Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 45, pp. 1-16.

Title: Modeling porcine pseudorabies with age structure
       
Authors: Yuhua Long  (Guangzhou Univ., Guangzhou, China)
         Yining Chen (Guangzhou Univ., Guangzhou, China)

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  R<sub>0</sub>=max{R<sub>01</sub>, R<sub>02</sub>}
 by addressing the  existence and global stability of equilibria.
 When R<sub>0</sub>&lt;1, the disease-free equilibrium is unique and globally asymptotically stable.
 The boundary equilibrium exists  and is globally asymptotically stable under the condition
 R<sub>01</sub>&lt;1 and R<sub>02</sub>&gt;1 or R<sub>01</sub>&gt;1 and R<sub>02</sub>&lt;1+&epsilon;.
 If both R<sub>01</sub>&gt;1 and R<sub>0</sub>&gt;1+&epsilon;,
 there is a unique disease-endemic equilibrium
 which is globally asymptotically stable.

Submitted January 22, 2021. Published May 25, 2021.
Math Subject Classifications: 92D25, 34D23, 92D40.
Key Words: Age-structured porcine pseudorabies model; equilibrium;
           basic reproduction number; global stability.