Several researchers such as Andreasenv et al. [19], in 1997, they develop a model that describes the dynamics of a finite number of strains that confer partial cross-protection among strains. The immunity structure of the host population is captured by an index-set notation where the index specifies the set of strains to which the host has been exposed. In 1999, Lin et al. [20], analyze an epidemiological model consisting of a linear chain of three co circulating influenza A strains that provide hosts exposed to a given strain with partial immune cross protection against other strains