# Tag Archives: vampires

## on vampires, exponential population growth, and scientific literacy

Eleven years I wrote a tongue-in-cheek blog post about vampires and stochastic processes. I was inspired by my course material about Markov chains and branching processes, which has application to the spread of infectious disease, to the vampire population dynamics in the Twilight series and other teenage vampire stories that were very popular at the time.

I have a great deal of skepticism about vampires.

Here’s my problem with vampires. I have a hard time believing that there would be just a few vampires out there and that the existence of vampires would be such a well-kept secret. After all, they reproduce rather easily (a single vampire could create thousands of offspring, whereas there are limits to human reproduction) and vampires don’t die easily. If there were vampires, they would almost certainly outnumber humans (but then vampires would run out of food).

This argument becomes even more overwhelming if you model a vampire population as a branching process or birth-death process and assume that each vampire in the population has probability Pj of producing j offspring (with j=0,1,2,… ). The vampire population would either explode or die out, depending on the expected number of offspring per vampire. But if you take into account the fact that vampires live many, many generations (they’re virtually immortal) and may create thousands of offspring, the population explodes (if you assume that each vampire creates at least one vampire, on average, before it dies). With those numbers, vampires would not be living under the radar–they would be everywhere!

I have yet to see a vampire movie that implicitly assumes that there is a reasonable model for vampire population dynamics (using a stochastic process framework or something else). And frankly, I’m pretty disappointed. Until I am offered a reasonable explanation for why there aren’t more vampires, I won’t be able to jump on the vampire bandwagon.

This issue had been bothering me since I first saw The Lost Boys, long before I knew about Markov chains. I enjoyed The Lost Boys, but I did not enjoy it’s inability to acknowledge exponential vampire population growth. Markov chains later helped me understand why my skepticism was valid.

The post went viral. Life was interesting for awhile. Twilight fans hated me.

My blog post was never intended to be taken seriously. It was not a serious critique of vampires, because vampires aren’t real.

Once in awhile, I google myself to see what turns up. Over the years, I have found that several vampire fan news sites and blogs that existed at the time (teenage vampire stories were very popular at the time) picked up my blog post and wrote serious articles about it.

Some of the concerning coverage of my post was on vampire fan websites that no longer exist online. A decade ago I remember discovering a vampire fan website for teenage girls with a domain that may have been iheartvampires.net that made a serious two minute “vampire news” video about my “research” in vampire population dynamics that supposedly proved that vampires could not exist. The host discussed my blog post like it was real research. I was disheartened by this. I would like to engage teenage girls about operations research and analytics but without the vampires. It’s only fun if it gets people more engaged with real research, science, and engineering.

A positive example is the one entitled “Vampire Ecology: Twilight vs. Buffy” on a science blog that argues that vampires could exist by linking to another tongue-in-cheek paper that takes human predation on vampires into consideration as a form of vampire population control. It doesn’t seem to take my post too seriously (phew).

I have given a lot of though to increasing scientific literacy in the general public for the last decade. The far-too-serious coverage of my silly vampire post did not dissuade me from engaging the public about my research. Instead, it encouraged me to be more intentional with how I communicate scientific principles to the public and motivated me to discuss real scientific issues with the general public as much as I can. I have blogged about some of my public talks and have appeared in the media many times. I have found that a lot of people are receptive to science and engineering research, especially if it seems relevant to their lives. I try to stick to applications of operations research, analytics, and industrial engineering in the public sector.

I’ve been encouraged by the discussion of real scientific principles during the COVID-19 pandemic. It’s been a positive side effect of a serious pandemic. I hope the public’s interest in science continues.

## Happy Halloween from Punk Rock OR

Happy Halloween! Here are five Halloween themed posts from Punk Rock OR:

university offers zombie apocalypse course to teach students survival skills

find the size of a zombie population during a zombie attack

interview with an undergraduate researcher (we discuss horror movies in the podcast)

pumpkin patches and queuing theory

how to (optimally) prepare for a zombie outbreak

on vampires and operations research

werewolves and star wars: two exam questions

vampire-inspired network flows

Do you have an OR Halloween costume?

## university offers zombie apocalypse course to teach students survival skills

Michigan State University plans to offer a zombie apocalypse course to teach students survival skills. The course will be offered by the School of Social Work. (Hat tip to Paul Rubin). The course won’t really teach students how to survive a zombie attack, rather, it uses a zombie apocalypse as a vehicle for teaching students about how to model catastrophic events and infectious diseases like pandemic flu.

This has me convinced that I should develop a course on OR models for a zombie apocalypse.

I am planning to develop a similar course that teaches introductory OR modeling to undergraduates by way of applications in emergency preparedness and emergency response. I had envisioned covering more traditional disasters, such as hurricanes and earthquakes. Maybe I should think outside the box.

What topics would you offer in an OR course on the zombie apocalypse? I would start with population models using birth-death models and/or differential equations (see one of my previous posts on this topic) and then look at how to staff deputies or federal marshals to combat the zombie hoards.

I plan to talk about zombies, werewolves, and vampires in the stochastic processes course I am teaching this semester. Here is a previous exam question.

## happy Halloween from Punk Rock Operations Research

Happy Halloween! Here are five Halloween themed posts from Punk Rock OR:

how to (optimally) prepare for a zombie outbreak

on vampires and operations research

werewolves and star wars: two exam questions

vampire-inspired network flows

pumpkin patches and queuing theory

Do you have an OR Halloween costume?

## werewolves and star wars: two exam questions

I’m recovering from the end of the semester.  I’m looking forward to a return to regular blogging.  I’ll start writing about the end of the semester.  I decided to have some fun with my stochastic processes final this semester and to write questions about werewolves and Star Wars (I was inspired by Tallys Yunes’s vampire network flow). I’ll be honest, I think that I had more fun with this than did my students.

The werewolf question: The werewolf population in the Richmond area can be modeled as a linear growth birth and death process.  Each werewolf independently reproduces at a rate of lambda = 0.15 werewolves/year and is killed by vampires at a rate of mu = 0.1/year.  If the population started with a pack of three werewolves in the year 1860, find the average size of the werewolf population today (150 years later).

The Star Wars question (pre-Episode IV): Suppose that every month, Darth Vader organizes a gathering on the Death Star to build morale and promote bonding among the Storm Troopers.  The Storm Troopers’ attendance at the gatherings is represented by a Markov chain.  Given that a Storm Trooper has attended the last gathering (state 0), they go to the next gathering with probability p0.  In general, given that they last attended the kth prior gathering, they go to the next gathering with probability pk, with 0 < pk < 1 , k = 0,1,2,3,4.   Storm Troopers are required to attend a gathering every six months, and hence, given that they last attended the 5th prior gathering, they go to the next gathering with probability 1 (p5 = 1).

a. Define the Markov chain for this problem, specify the classes, and determine whether they are recurrent or transient.

b. What is the cumulative density function representing the number of months until a Storm Trooper first returns to the gathering (i.e., the first return to state 0)?  Assume that they have just attended a gathering (i.e., they start in state 0).

b.  In the long run, what is the proportion of Storm Troopers that have attended one of the last three gatherings?

Related post:

Kudos to you if you find the correct solutions!

## welcome vampire enthusiasts!

If you’re a first time Punk Rock Operations Research visitor, thank you for visiting my blog. I am just a humble university professor. If you’re reading this, you are just as curious about vampires as I am. Many of you know quite a bit more about vampire population dynamics than I do. Thank you for sharing your knowledge and for recommending books and movies. I have a lot to learn!

If you haven’t heard of the field of operations research yet, it can be defined as the science of applying math and other analytical methods to make better decisions. Operations research applies interdisciplinary methods (including math, engineering, economics, computer science, statistics, business, etc.) to improve our world and to make better decisions–and to prove it mathematically! We usually apply math to more realistic problems than modeling vampire populations. 🙂

If you are curious, I urge you to read more about operations research online. A good place to start is another operations research blog–start with any on my Blogroll on the right side of this page. We’re geeks, but we have fun, too.

Other blog responses: