An evolutionary algorithm is used to evolve personal contact networks representing the individuals in a population and the interactions between them. Such networks can be used to track the progress of an epidemic, as it passes from infected individuals to others. Two fitness functions are used: epidemic duration and epidemic spread. Each of these is evaluated in the context of new variants being introduced during the course of the epidemic. Individuals infected with one variant obtain immunity to that variant and possible partial immunity to future variants. Two frameworks for epidemic variants are presented. In the first, infectivity is coupled directly to how well an individual's immunity covers the variant. In the second, infectivity is decoupled, causing a much higher number of infections but with many of lessened severity due to immunity.