Implications derived from a mathematical model for eradication of pseudorabies virus

Simple mathematical models based on experimental and observational data were applied to evaluate the feasibility of eradicating pseudorabies virus (PRV) regionally by vaccination and to determine which factors can jeopardise eradication. As much as possible, the models were uncomplicated and our conclusions were based on mathematical analysis. For complicated situations, Monte-Carlo simulation was used to support the conclusions. For eradication, it is sufficient that the reproduction ratio R (the number of units infected by one infectious unit) is < 1. However, R can be determined at different scales: at one end the region with the herds as units and at the other end compartments with the pigs as units. Results from modelling within herds showed that contacts between groups within a herd is important whenever R between individuals (R_ind) is 1 in one or more groups. This is the case within finishing herds. In addition, if the R_ind is more than 1 within a herd, the size of the herd determines whether PRV can persist in the herd and determines the duration of persistence. Moreover, when reactivation of PRV in well-vaccinated sows is taken into account, R_ind in sow herds is still less than 1. In sow herds with group-housing systems, it is possible that in those groups R_ind is 1. Results from modelling between herds showed that whether or not R_herd is < 1 in a particular region is determined by two factors: (1) the transmission of infection between nucleus herds and rearing herds through transfer of animals and (2) contacts among finishing herds and among rearing herds. The transmission between herds can be reduced by reduction of the contact rate between herds, reduction of the herd size, and reduction of the transmission within herds.