Spreading of multiple epidemics with cross immunization

Pathogen-host relationships are the result of an ongoing coevolutionary race where the immune system of the host attempts to eliminate the pathogen, while the successful pathogen mutates to become invisible for the host's immune system. We here propose a minimal pathogen-host evolution model that takes into account cross immunization and allows for evolution of a spatially heterogeneous immune status of a population of hosts. With only the mutation rate as a determining parameter, the model allows us to produce an evolutionary tree of diseases which is highly branched, but hardly ever splits into separate long-lived trunks. Side branches remain short lived and seldom diverge to the extent of losing all cross immunizations.