Some simple rules for estimating reproduction numbers in the presence of reservoir exposure or imported cases

TL;DR

This paper derives simple rules for estimating the basic reproduction number in populations with external sources of infection, such as reservoirs or imported cases, and applies these rules to Clostridium difficile data.

Contribution

It introduces a novel framework for understanding disease persistence driven by external sources, extending traditional R0 concepts to reservoir- and importation-driven diseases.

Findings

In the simplest case, R0<1 if external infection proportion exceeds disease prevalence.

C. difficile in hospitals can have R0<1, sustained by imported cases.

C. difficile in the general population can be reservoir-driven with minimal animal transmission.

Abstract

The basic reproduction number ($R_0$) is a threshold parameter for disease extinction or survival in isolated populations. However no human population is fully isolated from other human or animal populations. We use compartmental models to derive simple rules for the basic reproduction number for populations with local person-to-person transmission and exposure from some other source: either a reservoir exposure or imported cases. We introduce the idea of a reservoir-driven or importation-driven disease: diseases that would become extinct in the population of interest without reservoir exposure or imported cases (since $R_0<1$), but nevertheless may be sufficiently transmissible that many or most infections are acquired from humans in that population. We show that in the simplest case, $R_0<1$ if and only if the proportion of infections acquired from the external source exceeds the disease prevalence and explore how population heterogeneity and the interactions of multiple strains affect this rule. We apply these rules in two cases studies of Clostridium difficile infection and colonisation: C. difficile in the hospital setting accounting for imported cases, and C. difficile in the general human population accounting for exposure to animal reservoirs. We demonstrate that even the hospital-adapted, highly-transmissible NAP1/RT027 strain of C. difficile had a reproduction number <1 in a landmark study of hospitalised patients and therefore was sustained by colonised and infected admissions to the study hospital. We argue that C. difficile should be considered reservoir-driven if as little as 13.0% of transmission can be attributed to animal reservoirs.