An evolutionary algorithm is employed to evolve contact networks representing interactions between individuals in a population. These networks play a crucial role in providing insights into epidemic behaviour and how viruses propagate through the population. The networks are evolved using two fitness functions: one focused on maximizing infection severity and one focused on maximizing the total number of infections (spread). Both evaluate potential networks by simulating SIR epidemics in the context of epidemic variants. The impact of different types of immunity and different probabilities of new variants being generated are evaluated with respect to the number and severity of infections, the characteristics of the evolved contact networks, and the length of the epidemic. The evolutionary algorithm successfully created networks likely to result in more severe infections when focusing on epidemic severity and networks likely to result in a higher number of infections of any severity when focusing on spread, although the immunity type and variant probability both had significant impact.