Modeling porcine pseudorabies with age structure

Abstract

Porcine pseudorabies is an acute and highly contagious viral disease caused by the pseudorabies virus. It inflicts enormous losses to the pig-breeding industry. In this paper, we propose an age-structured mathematical model. We investigate the dynamics of this model characterized by the basic reproduction number ℜ0 = max{ℜ01, ℜ02} by addressing the existence and global stability of equilibria. When ℜ0 < 1, the disease-free equilibrium is unique and globally asymptotically stable. The boundary equilibrium exists and is globally asymptotically stable under the condition ℜ₀₁ < 1 and ℜ02 > 1 or ℜ01 > 1 and ℜ02 < 1 + ɛ, there is a unique disease-endemic equilibrium which is globally asymptotically stable.