The basic reproduction number for complex disease systems: defining R(0) for tick-borne infections.

Characterizing the basic reproduction number, R(0), for many wildlife disease systems can seem a complex problem because several species are involved, because there are different epidemiological reactions to the infectious agent at different life-history stages, or because there are multiple transmission routes. Tick-borne diseases are an important example where all these complexities are brought together as a result of the peculiarities of the tick life cycle and the multiple transmission routes that occur. We show here that one can overcome these complexities by separating the host population into epidemiologically different types of individuals and constructing a matrix of reproduction numbers, the so-called next-generation matrix. Each matrix element is an expected number of infectious individuals of one type produced by a single infectious individual of a second type. The largest eigenvalue of the matrix characterizes the initial exponential growth or decline in numbers of infected individuals. Values below 1 therefore imply that the infection cannot establish. The biological interpretation closely matches that of R(0) for disease systems with only one type of individual and where infection is directly transmitted. The parameters defining each matrix element have a clear biological meaning. We illustrate the usefulness and power of the approach with a detailed examination of tick-borne diseases, and we use field and experimental data to parameterize the next-generation matrix for Lyme disease and tick-borne encephalitis. Sensitivity and elasticity analyses of the matrices, at the element and individual parameter levels, allow direct comparison of the two etiological agents. This provides further support that transmission between cofeeding ticks is critically important for the establishment of tick-borne encephalitis.

Importance of bird-to-bird transmission for the establishment of West Nile virus.

West Nile virus (WNV) is principally considered to be maintained in a mosquito-bird transmission cycle. Under experimental conditions, several other transmission routes have been observed, but the significance of these additional routes in nature is unknown. Here, we derive an expression for the basic reproduction number (R0) for WNV including all putative routes of transmission between birds and mosquitoes to gauge the relative importance of these routes for the establishment of WNV. Parameters were estimated from published experimental results. Sensitivity analysis reveals that R0 is sensitive to transmission between birds via close contact, but not to mosquito-to-mosquito transmission. In seasons or in areas where the mosquito-to-bird ratio is low, bird-to-bird transmission may be crucial in determining whether WNV can establish or not. We explain the use of R0 as a flexible tool to measure the risk of establishment of vector-borne diseases.

Scaling from challenge experiments to the field: Quantifying the impact of vaccination on the transmission of bluetongue virus serotype 8.

Bluetongue (BT) is an economically important disease of ruminants caused by bluetongue virus (BTV) and transmitted by Culicoides biting midges. The most practical and effective way to protect susceptible animals against BTV is by vaccination. Data from challenge studies in calves and sheep conducted by Intervet International b.v., in particular, presence of viral RNA in the blood of challenged animals, were used to estimate vaccine efficacy. The results of the challenge studies for calves indicated that vaccination is likely to reduce the basic reproduction number (R(0)) for BTV in cattle to below one (i.e. prevent major outbreaks within a holding) and that this reduction is robust to uncertainty in the model parameters. Sensitivity analysis showed that the whether or not vaccination is predicted to reduce R(0) to below one depended on the following assumptions: (i) whether "doubtful" results from the challenge studies are treated as negative or positive; (ii) whether or not the probability of transmission from host to vector is reduced by vaccination; and (iii) whether the extrinsic incubation period follows a realistic gamma distribution or the more commonly used exponential distribution. For sheep, all but one of the vaccinated animals were protected and, consequently, vaccination will consistently reduce R(0) in sheep to below one. Using a stochastic spatial model for the spread of BTV in Great Britain (GB), vaccination was predicted to reduce both the incidence of disease and spatial spread in simulated BTV outbreaks in GB, in both reactive vaccination strategies and when an incursion occurred into a previously vaccinated population.

Mapping the basic reproduction number (R0) for vector-borne diseases: a case study on bluetongue virus.

Geographical maps indicating the value of the basic reproduction number, R0, can be used to identify areas of higher risk for an outbreak after an introduction. We develop a methodology to create R0 maps for vector-borne diseases, using bluetongue virus as a case study. This method provides a tool for gauging the extent of environmental effects on disease emergence. The method involves integrating vector-abundance data with statistical approaches to predict abundance from satellite imagery and with the biologically mechanistic modelling that underlies R0. We illustrate the method with three applications for bluetongue virus in the Netherlands: 1) a simple R0 map for the situation in September 2006, 2) species-specific R0 maps based on satellite-data derived predictions, and 3) monthly R0 maps throughout the year. These applications ought to be considered as a proof-of-principle and illustrations of the methods described, rather than as ready-to-use risk maps. Altogether, this is a first step towards an integrative method to predict risk of establishment of diseases based on mathematical modelling combined with a geographic information system that may comprise climatic variables, landscape features, land use, and other relevant factors determining the risk of establishment for bluetongue as well as of other emerging vector-borne diseases.