The stochastic model presented here is a comprehensive combination of quantitative RA components and disease transmission components to simulate both, the spread of disease within a country and the probability of introduction of the infectious agent. The flexible structure of the stochastic model reflecting the current import regulations allows including various additional domestic or import-related risk factors, such as short term animal movements or infection via livestock commodities. Such factors can be incorporated directly as additional numbers of infected herds to the summarizing sub-model or – if necessary – can be incorporated as separate spreadsheet models. Information on numbers of infected herds or animals and the cause of infection are normally available from statutory case reporting or diagnostic laboratory records.
The first objective of the study, to regard the consideration of infection spread between two consecutive surveys was achieved by the introduction of BSSF and BSSFadj for spread from domestic herds and imported animals, respectively. Compared to the deterministic precursor model, where a preliminary fixed value for the potential spread between surveys was included, the pre-SPF of the stochastic model reflected disease dynamics more realistically. In the context of repeated surveys, the model highlighted the potential importance of residual infections within the domestic population of a country or region officially free from the disease and the infectious agent, respectively. Especially when a country has to deal with rapidly spreading infections that are characterized by latent phases or that might show only mild to in-apparent clinical signs.
With the introduction of a novel spread factor, explicit transmission modelling in terms of a SIR model was avoided. Depending on the infectious agent's epidemiology, the model allowed in the worst case scenario only for an increase of HP (BSSF ≥1) between two consecutive surveys, whereas the alternative scenario allowed also for a decrease of HP between two surveys (BSSF values < 1 to ≥1). The alternative scenario modelled a natural extinction course of infection in the case of chronic or slowly spreading infectious agents (e.g. bovine leucosis virus), whereas the worst case scenario was more adapted to rapidly spreading infections with latent disease phases followed by reactivation (e.g. BoHV-1). The different model outputs of the two scenarios above were related to the influence of BSSF on the outcome of the individual infection pathways, as highlighted in the sensitivity analysis of model input parameters.
To include the changes in the EU-import regulations, the BSSF was adjusted for seasonality of import and categories of export countries, this realistically reflected the complex dynamics of cattle populations and the trading patterns between two surveys. However, sound data are lacking to consider spread from clustered outbreaks or clustered sources of infection. As an approximation to clustered spread from imported animals to domestic herds, the release of animals from the two import pathways to their destination farms were treated differently: Delivery of single animals versus groups of animals in the direct import pathway and the indirect import pathway, respectively. Because of the moderate contribution of the indirect pathway to the final model output, a scenario where individual animals were released each to different destination herds did not significantly affect the model's final outcome. The distinct separation of release patterns per import pathway category was therefore a pragmatic approach to address the second objective of the study, but release of groups or single animals in reality may also occur in the other pathway. Consistent data on grouping and delivery patterns to destination farms are expected in future, as the new import regulations have been applied only since July 2004. In the future the model could be adapted to account for heterogeneous spread (clustering of outbreaks), or different susceptibilities of herds for infection (e.g. due to potential risk factors such as larger herd size or intense animal movements, known from other countries).
The high influence of residual domestic HP on the pre-SPF in the model was not surprising (Figure ): The adoption of risk-based national surveys presumably shifted the mean of the assumed residual HP beta-distribution to higher values due to a smaller sample size. Model outputs pointed out a significant increase in pre-SPF exceeding the estimates of the deterministic model (Table ), when using hypothetical standard sample sizes to define input HP.
With regard to the third objective of the study, the option of including a detection probability of newly infected herds in terms of general surveillance showed significantly higher pre-SPF estimates, too. In the case of rapidly spreading infections disease notification and interventions to halt the course of an epidemic are to be expected.
In the case of parameterization of the model with BoHV-1 we tested and excluded the scenario that included aspects of general surveillance and detection of outbreaks, although the outputs suggested lower HP
and higher Pre-SPF estimates. The only estimate for detection probability for BoHV-1 available was derived from a study on Dutch dairy herds that might have different herd sizes and management strategies [4
]. However, more investigations on detection probabilities of BoHV-1 outbreaks of countries officially free from the infectious agent would lead to reconsideration of this scenario.
For BoHV-1 data and surveys, it was demonstrated, how to account for various factors affecting the health status and disease dynamics of a national cattle population between two surveys to substantiate freedom from infection. The present model was also successfully applied to national risk-based surveillance for freedom from bovine leucosis virus, the causative infectious agent of enzootic bovine leucosis, a more chronic disease and less contagious infection (data not shown).
The number of resulting infected domestic herds through imported BoHV-1 positive animals per pathway was in line with findings of European risk assessments [3
]. E.g. the contribution of infection through animals originating from countries not BoHV-1 free was considered very small, because of the high likelihood of detection of positive animals during pre-export quarantine. Whereas introduction of positive animals from countries BoHV-1 free was mainly dependant on the export country's survey results or the assumed HP
. Experts also mentioned sanitary conditions during up-loading and transport to be an additional source of infection, but in the present study detailed data from export countries on transport conditions were unavailable.
Our BSSF validation suggested realistic values if compared to reports from other BoHV-1-free countries or regions that conduct full surveys. Reporting from Denmark, Bolzano and Austria indicated that spread of infection between herds was very limited, usually 0–1 secondary cases [3