Dynamic Analysis Of Several Kinds Of Porcine Pseudorabies Models

Porcine pseudorabies is an acute and highly contagious viral disease caused by pseudorabies virus.It inflicts enormous losses to the pig breeding industry.In this paper,based on the idea of compartment modeling,we establish two models,one is susceptible-exposed-infected-treated(SEIT)model with vertical transmission,the other is susceptible piglets,infected piglets,susceptible adult pigs,infected adult pigs,recovered adult pigs and susceptible adult pigs(S₁S₁S₂S₂S₂S₂) model with age structure.This paper is divided into three chapters:The first chapter introduces the background,research overview and main results of pseudorabies in pigs,and lists preliminaries to be used in this paper.In the second chapter,we formulate a SEIT model with vertical transmis-sion and disease-related deaths.The existence and stability of equilibria of the model are characterized by the basic reproduction number.We show that the disease-free equilibrium is unique and globally asymptotically stable.Construct-ing Lyapunov function and using the theory of competitive system,we obtain the global asymptotical stability of a unique disease-endemic equilibrium.Considering the different influence of the disease on pigs of different ages,we propose the S₁S₁S₂S₂S₂S₂ model with age structure.We investigate the dynamics of this model characterized by the basic reproduction number by addressing the existence and global stability of equilibria.When there is no vertical transmis-sion,the existence and global stability of equilibria are analyzed.When there is vertical transmission,we obtain that there is no disease-free equilibrium.The exis-tence and global asymptotical stability of boundary equilibria and disease-endemic equilibrium are also considered.