Deterministic epidemic waves

Abstract

In the well-known deterministic model for the spread of an epidemic, one considers a population of uniform density along a line and divides the population into three classes: susceptible but uninfected, infected and infectious, infected but removed. If we denote space and time variables by s, t and let x ( s, t ), y ( s, t ), z ( s, t ) be the proportions of the population at ( s, t ) in these three classes, then x + y + z = 1 and we suppose that Here Ῡ( s, t ) denotes a space average ∫ y ( s + σ) p (σ) d σ, where p is a probability density function; b is the removal rate; the scale of t has been adjusted to remove a constant that would otherwise occur in (1).