The problem of modifying a network topology in such a way as to delay the propagation of a disease with minimal disruption of the network capacity to reroute goods/items/passengers is considered here. We find an approximate solution to the Susceptible-Infected-Susceptible (SIS) model, which constitutes a tight upper bound to its exact solution. This upper bound allows direct structure-epidemic dynamic relations via the total communicability function. Using this approach we propose a strategy to remove edges in a network that significantly delays the propagation of a disease across the network with minimal disruption of its capacity to deliver goods/items/passengers. We apply this strategy to the analysis of the UK airport transportation network weighted by the number of passengers transported in the year 2003. We find that the removal of all flights connecting four origin-destination pairs in the UK delays the propagation of a disease by more than 300\%, with a minimal deterioration of the transportation capacity of this network. These time delays in the propagation of a disease represent an important non-pharmaceutical intervention to confront an epidemics, allowing for better preparations of the health systems, while keeping the economy moving with minimal disruptions.