| Abstract: |
| After the beginning of the COVID-19 pandemic around the world, travel restriction policies internationally and domestically have been significant issues. In mathematical epidemiology, there are several mathematical modelings about the impact of varying residence times or travel restrictions, such as lockdowns on the infectious disease dynamics in a heterogeneous environment. We set two kinds of multi-patch models: Lagrangian and Euler models. For the Euler model, we explored how the travel frequency (restriction) affects the pattern of disease dynamics for a multi-patch model. For the Lagrangian model, we proved that the basic reproduction number is monotonically decreasing with respect to the travel restriction factor. Also, we derived the final size relation by using the weighted geometric mean. Numerical simulations illustrate that the final size of the outbreak depends on the travel restriction measure as well as the transmissibility. Moreover, we investigated patch-specific optimal treatment strategies. |
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