Mathematical disease modeling has long operated under the assumption that a single disease is caused by a single pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of contagions and has allowed the community to focus on the complexity of other factors such as population structure. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their evolutionary dynamics with the host immune system, can play a large role in shaping epidemics. Here, we introduce a simple disease model with an underlying genotype network (Wagner, 2014), allowing the disease to mutate along network pathways as it spreads in a well-mixed host population. This genotype network allows us to define a genetic distance across strains and therefore model the transcendence of immunity often observed in real world pathogens (Katzelnick, 2017; Peeters, 2017). We study the emergence of epidemics in this model, or so-called epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases as well as localization around key strains of the associated pathogen. More generally, our model illustrates the richness of behaviors that are possible even in well-mixed host populations once more complex genetic structures are considered to go beyond the “one disease equals one pathogen” paradigm.