. I still don’t have much of a speaking voice, I still get coughing fits, and my stomach is still a bit queasy, but I feel generally okay.

My wife recovered a little more quickly than I, but even she is still coughing occasionally.

I hope that we both paid our dues to the demons of the common cold or the evil spirits of the flu for several years to come.

Meanwhile, I already had a lot of catching up to do before I fell ill… now, my TODO list looks bad enough to make me feel desperately, depressingly sick again. Will I ever catch up?

It is almost the end of October, and I only added one blog entry so far this month. One reason is that we had a minor health scare: when my wife traveled to Hungary last month, she landed in a hospital on arrival, as she had an unexplained seizure during her flight.

She is doing well, thankfully. She returned home safely, with no lasting effects. There will still be a few more tests to be sure, but the scare is largely over.

This unfortunate incident, however, allowed us to experience first-hand the state of the health care system in Hungary, about which we read so much in recent years. Yes, as it is well known, the system is badly underfunded: salaries are miserably low, and sometimes, even basic supplies are lacking.

But we cannot utter a bad word about the health care professionals that my wife encountered. They were impeccably professional and helpful, going out of their way to assist us, even beyond the call of duty. When my wife’s cell phone was acting up, one nurse volunteered to help fix it with my assistance. When I explained to a doctor that I cannot visit her in person because I happen to be a continent away, he handed the phone to my wife, allowing us to have a conversation (finally!) using a hospital line for a few minutes. They helped with insurance matters, too, and they issued a very thorough discharge report, complete with a CD-ROM containing the results of a CT scan.

All in all, we have nothing but praise for these overworked and underpaid health care workers, some minor mishaps notwithstanding. They were kind, they were helpful, and every one of them that I spoke with was ready to assist, forthcoming, and flawlessly polite. Thank you for your kind care. Köszönjük szépen.

Alexander Fleming discovered Penicillin in 1928. He received the Nobel prize for his discovery in 1945.

A Facebook friend shared his Nobel lecture. Particularly, the following quote:

The time may come when penicillin can be bought by anyone in the shops. Then there is the danger that the ignorant man may easily underdose himself and by exposing his microbes to non-lethal quantities of the drug make them resistant. Here is a hypothetical illustration. Mr. X. has a sore throat. He buys some penicillin and gives himself, not enough to kill the streptococci but enough to educate them to resist penicillin. He then infects his wife. Mrs. X gets pneumonia and is treated with penicillin. As the streptococci are now resistant to penicillin the treatment fails. Mrs. X dies. Who is primarily responsible for Mrs. X’s death? Why Mr. X whose negligent use of penicillin changed the nature of the microbe. Moral: If you use penicillin, use enough.

Fleming thus foresaw the dangers of emerging antibiotic resistance. Too bad the world failed to listen. Now, a growing number of people die from once treatable (e.g., post-operative) infections because the evolution of bacteria outpaced our ability to develop new antibiotics.

Frances Kathleen Oldham Kelsey died this morning. She was 101 years old.

Dr. Kelsey’s name is the subject of legend among thalidomide sufferers. Born in Canada, Dr. Kelsey moved to the United States, where eventually she became an employee of the Food and Drug Administration in 1960. The first file on her desk was about thalidomide, a drug that is now known to have caused many thousands of birth defects worldwide.

Concerned about the drug’s suspected side effects, Dr. Kelsey refused to approve it without full clinical trials. She was vindicated when the numerous birth defects caused by thalidomide came to light. The USA was thus spared a scourge that was inflicted by thalidomide on many other countries, including Canada.

Eventually, Dr. Kelsey was even recognized by the president of the United States, John F. Kennedy.

Dr. Kelsey’s Canadian recognition came much later. In 2015, she was finally awarded the Order of Canada. Her family asked that the award ceremony be moved up as her health was in rapid decline. Accordingly, Elizabeth Dowdeswell, Ontario’s Lieutenant-Governor, visited the Kelsey home yesterday. Dr. Kelsey was reportedly aware and was thrilled.

Frances Kathleen Oldham Kelsey died less than 24 hours later. But what an amazing life she lived.

Vaccinations are not without risk, some say. Why should the evil government compel me to expose my child to a known risk, they ask. Why is it my problem if someone else’s child is not vaccinated, they argue.

Well… it boils down to simple math, really. Suppose that once infected, a person remains infectious for a period of time denoted by $$\delta t$$. The virulence of the disease is measured by the number of people that a single patient can infect during this period of time. It is called the basic reproduction number, denoted by $$R_0$$. If this number is greater than one, we have the potential for an epidemic.

So then, after some time $$t$$ has elapsed, the number $$N(t)$$ of people who are infectious at that moment $$N(t)=N_0R_0^{t/\delta t}$$, if $$N_0$$ was the number of infected people at $$t=0$$. At least this will be the correct number during the early stages of the epidemic; later, infection rates slow down as a growing number of people will have already caught the disease and the survivors will have developed immunity to it.

But we are interested in the early stages indeed, because the idea is to prevent an epidemic in the first place. So this simple model is adequate.

Now what happens when you vaccinate people? Even if everyone gets vaccinated, vaccines are not 100% effective. If the efficiency of a vaccine is given by $$\epsilon$$ (a number between 0 and 1, with 1 meaning 100% efficiency), the aforementioned formula is modified: $$N(t)=[(1-\epsilon)R_0]^{t/\delta t}$$. If $$(1-\epsilon)R_0<1$$, we win: an epidemic is avoided.

But what happens when not everyone gets vaccinated? Some people obviously cannot be: very young babies, people with compromised immune systems, etc. Let’s say the vaccination rate is given by $$\rho$$. Once again, the formula for $$N(t)$$ needs to be revised: $$N(t)=[(1-\epsilon\rho)R_0]^{t/\delta t}$$.

And this is where the problem lies: if $$(1-\epsilon\rho)R_0>1$$, the potential for an epidemic exists.

Take the case of measles, for which $$R_0=12…18$$. Even if we take the lower limit of the given range, $$R_0=12$$, it is one of the most virulent contagious diseases out there. The measles vaccine is supposedly 95% effective: $$\epsilon=0.95$$. So then, $$(1-\epsilon)R_0=0.6$$, and we are good: in a fully vaccinated population, measles would disappear in short order. This is indeed what happened when measles vaccinations became common in much of the world starting in the 1970s.

But now, let us think about $$\rho$$. The math is easy: If $$\rho<0.965$$ (that is, if more than 3.5% of the population are unvaccinated), $$(1-\epsilon\rho)R_0>1$$. Herd immunity is lost: the disease spreads.

And lest we forget, measles is a very deadly disease. Parents who play Russian roulette with their children on the basis of unsubstantiated fears concerning the vaccine’s effectiveness and side effects forget that often the only reason their child survives the infection is because they have access to first-world health care… the same health care that would have prevented the illness in the first place, if not for the parents’ arrogant stupidity.

These parents should be reminded that in poorer parts of the world, their counterparts often risk their lives to get their children vaccinated. Like parents in Somalia who, defying a ban on polio vaccination by al-Shabaab, smuggle their children to government-controlled areas to get the life-saving vaccine. Obviously these Somali parents are a lot smarter, a lot wiser than first-world anti-vaxxers, be it new age parents who prefer “happy thoughts” (or whatever) over medically approved methods, or nutty right-wingers who distrust the government on everything.

In short, if your political or religious views, or your scientific illiteracy compel you to be as stupid as a doorknob, please find a way to express your stupidity without endangering the health and lives of others.