Connecting multiple populations with the same parameters results in reduced pathogen prevalence and dampened cycles in populations further down the chain. Here, populations are connected such that \(A\rightarrow B\rightarrow C\rightarrow D\). Each column indicates a population, while each row is one of the three population classes laid out above and in the Methods, i.e. those currently infectious with the given strain, those with (complete) specific immunity to the given strain, and those with partial cross-protective immunity to the given strain. The mean level of immunity (both specific (middle row) and cross-reactive (bottom row)) increases in each sequential population, while the mean level of currently infectious individuals (top row) decreases. All populations have parameters σ = 8, μ = 0.1, δ = 0.05, γ = 0.66 and a β chosen to make \(\tilde{R_0}\) = 2 for all populations. We use a two-loci, two-allele strain structure, but show only one strain for clarity (but see supporting information Fig \ref{134222}).