We next examine the effect of coupling between distinct regions on the dynamics previously observed in the single patch model. In particular, we consider how migration between non-identical patches affects the stability of the steady state. We investigate the dynamics of the coupled systems by numerically integrating (1)-(5) and by tracking the bifurcations using a continuation routine (Doedel et al. 1997) . As mentioned in the previous section, the model has a Hopf bifurcation at critical values of the bifurcation parameters φ, the ADE factor, and , the cross immunity strength. We Fig. 3 Critical values of the parameters (a) and (b) φ at which the Hopf bifurcation occurs for coupled patches, as a function of the contact rate in patch 1, for two values of the migration rate, ν = 0.02 (solid black) and ν = 0.05 (dashed gray). The contact rate in patch 2 is fixed at β 2 = 200. In (a), φ = 1 (no ADE). In (b), = 0 (no cross immunity). μ 1 = μ 2 = 0.02 and other parameters are as in Table 1 study the effect of coupling and asymmetry on the stability by observing their effect on the location of the Hopf bifurcations. We consider cross immunity and ADE separately; that is, we analyze the system either with ADE and no cross immunity or with cross immunity and no ADE. Including both cross immunity and ADE together leads to qualitatively similar behavior to that reported here, at least locally when the asymmetry is not too large.