A model of the spread of viruses in a network of cities is considered, taking into account a delay caused by the long incubation period of the viruses. The usual infection spread and dynamics with a delay are compared. A temporary asymmetry of the infection spread has been identified, when the time of the pandemic developing significantly exceeds the time for its completion. Numerical simulations of the spread of viruses in a network of interconnected large and small cities were carried out, and pandemic features in a small world were revealed, including the possibility of re-infection of the megalopolises.