Dynamics for Advective-cooperative System With Free Boundaries Ina Nondegenerate Epidemiological Model

Abstract The present paper is devoted to the investigation of the long time dynamics for advective-cooperativesystem with free boundaries, which models the infectious diseases transmitted via digestive system such as fecal-oraldiseases, cholera, hand-foot and mouth, etc... The couple advective yield significant obstacle that we cannot employthe approach of [1, 16]. To overcome this, we must prove the existence and the variational formula for the principaleigenvalue of a linear system with advective-cooperative, then use it to obtain the right limits as the dispersal ratesand domain tend to zero or infinity. Additionally, we conduct numerical simulations to validate our theoreticalresults, and explore the effects of various parameters.