Collective dynamics and model verification: Connecting kinetic modeling to data

Marketing on Populations modelled as random graphs

Reinhard Illner

University of Victoria, Canada

The penetration of a well-mixed population by a new product is modelled by an Ordinary Differential Equation known as the Bass model (After Frank Bass, 1969). Realistic marketing scenarios will include matters such as competition between several products, word-of-mouth vs. advertising marketing, and the randomness of connections inside the population. In recent joint work with Edwards, Ma and Li, we have developed models which address these refinements; in particular, the population is not assumed to be well-mixed, but is modelled as a random graph of configuration type. I will present models of SI- type, in which a buyer will keep a product indefinitely once it has been purchased, and the more difficult case of modelling SIS scenarios, where product failure or fatigue will eventually return a customer to the susceptible category, I.e., the class of potential buyers. Analogies and differences to epidemiological scenarios will be discussed, and we some numerical simulations will be shown.