Section: New Results

Metapopulation

In the framework of metapopulation models we have obtained some new results. We have studied a metapopulation model with $n$ patches. The migration model is with residents and travelers and the epidemic model is of SIS type. In particular, we have proved analytically the conjecture of Arino and van den Driessche [12] . The global behavior of the system is addressed in [10] .

We are also currently studying, with our brazilian partners in the framework of the CAPES-COFECUB project (see international program), a metapopulation model for studying the propagation of dengue in the state of Rio. We use data provided by the foundation FIOCRUZ. These data concern different epidemics in RIO between 1986 to 2006. The effects of transportation system are taken into account.

Figure 1. Transportation system in Rio

We have considered a reduced system represented by Figure 2 . The outputs of the model compare favorably with the actual data (Figure 3 ).

Figure 2. Reduced metapopulation model

Figure 3. Model vs data