Let’s consider the SIR model. As we are at Halloween, let us consider the illnes

Question

Let’s consider the SIR model. As we are at Halloween, let us consider the illness, lycanthropy. Lycanthropy is the disease that turns humans into werewolves.

a. Given that werewolves can only spread the disease during the full moon, what would you have to do to modify the SIR model to reflect this?

b. Once a werewolf, always a werewolf. But humans can kill werewolves with a silver bullet. How would this interaction be modeled in your equations (what I am asking for is a complete set of modified SIR equations that capture the results of your answer in part a with the ability of humans to kill werewolves)?

Explanation / Answer

1a.

Full moon comes in every 28 nights; therefore, we get the rate of recovery or death by inverting duration of infection. It is due to the following relationship:

Y =1/D

Here Y is the rate of recovery or death

D = duration of infection

The SIR graph would reflect by the above values because the period between numbest of infection (I) and the number recovered (R) is duration of infection (D).

1b. The time variables of S, I and R are s(t), i(t) and r(t). These have following relationships.

s(t)+ i(t) + r(t) =1

Therefore at each time when a werewolve die, the i(t) would decrease and hence the r(t) would increase. This would not alter the outcome of the equation but will change the rate of recovery, which will reflect the SIR graph.a

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