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