This chapter initiates our study of diffusion and models it as a process whose spreading mechanism is independent of any neighborhood considerations. This means that the procedure by which the process propagates from a certain node to any one of its neighbors is unaffected by the conditions prevailing in the neighborhoods of those two nodes – thus, in particular, it is unrelated to the states displayed by their other neighboring nodes. In this sense, one can conceive the phenomenon as akin to biological infection, a process that is often mediated through local contact at a rate that depends on the aggregate exposure to infected neighbors. With this analogy in mind, we shall label such a process as epidemic diffusion. But, of course, diffusion in socioeconomic environments is often different, subject to neighborhood (as well as payoff-related) considerations. To study it under these conditions, therefore, we need a different framework of analysis, which is introduced in Chapter 4.

ALTERNATIVE THEORETICAL SCENARIOS

Epidemiology is an old and well-established field of research, both empirical and theoretical. Its canonical models fall into two categories:

• SIR (susceptible-infected-recovered), where the life history of each node (or agent) passes from being susceptible (S), to becoming infected (I), to finally being recovered (R), always moving in a unidirectional fashion.

• SIS (susceptible-infected-susceptible), where each node passes from being susceptible (S) to turning infected (I), to becoming again susceptible (S), thus allowing for a bidirectional transition between the two possible states.