The purpose of this work is to analyze the stability of a model for multistrain diseases with interacting strains, using dengue as an example, in a system of two coupled patches. Since chaotic outbreaks are likely to produce a higher number of infected individuals, understanding the stability properties may play an important role in public health. The case of non-identical parameters in the two patches will be of particular interest, as this serves as a model for spatial heterogeneity. The paper is divided as follows. In Sect. 2 we introduce the epidemic model. Section 3 summarizes the bifurcation structure for a single patch. In Sect. 4 we present numerical results for bifurcations in two coupled patches. Section 5 motivates these results via analysis of a simple, lower dimensional model, and Sect. 6 concludes.