S Z R Models

It seems somehow appropriate to reanimate this blog post from last year

I introduced the basic SIR model for a simple epidemic to you. this model actually has a long history and was first described by Kermack and McKendrick in 1927.

As I indicated this model has since been expanded to include virtually every disease scenario you can imagine.

Last year a group of Canadian mathematicians used this SIR format as the basis for an analysis of a zombie epidemic. Their paper: WHEN ZOMBIES ATTACK!: MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION ) - somehow it seemed appropriate to keep that in capitals) - describes a model that should look basically familiar to you.

Notice in their S Z R model (Z for Zombie of course) there are two extra transitions - from R back to Z (reanimation of the dead is well established in the zombie movie genre) and a movement directly from S to R (non zombie related death).

This is, perhaps unsurprisingly, the first mathematical analysis of an outbreak of zombie infection. While the scenarios considered are obviously not realistic, it is nevertheless instructive to develop mathematical models for an unusual outbreak. This demonstrates the flexibility of mathematical modelling and shows how modelling can respond to a wide variety of challenges in ‘biology’.

In summary, a zombie outbreak is likely to lead to the collapse of civilisation, unless it is dealt with quickly. While aggressive quarantine may contain the epidemic, or a cure may lead to coexistence of humans and zombies, the most effective way to contain the rise of the undead is to hit hard and hit often. As seen in the movies, it is imperative that zombies are dealt with quickly, or else we are all in a great deal of trouble.

S Z R Models

I introduced the basic SIR model for a simple epidemic to you. this model actually has a long history and was first described by Kermack and McKendrick in 1927.

As I indicated this model has since been expanded to include virtually every disease scenario you can imagine.

Last year a group of Canadian mathematicians used this SIR format as the basis for an analysis of a zombie epidemic. Their paper: WHEN ZOMBIES ATTACK!: MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION ) - somehow it seemed appropriate to keep that in capitals) - describes a model that should look basically familiar to you.

Notice in their S Z R model (Z for Zombie of course) there are two extra transitions - from R back to Z (reanimation of the dead is well established in the zombie movie genre) and a movement directly from S to R (non zombie related death).

This is, perhaps unsurprisingly, the first mathematical analysis of an outbreak of zombie infection. While the scenarios considered are obviously not realistic, it is nevertheless instructive to develop mathematical models for an unusual outbreak. This demonstrates the flexibility of mathematical modelling and shows how modelling can respond to a wide variety of challenges in ‘biology’.

In summary, a zombie outbreak is likely to lead to the collapse of civilisation, unless it is dealt with quickly. While aggressive quarantine may contain the epidemic, or a cure may lead to coexistence of humans and zombies, the most effective way to contain the rise of the undead is to hit hard and hit often. As seen in the movies, it is imperative that zombies are dealt with quickly, or else we are all in a great deal of trouble.

Gerbils and coffee

If you are reading this (someone is, right?) then you've probably noticed I try to post daily. Sometimes I have something in mind for the post, something I've found while preparing the lecture or something I didn't have time to mention. Sometimes I won't have anything particular in mind so I take a look at some websites to see what disease related stories I might have missed lately that are nice and topical. A good source for science stories, of all types, is Science Daily. They nearly always have some great articles and, conveniently, you can select stories by topic. For example here are their current Infectious Disease stories. Here's an item I missed a couple of weeks back. It has both gerbils and coffee - what's not to like? (I particularly like the way that although the coffee link is really rather tenuous the computer generated 'Related Stories' suggests a whole bunch of coffee related stories).

By moving through the coffee via the empty spaces between the ground coffee particles, the water picks up the flavour of the coffee. Stephen Davis and colleagues at the Faculty of Veterinary Medicine, Utrecht University, report in Nature their discovery that the spread of the bubonic plague bacteria in Central Asia by gerbils, works much the same way.

Plague bacteria percolate through the landscape transmitted by fleas from one great gerbil family to the next, from burrow system to burrow system. It’s the first time percolation theory is used to accurately describe the natural dynamics of an infectious disease. The discovery might be helpful to understand how outbreaks of disease occur in other populations. It may, for example, shed new light on spread of bovine tuberculosis in badgers, and spread of viral diseases in populations of African lions.

The only thing that bugs me about Science Daily is that they don't seem to provide direct citations to the source articles - just a couple of hints like the authors name and journal. It usually isn't hard to track down but I don't know why they don't give the full citation. Here's a link to the original paper - The abundance threshold for plague as a critical percolation phenomenon. It has a lot fewer references to coffee but it does have a very cool satellite photograph of gerbil burrows.

Solver for the SIR Model of the Spread of Disease

Here's a link if anyone is interested in more of the SIR model. It's the exact same model we talk about in class. You can plug in any number you want and see for yourself how fast a disease can spread. Here's the link