Epidemics as Diffusion Waves

Abstract

‘Epidemics as Diffusion Waves’ establishes the parameters of the book. It begins by defining the basic building blocks of the study: infection, contagion, and disease. Key epidemiological concepts and terms are introduced and defined, and classic compartmental (susceptible → infective → recovered; SIR) approaches to epidemic modelling are outlined. Epidemic waves in the time domain are examined in terms of their shape (logistic model, Kendall waves), as repetitive wave trains (Bartlett threshold model), and as branching networks (Reed–Frost model). The second half of the chapter examines epidemic waves in the space domain. The swash–backwash model of the single epidemic wave introduces the concept of the spatial basic reproduction number R0A, the geographical analogue of the basic reproduction number R 0. Spatial simulations of diffusion waves are explored through the work of Torsten Hägerstrand. The chapter concludes with a consideration of dyadic (lag correlation and spatial interaction) approaches to epidemic modelling.