For clarity, we describe in detail the terms appearing in (5) describing the time evolution of the secondary infectives x q,ij . These are individuals who were previously infected with strain i and are currently infected with strain j . Individuals recovered from an infection with i and no longer retaining cross immunity (r q,i ) can become infected by any infective with strain j . We use mass action contact between infectives and non-invectives, contributing a term β q r q,i (x q,j + φ k =j x q,kj ) (where the secondary infectives have enhanced contagion given by the ADE factor φ). Cross immune individuals c q,i become infected with a reduced probability (1 − ). Linear terms −σ x q,ij and −μ q x q,ij appear as secondary infectives recover with rate σ or are lost to natural death with rate μ q . Finally, individuals are exchanged between patches q and q with rate ν, yielding migration terms −νx q,ij + νx q ,ij .