The type-reproduction number T in models for infectious disease control.

Abstract

A ubiquitous quantity in epidemic modelling is the basic reproduction number R0. This became so popular in the 1990s that ‘All you need know is R0!’ became a familiar catch-phrase. The value of R0 defines, among other things, the control effort needed to eliminate the infection from a homogeneous host population, but can be misleading when applied to a heterogeneous population for the same purpose. We have defined the type-reproduction number T for an infectious disease, and shown that this not only has the required threshold behaviour, but also correctly determines the critical control effort for heterogeneous populations. The two quantities coincide for homogeneous populations. In this paper we further develop the new threshold quantity as an indicator of control effort required in a system where multiple types of individuals are recognised when control targets a specific type.