Aujeszky’s Disease virus, (ADV) is a contagious viral disease that affects the central nervous system of all animals, but swine are its natural host. Its main symptoms include abortions and stillbirths in sows, nervous signs in young pigs and respiratory disease in older pigs. ADV is a very important economic problem in Ireland, where substantial losses are incurred in the farming community each year. We consider various differential equation models of ADV with homogeneous and proportional mixing between seropositive and seronegative animals. We derive various expressions for the basic reproduction ratio R0, and the infectious contact rate, a. Using these, we perform equilibrium and stability analysis for both non-vaccinated and vaccinated models. Finally, we look at various graphs of the systems of differential equations created, where we consider values, both above and below one, for R0, a. We find that it may be possible that the disease will die out by itself when R0, a < 1. With the possibility of future trade restrictions being brought about by EU regulations, a nationwide eradication programme has been proposed. Ireland currently exports over 50% of its pigmeat, so any trade restrictions would have a huge economic impact. If the eradication programme is to be implemented, it is imperative that it be run efficiently, so as to minimise the possibility of the loss of valuable export revenue. Implications for control / eradication strategies are also considered.