Newspapers had a hay-day last year following the publication of a paper
out of the University of Ottawa that discussed Bieber Fever. Some articles
included:

- Science Confirms:
Bieber Fever Is More Contagious Than the Measles (The Atlantic)
- Bieber fever is
worse than measles, according to actual science (National Post)
- Bieber fever more
contagious than measles, claim scientists (The Week)
- 'Bieber Fever'
more infectious than measles (CBC)

Of all of these, I'm most disappointed in the CBC - I often pay
attention to the CBC, and it's discouraging to know that they might be equally
as wrong about other things as they are about this.

What's going on here? A professor from the University of Ottawa
published a paper where a new
model was developed to look at Bieber Fever, and the paper does indeed include
the quote "It follows that Bieber Fever is extremely infectious, even more
than measles, which is currently one of the most infectious diseases. Bieber
Fever may therefore be the most infectious disease of our time." Oh my
god, those newspapers must be right! Science has confirmed our worst fears!
This must be backed by hard facts and empirical evidence!

Well, no. The paper appears to be a chapter in a book that examines diseases through
various mathematical models. Each of the papers in the book (four of which are
written by the Bieber Fever author) takes on a different disease and models it,
then examines mathematically the effects of different approaches to the
disease, like pulse vaccination or changes in infection or relapse rate. I
can't comment on the quality of the other chapters in the book, but they seem
to be well-developed and certainly based on real diseases.

The Bieber Fever paper is a little bit
different though. First of all, it is clearly written in a tongue-in-cheek
manner that I think flew over the heads of most major newspapers. The humor and
sarcasm actually make it quite an entertaining read, and if the piece was
written as a humorous look into a creative way of adapting a disease model
(which is my suspicion), then it could certainly be a fun case study for
biology or math students. It is definitely not something worth raising alarms
over in newspapers, though, as the model's predictions aren't validated against
any actual statistics and its math is misleading, allowing them to draw this
ridiculous comparison to measles that grabbed newspaper attention.

Mathematical disease modelling is a pretty cool field. The most basic
model that can be developed is an SIR model - a population
is divided up into three groups (Susceptible, Infected, and Removed), and
people move through the groups depending on disease parameters and the size of
the groups at a given time. For instance, if a lot of people are Infected, the
chance of a healthy Susceptible person getting infected is quite high (perhaps
due to lots of people sneezing on them), but as more people are Removed
(happily by recovery and immunity, or sadly by death), it may become harder for
the disease to propagate.

In this model,

*βIS*represents the rate that healthy people become sick - effectively, it is the chance that in a given time a Susceptible person will encounter an Infected person, multiplied by the chance that that encounter will transmit the disease. On the other end,*γI*represents the rate at which sick people become healthy, effectively the number of Infected people divided by how long it takes them to get healthy (or die, I suppose).
As long as the rate of people becoming sick (

*βIS*) is larger than the rate people are recovering (*γI*), then the disease will reach an epidemic of some type - otherwise it will quickly die out. For simple models, the ratio of these rates is known as the Basic Reproduction Number (R_{0}) of a disease, and correlates to the number of new diseases a sick person will cause. This is pretty easy to visualize - if the ratio R_{0}is bigger than 1, then by the time someone recovers from their illness they’ll have spread it to at least one more person, and the disease will grow. If you're unlikely to make someone else sick when you fall ill, the disease’s R_{0}will be less than 1, and the disease will go away without much of an outbreak.
For reference, the flu typically has an R

_{0}of 2-3, HIV is around 2-5, Smallpox is 5-7, and Measles is**. For every person who got Measles, the disease was so infectious and you had it for long enough that you were expected to transmit it to between twelve and eighteen people before you either recover or die.**__12-18__
Frightening stuff. Fortunately, analyses of diseases with these mathematical
models shows that as long as a certain proportion of a population is immunized
by vaccine, epidemics can be avoided. That proportion needed is (1-1/R

_{0}) - so a typical flu needs 60% immunization to prevent outbreak, and measles needs over 90%. If you're still unsure about getting a flu shot, just remember that if a population doesn't hit ~60% immunity, it is very much worse off for those who don't have the vaccine or who are otherwise susceptible.
The Bieber paper develops a more complicated mathematical disease model.
It looks something like this:

The author, Robert Smith? (not a typo), proposed a model where media
effects have a large impact on the disease. Positive media (P in the picture)
can increase the rate at which healthy people become Bieber-infected, and can
also make recovered individuals susceptible to re-infection, and Negative media
can heal the sick or immunize the susceptible (how miraculous).

Using the numbers that Smith? has in his paper, the spread of Bieber
Fever in a typical school of 1,500 students would look something like this:

After about 2 months, the system reaches an equilibrium with about 85%
of people being Bieber Fanatics. The paper makes a couple of assumptions: first
of all, people are assumed to "grow out" of Bieber Fever after a
period of two years. People are also expected to interact with everyone else in
the population at least once a month, and have a transmission rate of 1/1500.
This means that the average infected person will infect 1 person a month for 24
months, giving Bieber Fever an R

_{0}of 24.
SWEET MOTHER OF GOD IT'S WORSE THAN MEASLES!?!?

Not even a little bit! The transmission rate is absolutely just assumed
out of nowhere - no stats, evidence, or explanation given. Similarly, the
length of the disease is made up, with the explanation "But let’s be
honest, we all know which one it really is, don’t we?" (Smith?, p. 7).
Essentially, the authors were given a calculation where they had to assume
three numbers and multiply them together, and newspapers are surprised that the
answer to the multiplication was

*high*. Even the mechanics of the positive and negative media effects are questionable, though the model they developed could help provide insight into other diseases with relapse mechanisms.
The paper is cute, clever, and provides a mathematical analysis of a convoluted
set of differential equations - for all of these things it serves a nice
purpose as a tongue-in-cheek entry into a textbook examining mathematical
modelling of infectious diseases. But newspapers taking essentially the result
of an unfounded

*set of assumptions*out of proportion and reporting them as "*Science Confirms*!" will always annoy me to no end.
One last thing. This is what a graph would look like if the same school
was hit with measles:

Now

*that's*an epidemic - three people sick can infect up to 1,200 in less than a week. Remember this when deciding whether or not to immunize your baby.
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