Global dynamics on a delayed double-strain influenza model with vaccination and cross-immunity

Abstract In this paper, a delayed double-strain influenza model with vaccination and cross-immunity is proposed to explore the effect of coinfection of double-strain on disease spread. First, the nonnegativity and ultimate boundedness of solution are proved. Second, the basic reproduction numbers of strains 1, 2, and the whole model are defined respectively, by which criteria on the local and global asymptotic stability of (disease-free, dominant) equilibria are established. The uniform persistence of (strains 1, 2 coexistent) disease is obtained as well. Finally, the validity of the theoretical results is demonstrated by numerical simulations. We find that neglecting cross-immunity and vaccination would misestimate the size of influenza outbreaks. Cross-type multivalent vaccines will be the main direction for effective control measure for influenza.