  Infectious diseases spread through human networks.
Susceptible-Infected-Removed (SIR) model is one of the epidemic models to
describe infection dynamics on a complex network connecting individuals. In the
metapopulation SIR model, each node represents a population (group) which has
many individuals. In this paper, we propose a modified metapopulation SIR model
in which a latent period is taken into account. We call it SIIR model. We
divide the infection period into two stages: an infected stage, which is the
same as the previous model, and a seriously ill stage, in which individuals are
infected and cannot move to the other populations. The two infectious stages in
our modified metapopulation SIR model produce a discontinuous final size
distribution. Individuals in the infected stage spread the disease like
individuals in the seriously ill stage and never recover directly, which makes
an effective recovery rate smaller than the given recovery rate.
