Competition between low and high pathogenicity avian influenza in a two-patch system

Over the last decade, the epidemiology of avian influenza has undergone a significant transformation. Not only have we seen an increase in the number of outbreaks of the deadly strain known as highly pathogenic avian influenza (HPAI), but the number of birds infected, and the cost of control has risen drastically. Live poultry markets play a huge role in the bird to bird transmission of avian influenza. We develop a two patch model to determine the competition between low pathogenic avian influenza (LPAI) and HPAI strains when migration is present. We define the two patches as live poultry markets in which the patches are connected through migration. We use a system of differential equations to analyze the existence-stability of the LPAI and HPAI equilibria and established results for the critical threshold R0. We observed that in general migration in both directions increases the abundance of poultry infected with the HPAI strain. Migration promotes the coexistence in Patch 2 while in Patch 1 the region of coexistence fluctuates when migration is active between both patches.