For many diseases, 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 in populations where an endemic disease is sustained by a combination of local transmission within the population 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 case 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.

对于许多疾病，基本生殖数（${\mathrm{[R}}_0$）是孤立人群中疾病灭绝或生存的阈值参数。但是，没有任何人类与其他人类或动物完全隔离。我们使用分区模型来推导针对人群的基本繁殖数量的简单规则，在这些人群中，流行病是通过人群内部的局部传播和其他来源的暴露（水库暴露或外来病例）的结合而持续存在的。我们介绍了以水库驱动或进口驱动的疾病的思想：如果没有水库暴露或外来病例，则在目标人群中将灭绝的疾病（自${\mathrm{[R}}_0<\mathrm{1个}$），但仍然可以充分传播，以致于该人群中的人类感染了许多或大多数感染。我们证明在最简单的情况下，${\mathrm{[R}}_0<\mathrm{1个}$当且仅当从外部来源获得的感染比例超过疾病流行率，并探讨种群异质性和多种菌株之间的相互作用如何影响该规则。我们将这些规则应用在艰难梭菌感染和定植的两个案例研究中：医院设置的艰难梭菌占进口病例，而普通人群的艰难梭菌占暴露于动物水库的比例。我们证明，即使是医院适应性高传播的艰难梭菌NAP1 / RT027菌株在一项具有里程碑意义的住院患者研究中，其生殖数＜1，因此由研究医院的定植和感染住院来维持。我们认为，如果只有13.0％的传播可归因于动物水库，则应将艰难梭菌视为水库驱动。