  In this paper, we examine the long-time dynamics of an epidemic model whose
diffusion and reaction terms involve nonlocal effects described by suitable
convolution operators.The spreading front of the disease is represented by the
free boundaries in the model. We show that the model is well-posed, its
long-time dynamical behaviour is characterised by a spreading-vanishing
dichotomy, and we also obtain sharp criteria to determine the dichotomy. Some
of the nonlocal effects in the model pose extra difficulties in the
mathematical treatment, which are dealt with by introducing new approaches. The
model can capture accelerated spreading, and its spreading rate will be
discussed in a subsequent work.
