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 sizeʹ and `the amount of permitted variation in herd sizeʹ upon disease prevalence in equilibrium are considered using both the exact equilibrium distribution of the process and our approximations.