Cross-species epidemic dynamic model of influenza

Influenza viruses originate from birds, and transmit to pigs and humans with the development of history. Previously, we took more attention on the study of human influenza epidemic, and neglected the roles played by the birds and pigs in influenza transmission. In this paper, we constructed a multi-SIR model to reflect the influenza transmission from birds, to pigs, to humans. We got the condition to guarantee the existence of epidemic equilibrium point and analyzed the stability of the epidemic equilibrium point and disease-free equilibrium point. From the results of numerical simulation, we got the significant role of pigs as intermedia hosts in the transmission of influenza viruses.