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Infected component over one period of the closing-reopening cycle at α = 0 (pointwise threshold, black) and α = 1 (rolling average threshold, bright green). The overshooting of the threshold I C = 1600 in the rolling average case is more clearly visible here. From Theorem 4.1, we know that the threshold is overshot by approximately 135 active cases for a duration of just under 5.5 days. This length of time corresponds to roughly 5% of the duration of the cycle.

Infected component over one period of the closing-reopening cycle at α = 0 (pointwise threshold, black) and α = 1 (rolling average threshold, bright green). The overshooting of the threshold I C = 1600 in the rolling average case is more clearly visible here. From Theorem 4.1, we know that the threshold is overshot by approximately 135 active cases for a duration of just under 5.5 days. This length of time corresponds to roughly 5% of the duration of the cycle.

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Moving averages and other functional forecasting models are used to inform policy in pandemic response. In this paper, we analyze an infectious disease model in which the contact rate switches between two levels when the moving average of active cases crosses one of two thresholds. The switching mechanism naturally forces the existence of periodic...

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... 3 provides a visual depiction of the continuation, providing a global view of how the closingreopening cycle is deformed during the homotopy from α = 0 to α = 1. To provide visual feedback of the overshooting analysis, the infected components at the endpoints of continuation are plotted in Figure 4. Figure 3, we can clearly see the difference in the geometry of the closing-reopening cycle in the case of pointwise (α = 0) and rolling average (α = 1) thresholds. ...
Context 2
... provide visual feedback of the overshooting analysis, the infected components at the endpoints of continuation are plotted in Figure 4. Figure 3, we can clearly see the difference in the geometry of the closing-reopening cycle in the case of pointwise (α = 0) and rolling average (α = 1) thresholds. As predicted, we get overshooting of the closing and reopening thresholds with the rolling averages, with cycles spending aproximately 5% of the time above the reopening threshold; see Figure 4. From the table in Theorem 4.1, we see that the period p is larger and the first crossing time c occurs later. ...

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