# Behavioral Regimes in the Evolution of Extremal Epidemic Graphs

### Daniel Ashlock and Fatemeh Jafargholi.

Submitted to the 2008 Congress on Evolutionary Computation

Models of epidemic spread often incorporate con- tact networks
along which the epidemic can spread. The charac- ter of the network
can have a substantial impact on the course of the epidemic. In this
study networks are optimized to yield long- lasting epidemics. These
networks represent an upper bound on one type of network behavior. The
evolutionary algorithm used searches the space of networks with a
specified degree sequence, with degrees representing the number of
sexual partners of each member of the population. The representation
used is a linear chromosome specifying a series of editing moves
applied to an initial network. The initial network specifies the
degree sequence of the searched networks implicitly and the editing
moves preserve the degree sequence. The evolutionary algorithm uses a
non-standard type of restart in which the currently best network in
the population replaces the initial network. This restart operator is
called a recentering operator. The recentering operator moves the
evolving population to successively higher fitness portions of the
network space. In this study the algorithm is applied to networks with
average degree from 2.5 to 7. In low-degree networks, short epidemics
result from failure of the disease to spread through the relatively
sparse links of the network. In high-degree networks, short epidemics
result from the rapid infection of the entire population. The
evolutionary algorithm is able to optimize both high and low degree
networks to significantly increase the epidemic duration.