The Influence of Varying Incidence and Migration Induced by Media Coverage on a Delayed Two-Strain Patch Epidemic Model

In this paper, a delayed two-strain patch SIS epidemic model is proposed with varying incidence and migration of susceptible individuals induced by media coverage of infected individuals. For the subsystem without migration, criteria on the globally asymptotical stability of disease-free equilibrium and Hopf bifurcations at the dominant and coexistent equilibria are established, where the global Hopf bifurcations are unbounded. For the model with migration, the basic reproduction number [Formula: see text] is derived, by which criteria on the locally and globally asymptotic stability of disease-free equilibrium are derived. The uniform persistence of (strain 1 or 2 dominant and coinfection) diseases is verified, respectively. The theoretical results are illustrated by numerical simulation, from which we find that [Formula: see text] is nonmonotonic with the migration rates between patches. Ignoring the multistrain factor will greatly underestimate the scale of disease, and even obtain the opposite conclusion (disease extinction or persistence). Delay could cause periodic oscillation, and the multistrain and migration between patches could further produce chaos. Both the media effect with delay and migration could greatly influence the transmission dynamics of disease from stability to instability and then to chaos, which would further increase the difficulty of disease control.