The above relationships between the impact measures and the resource distributions ought to be determined a priori of implementing a cross-regional scenario (see Section 3). Here, we consider each region k as the initial outbreak region. We assume, however, that as the pandemic evolves, the disease infectivity will naturally subside. Hence, the regression equations need to be re-estimated at every new outbreak epoch, for each region k ∈ C n , using the singleregion simulation models, where each simulation must be initialized to the current outbreak status in region k in the cross-regional simulation. As an alternative to using a computationally burdensome approach of re-estimating the regression equations, a modeler may choose to use a certain decay factor α n [76] to adjust the estimates of the regional impact measures at every nth outbreak epoch, in the following way: