The FSS sent me this paper modeling the spread of zombies as an infectious disease. Well, really they are using an ODE, but it is the same kind you use for infectious diseases that actually exist. The results are unsurprising to anyone who has ever seen a zombie movie, but I do appreciate that Max Brooks' solution in World War Z seems to be favored: swift eradication by coordinated effort.
The next go around on this particular model would probably try to include seasonal variables like Brooks talked about, zombies freezing in the winter and thawing in the spring, zombies roaming the ocean bottom, and so on.
This is a good example of what could be called the formal sciences. When applied to actual diseases, this method allows us to understand and predict the behavior of uncounted disease microbes as they spread through a population, but without reference to the physics or biology involved in much detail. Only some very general details are needed to set up the differential equation, but the result is still applicable to what happens in reality. The formal sciences are a recent invention, coming only during and after the Second World War. They are especially notable because they very obviously ignore Popperian notions about science, and simply produce highly certain conclusions that are easily verifiable.
h/t The Family Social Scientist