Dynamics for advective-cooperative system with free boundaries in a nondegenerate epidemiological model

The present paper is devoted to the investigation of the long time dynamics for advective-cooperative system with free boundaries, which models the infectious diseases transmitted via digestive system such as fecal-oral diseases, cholera, hand-foot and mouth, etc,... The coupled advective terms yield significant obstacles, which require a different approach to analyze the system’s dynamics. To overcome this, we must prove the existence and the variational formula for the principal eigenvalue of a linear system with advective-cooperative, then use it to obtain the right limits as the dispersal rates and domain tend to zero or infinity. Additionally, we conduct numerical simulations to validate our theoretical results, and explore the effects of various parameters.