Infectious disease is no longer a local problem. Modern populations are more mobile than ever before, and with this mobility comes active global mixing of infectious disease. To understand the spread of diseases such as influenza, we use a multi-city epidemic model. We extend the SEIR (susceptible-exposed-infectious-recovered) model to incorporate population migration between cities, and use this model to analyze the geographic spread of influenza. We investigate the effectiveness of travel restrictions as a control against the spread of influenza.

First we obtain the basic reproduction number for the single city case, and observe two other control strategies suggested by this case: increasing the number of clinically ill individuals that are treated, and reducing the interval between infection and treatment of such individuals.

We evaluate the effectiveness of the three control strategies with numerical simulations. It is shown that travel restrictions are less effective than the other two strategies. In general, travel restriction tends to delay the spread of the disease into new cities. However, it can increase the peak height of infected populations in all cities. An understanding of the epidemiological structures of related cities is strongly recommended in order to effectively apply the travel restriction strategy.