  Mathematical disease modelling has long operated under the assumption that
any one infectious disease is caused by one transmissible pathogen spreading
among a population. This paradigm has been useful in simplifying the biological
reality of epidemics and has allowed the modelling community to focus on the
complexity of other factors such as population structure and interventions.
However, there is an increasing amount of evidence that the strain diversity of
pathogens, and their interplay with the host immune system, can play a large
role in shaping the dynamics of epidemics. Here, we introduce a disease model
with an underlying genotype network to account for two important mechanisms.
One, the disease can mutate along network pathways as it spreads in a host
population. Two, the genotype network allows us to define a genetic distance
across strains and therefore to model the transcendence of immunity often
observed in real world pathogens. We study the emergence of epidemics in this
model, through its epidemic phase transitions, and highlight the role of the
genotype network in driving cyclicity of diseases, large scale fluctuations,
sequential epidemic transitions, as well as localization around specific
strains of the associated pathogen. More generally, our model illustrates the
richness of behaviours that are possible even in well-mixed host populations
once we consider strain diversity and go beyond the "one disease equals one
pathogen" paradigm.
