Dynamic behavior of swine influenza transmission during the breed-slaughter process.

Global influenza pandemics have brought about various public health crises, such as the 2009 H1N1 swine flu. Actually, most swine influenza infections occur during the breed-slaughter process. However, there is little research about the mathematical model to elaborate on the swine influenza transmission with human-pig interaction. In this paper, a new breed-slaughter model with swine influenza transmission is proposed, and the equilibrium points of the model are calculated subsequently. Meanwhile, we analyze the existence of the equilibrium points by the persistence theory, and discuss their stability by the basic reproduction number. And then, we focus on the invasion process of infected domestic animals into the habitat of humans. Under certain conditions as in Theorem 2, we construct a propagating terrace linking human habitat to animal-human coexistent habitat, then to swine flu natural foci, which is divided by spreading speeds.