Modeling And Analysis For The Transmission Of Seasonal Influenza And Avian Influenza

The subtype H5N1of influenza A virus, the so-called "H5N1avian influenza", is a highly pathogenic subtype of influenza A virus. It can evolves through two types of evolutionary mechanisms-continous mutation and spontaneous mutation. These two evolutionary mech-anisms allow the pathogen to infect humanbeing repeatedly, as well as occasionally create a new influenza virus with large morbidity and mortality, we call it as pandemic H5N1virus. In this paper,a novel multi-strain model that incorporates both evolutionary mechanisms and three types of strains: seasonal human strains, bird-to-human transmittable H5N1strains and evolved pandemic H5N1strain, is formulated and analyzed. Assuming that there exists co-infection between strains. For the basic endemic model with bilinear incidence and the constant total population size,explicit expressions of the basic reproduction number and the invasion reproduction number are obtained, the existence conditions of disease-free equlib-rium, unique dominance equlibrium and coexistence equlibrium of strains are given, the stabilities of some equilibra are discussed.