A similar model to the one of (1)-(5) has recently been used to analyze the dynamics of dengue fever in a single well-mixed population (Bianco et al. 2009 ). The ADE φ and cross immunity strength were varied as bifurcation parameters. In the absence of cross immunity ( = 0), ADE alone generates instability, desynchronization, and ultimately chaotic outbreaks Schwartz et al. 2005) . A Hopf bifurcation is observed for a critical value of the ADE factor φ, above which oscillatory solutions are obtained. Weak cross immunity stabilizes the system, while strong cross immunity triggers instability and chaos even in Table 1 the absence of ADE (Bianco et al. 2009 ). In the latter case, destabilization occurs via a Hopf bifurcation for a critical value of the cross immunity strength . At the bifurcation, three identical complex pairs of eigenvalues of the Jacobian simultaneously become unstable. Although Bianco et al. (2009) discusses the full two parameter bifurcation structure (in and φ), we will consider the cross immunity and ADE effects separately in the present work. Figure 2a shows the bifurcation behavior of the single patch model with no cross immunity as the contact rate β is varied. The bifurcation structure was computed using a continuation routine (Doedel et al. 1997 ). The ADE value at which the bifurcation occurs increases slightly as β increases, and the dependence is approximately linear. The period of the periodic orbit, shown in Fig. 2b for a fixed ADE value, also varies with β. (Note that multistrain models with ADE can display subcritical Hopf bifurcations, Billings et al. 2007 , so the periodic orbit shown in Fig. 2b exists throughout the range of β values shown.) Similarly, varying the contact rate β in the absence of ADE affects the location of the Hopf bifurcation in cross immunity and its characteristic frequency of oscillation. Likewise, varying the other social parameter, the birth rate μ, affects the location and frequency of the Hopf bifurcations in φ and (data not shown).