Diffusion Models

Abstract

This chapter focuses on diffusion, which is a common feature of many social and biological systems. Innovative consumer products frequently "take off" and "go viral", with sales driven by the word of mouth effect, as their adoption spreads through a population. Infectious diseases can transmit rapidly through a population, accelerating from seemingly low incidence levels, to sizable numbers in a short space of time. Here, the focus is on models of infectious diseases. These have an important decision support function for public health professionals faced with challenge of responding to an infectious disease outbreak. The first model is the classic SIR structure, which divides the population into those who are susceptible, infected and recovered. This model is then extended to cater for multiple age cohorts, so that diverse mixing patterns can be simulated. Finally, a scalable R model of infectious diseases is introduced, combining matrix operations with vectorized differential equations.