  The size and shape of the region affected by an outbreak is relevant to
understand the dynamics of a disease and help to organize future actions to
mitigate similar events. A simple extension of the SIR model is considered,
where agents diffuse on a regular lattice and the disease may be transmitted
when an infected and a susceptible agents are nearest neighbors. We study the
geometric properties of both the connected cluster of sites visited by infected
agents (outbreak cluster) and the set of clusters with sites that have not been
visited. By changing the density of agents, our results show that there is a
mixed-order (hybrid) transition where the region affected by the disease is
finite in one phase but percolates through the system beyond the threshold.
Moreover, the outbreak cluster seems to have the same exponents of the backbone
of the critical cluster of the ordinary percolation while the clusters with
unvisited sites have a size distribution with a Fisher exponent $\tau<2$.
