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Mathematical formulations for the basic reproduction ratio (R0) 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 R0 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 R0 of differences in vector abundance, vector competence and vector host preference between vector species. Our results indicate that R0 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 R0 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 R0. 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. [ABSTRACT FROM AUTHOR]

Understanding where and how fast an infectious disease will spread during an epidemic is critical for its control. However, the task is a challenging one as numerous factors may interact and drive the spread of a disease, specifically when vector- borne diseases are involved. We advocate the use of simultaneous autoregressive models to identify environmental features that significantly impact the velocity of disease spread. We illustrate this approach by exploring several environmental factors influencing the velocity of bluetongue (BT) spread in France during the 2007-2008 epizootic wave to determine which ones were the most important drivers. We used velocities of BT spread estimated in 4,495 municipalities and tested sixteen covariates defining five thematic groups of related variables: elevation, meteorological-related variables, landscape- related variables, host availability, and vaccination. We found that ecological factors associated with vector abundance and activity (elevation and meteorological-related variables), as well as with host availability, were important drivers of the spread of the disease. Specifically, the disease spread more slowly in areas with high elevation and when heavy rainfall associated with extreme temperature events occurred one or two months prior to the first clinical case. Moreover, the density of dairy cattle was correlated negatively with the velocity of BT spread. These findings add substantially to our understanding of BT spread in a temperate climate. Finally, the approach presented in this paper can be used with other infectious diseases, and provides a powerful tool to identify environmental features driving the velocity of disease spread. [ABSTRACT FROM AUTHOR]