  In this paper, we consider a general single population model with delay and
patch structure, which could model the population loss during the dispersal. It
is shown that the model admits a unique positive equilibrium when the dispersal
rate is smaller than a critical value. The stability of the positive
equilibrium and associated Hopf bifurcation are investigated when the dispersal
rate is small or near the critical value. Moreover, we show the effect of
network topology on Hopf bifurcation values for a delayed logistic population
model.
