Dynamics of a delayed nonlocal reaction-diffusion heroin epidemic model in a heterogenous environment

To study the consumption of heroin in a heterogeneous environment, we pro-pose and analyze a spatiotemporal model with a distributed delay. Using thespectral theory, we determine the basic reproduction numberR0, which serves athreshold role. If R-0<1, then the addiction-free steady state is globally asymp-totically stable while if R-0>1, then there is at least one addictive steady state.Moreover, when R-0>1, if one of the dispersal coefficients is zero, then there isonly one addictive steady state, and it is globally asymptotically stable; if bothdiffusions of susceptible and addicted individuals are present, we cannot identifythe temporal behavior of solutions, and hence, we study the asymptotic profileof addictive steady states when one of the dispersal coefficients tend to zero