Department of Epidemiology and Population Health, Institute of Infection and Global Health, University of Liverpool, Leahurst, Neston, United Kingdom.
PLoS One. 2013;8(1):e53128. doi: 10.1371/journal.pone.0053128. Epub 2013 Jan 8.
Mathematical formulations for the basic reproduction ratio (R(0)) exist for several vector-borne diseases. Generally, these are based on models of one-host, one-vector systems or two-host, one-vector systems. For many vector borne diseases, however, two or more vector species often co-occur and, therefore, there is a need for more complex formulations. Here we derive a two-host, two-vector formulation for the R(0) of bluetongue, a vector-borne infection of ruminants that can have serious economic consequences; since 1998 for example, it has led to the deaths of well over 1 million sheep in Europe alone. We illustrate our results by considering the situation in South Africa, where there are two major hosts (sheep, cattle) and two vector species with differing ecologies and competencies as vectors, for which good data exist. We investigate the effects on R(0) of differences in vector abundance, vector competence and vector host preference between vector species. Our results indicate that R(0) can be underestimated if we assume that there is only one vector transmitting the infection (when there are in fact two or more) and/or vector host preferences are overlooked (unless the preferred host is less beneficial or more abundant). The two-host, one-vector formula provides a good approximation when the level of cross-infection between vector species is very small. As this approaches the level of intraspecies infection, a combination of the two-host, one-vector R(0) for each vector species becomes a better estimate. Otherwise, particularly when the level of cross-infection is high, the two-host, two-vector formula is required for accurate estimation of R(0). Our results are equally relevant to Europe, where at least two vector species, which co-occur in parts of the south, have been implicated in the recent epizootic of bluetongue.
存在数学公式来计算几种虫媒病的基本繁殖率（R(0)）。通常，这些公式是基于单宿主-单媒介系统或双宿主-单媒介系统的模型。然而，对于许多虫媒病，两种或更多种媒介物种通常共同存在，因此需要更复杂的公式。在这里，我们推导出一种双宿主-双媒介的蓝舌病 R(0)公式，蓝舌病是一种反刍动物的虫媒感染病，可能会产生严重的经济后果；例如，自 1998 年以来，仅在欧洲就导致了超过 100 万只羊死亡。我们通过考虑南非的情况来说明我们的结果，南非存在两种主要宿主（绵羊、牛）和两种媒介物种，它们具有不同的生态和媒介能力，并且存在良好的数据。我们研究了媒介丰度、媒介能力和媒介对宿主的偏好之间的差异对 R(0)的影响。我们的结果表明，如果我们假设只有一种媒介传播感染（实际上有两种或更多种），并且/或者忽略媒介对宿主的偏好（除非首选宿主不太有益或更丰富），那么 R(0)可能会被低估。当两种媒介物种之间的交叉感染水平非常低时，双宿主-单媒介公式提供了很好的近似。当这种交叉感染水平接近种内感染水平时，每个媒介物种的双宿主-单媒介 R(0)的组合成为更好的估计。否则，特别是当交叉感染水平很高时，需要使用双宿主-双媒介公式来准确估计 R(0)。我们的结果同样适用于欧洲，在那里，至少有两种媒介物种，它们在南部的部分地区共同存在，与最近的蓝舌病流行有关。
