Johne’s disease is an infectious gastrointestinal disease in ruminants caused by Mycobacterium avium subsp. paratuberculosis that causes diarrhea, emaciation, decreased milk production and eventually death. The disease is transmitted in utero and via milk and colostrums to calves, and fecal-orally to all age classes. Financial losses due to the disease are estimated to be over $200 million in the US dairy industry. The goal of this study was to evaluate the cost effectiveness of control measures based on diagnosis with a sensitive ELISA, EVELISA. An agent-based, discrete time model was developed to simulate Johne’s disease dynamics in a US dairy herd. Spatial aspects of disease transmission were taken into account by using six spatial compartments. The effects on disease prevalence were studied with and without transmission routes included in the model. Further, using the model, cost effectiveness of ELISA-based Johne’s disease control was evaluated. Using the parameters we collected and assumed, our model showed the initial prevalence of Johne’s disease (33.1 ± 0.2%) in the farm increased to 87.7 ± 1.7% in a 10 year-simulation. When ELISA-based control measures were included in the simulation, the increase in prevalence was significantly slowed down, especially when EVELISA was used. However, the level of the prevalence was still higher than the initial level after 10 year simulation even with the ELISA-based diagnostic intervention. The prevalence was further reduced when quarterly ELISA testing was included. The cost analysis showed that the quarterly ELISA and EVELISA testing could bring $44.8 and $51.5/animal/year more revenues, respectively, to a dairy farm.Electronic supplementary materialThe online version of this article (doi:10.1186/s13567-015-0195-y) contains supplementary material, which is available to authorized users.

The Loewner differential equation provides a way of encoding growing families of sets into continuous real-valued functions. Most famously, Schramm-Loewner evolution (SLE) consists of the growing random families of sets that are encoded via the Loewner equation by a multiple of Brownian motion. The purpose of this paper is to study the families of sets encoded by a multiple of the Weierstrass function, which is a deterministic analog of Brownian motion. We prove that there is a phase transition in this setting, just as there is in the SLE setting. 159 4. Proof of the phase transition 163 Acknowledgement 164 References 164 MSC2010: 30C35.