We found that the network configurations with higher variation in indegree (i.e. the number of other populations each population receives migration from) distributions (supporting information Fig \ref{403698}), such as those found in the tree and Barabasi-Albert networks, tend to have higher levels of infection over time, despite similar levels of immunity as the other three network types (Fig \ref{948197}). We saw similar patterns to those in infectious individuals when looking at time between epidemic peaks across network types. While fewer of the populations ended up with cyclical dynamics in the Barabasi-Abert graphs, the mean period of the cycles tended to be slightly higher and have higher variance, but this was not robust to alternative parametrizations (supporting information Fig \ref{376031}).