Global analysis for a two-strain avian influenza model with distributed delay and environmental transmission

A two-strain avian influenza model with distributed delay and environmental spread in humans is investigated. The model describes well the transmission of avian influenza between poultry and humans. In this study, we introduce the behavior of both high pathogenic avian influenza (HPAI) as strain two and low pathogenic avian influenza (LPAI) as strain one in a domestic poultry population. We also include the distribution of the strain two through the contaminated environment. We compute the strain reproduction numbers R1, R2 and the invasion R̂1, R̂2. We find that besides the disease-free equilibrium, there exist a dominance equilibrium for each strain and many coexistence equilibrium of both strain one and strain two if R1 = R2. Using a Lyapunov functional, we are able to establish global stability of the disease-free equilibrium if max{R1,R2} < 1. If Ri, the reproduction number of strain i is larger than one, then a single-strain equilibrium, corresponding to strain i exists. This singlestrain equilibrium is locally stable whenever R̂i > 1. Using a Lyapunov functional, we establish that the corresponding single-strain equilibrium εi is globally stable. When R1 = R2 > 1 and R̂1 = R̂2 = 1, there are perhaps many coexistence equilibria of both strain one and strain two. Supported partially by the NNSF of China (11271314,11601465) and Plan For Scientific Innovation Talent of Henan Province (144200510021). M. M. is partially supported by NSF DMS-1220342. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] 1 Environmental transmission to humans may explain why avian influenza A (H7N9) virus has appear in humans in different places in China in 2013 and 2014.