A stochastic model for disease transmission in a managed herd, motivated by Neospora caninum amongst dairy cattle

A stochastic model for the spread of Neospora caninum infection within a herd of dairy cattle is studied, in particular the long-term (equilibrium) behaviour of the model. The model incorporates the interesting feature that total herd size is constrained to lie within a fairly small interval, but not held exactly constant. Approximations for the joint distribution of numbers of susceptible and infected individuals present in equilibrium are derived based upon a diffusion approximation to the infection process. The effect of both 'typical herd size' and 'the amount of permitted variation in herd size' upon disease prevalence in equilibrium are considered using both the exact equilibrium distribution of the process and our approximations.