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