Let’s consider the sir model. as we are at halloween, let us consider lycanthropy - werewolves. lycanthropy is spread by the bite of an infected individual. this occurs only during the full moon (as all other nights the individual is just a normal human). a fraction, g, of bitten individuals die and another fraction, w, become werewolves. there is a cure for lycanthropy and that is consuming a tincture of wolfsbane (aconitum lycoctonum). the problem is that the cure works with a frequency c and with a frequency of 1-c is fatal. the cure is difficult to administer and only b percent of werewolves have the cure administered to them. if the cure is successful, the person cannot ever become a werewolf again.

humans can kill werewolves with a silver bullet. how would you model this effect in the standard sir equation?

given the full interactions, provide a complete set of equations that would model the werewolf/human interaction? remember you need to account for humans killing werewolves at some rate, werewolves killing humans and werewolves converting humans to werewolves. you also need to account for werewolves being cured or killed by a treatment of wolfsbane. start by drawing a box and arrow diagram. each arrow should account for a type of interaction and there should be a box for each state of human or werewolf. once you have that you can write the terms for the equations.

is there any difficulty in using the differential equations of the sir for modeling werewolves? how might you change the model to account for any problems?