| Abstract: |
| Mathematical modeling of disease spread became more important than ever during the COVID-19 pandemic. Forecasting infections and hospitalizations to take appropriate mitigations measure has been key to contain the pandemic as well as possible. Mitigations measures were however taken locally, and a lack of coordination between nations allowed for new variants to emerge and travel around the globe. Understanding how travels restrictions impact the spread of the virus globally is the focus of our work. This can be described as a hybrid system that arise from interactions between continuous state dynamics and discrete state dynamics. The local continuous dynamics is captured by SEIR models while the global dynamic is represented by a graph. We introduce guard conditions to trigger the discrete events, define what an execution is in that framework and illustrate the concept using numerical simulations. |
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