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Modeling environmental transmission of MAP infection in dairy cows

1. Department of Mathematics, University of Peradeniya, Peradeniya, KY 20400, Sri Lanka
2. Department of Forestry, Wildlife and Fisheries, University of Tennessee, Knoxville, TN 37996, USA
3. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA

Johne's disease is caused by Mycobacterium avium subspecies paratuberculosis(MAP). It is a chronic, progressive, and inflammatory disease which has a long incubation period. One main problem with the disease is the reduction of milk production in infected dairy cows. In our study we develop a system of ordinary differential equations to describe the dynamics of MAP infection in a dairy farm. This model includes the progression of the disease and the age structure of the cows. To investigate the effect of persistence of this bacteria on the farm on transmission in our model, we include environmental compartments, representing the pathogen input in an explicit way. The effect of indirect transmission from the bacteria in the environment and the culling of high-shedding adults can be seen in the numerical simulations. Since culling usually only happens once a year, we include a novel feature in the simulations with a discrete action of removing high-shedding adults once a year. We conclude that with culling of high shedders even at a high rate, the infection will persist in the modeled farm setting.

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Keywords Johne's disease for dairy cattle; environmental transmission; system of differential equations; discrete testing; basic reproduction number

Citation: Kokum R. De Silva, Shigetoshi Eda, Suzanne Lenhart. Modeling environmental transmission of MAP infection in dairy cows. Mathematical Biosciences and Engineering, 2017, 14(4): 1001-1017. doi: 10.3934/mbe.2017052

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