Dynamics and asymptotic profiles on an age-structured SIS epidemic model with random diffusion and advection

In this paper, we introduce an age-structured SIS (susceptible-infectious-susceptible) epidemic model with random diffusion and advection, in which birth and transmission rates depend on individuals. First, the well-posedness of this model was obtained. Next, we established the existence and uniqueness of the nontrivial nonnegative steady state, and derived the basic reproduction number which is also a threshold for the existence of nontrivial nonnegative steady states. Then, we studied the local stability of the nontrivial nonnegative steady state. In particular, we determined the upper and lower bounds of the principal eigenvalue to better obtain the local stability. Finally, we investigated the asymptotic profiles of the principal eigenvalue and the nontrivial nonnegative steady state with respect to diffusion rate and advection rate, respectively.